%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT168+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 : n028.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 05:06:14 PM UTC 2026
% Result : Theorem 5.24s 5.75s
% Output : CNFRefutation 16.43s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1081)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096,axiom,
! [X4] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> ( ( hAPP(v_h____,X4) = v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
& ( hAPP(v_h____,X4) != v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).
fof(fact__096_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,
~ ! [X37] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> ( ! [X20] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X37))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X20))),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),X37),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,
! [X8,X12,X27,X1,X5,X2,X15,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X15,X2,X5,X1,X27)
=> ( c_Finite__Set_Ofinite(X15,X12)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X15),X8),X12))
=> hAPP(X27,c_Set_Oinsert(X15,X8,X12)) = hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X27,X12)) ) ) ),
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,
! [X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X10,c_Set_Oimage(X15,X10,X2,X12))),c_Finite__Set_Ocard(X15,X12)))
=> ~ c_Fun_Oinj__on(X15,X10,X2,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
fof(fact_card__def,axiom,
! [X12,X10] :
( ( c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ocard(X10,X12) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12) )
& ( ~ c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ocard(X10,X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
fof(fact_notin__Lin__iff,axiom,
! [X7,X8,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),c_Arrow__Order__Mirabelle_OLin))
=> ( 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),X7)),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),X7),X8)),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X21,X22,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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),X22),X21)),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),X21),X22)),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_PiE,axiom,
! [X8,X11,X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X15)),X2),c_FuncSet_OPi(X10,X15,X12,X11)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X8)),hAPP(X11,X8)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_subset__insert,axiom,
! [X11,X12,X8,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),c_Set_Oinsert(X10,X8,X11)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
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,
~ ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X38))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X38),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__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,
~ ! [X39] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X39))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X39),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_less__fun__def,axiom,
! [X1,X2,X10,X15] :
( class_Orderings_Oord(X15)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X15)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X15),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X15),X1),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_add__leE,axiom,
! [X46,X47,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X47)),X46))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X47),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_not__add__less1,axiom,
! [X53,X54] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X53)),X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X54,X53] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X54)),X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_ex__least__nat__less,axiom,
! [X19,X17] :
( ~ hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X17,X19))
=> ? [X57] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X19))
& ! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X57))
=> ~ hBOOL(hAPP(X17,X4)) )
& hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_insertCI,axiom,
! [X21,X11,X22,X10] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X22),X11))
=> X22 = X21 )
=> hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oinsert(X10,X21,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_insert__ident,axiom,
! [X11,X12,X8,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X11))
=> ( c_Set_Oinsert(X10,X8,X12) = c_Set_Oinsert(X10,X8,X11)
<=> X12 = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_not__less__eq__eq,axiom,
! [X19,X49] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19)),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X19,X49] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,X49))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_xt1_I9_J,axiom,
! [X35,X36,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),X35))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X7),X8))
| X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_order__less__asym,axiom,
! [X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X36,X35,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_card_Oinsert,axiom,
! [X8,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X10,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
fof(fact_less__le__not__le,axiom,
! [X7,X8,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X7),X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_card__insert__if,axiom,
! [X8,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)) = c_Finite__Set_Ocard(X10,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X10,X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X49,X19] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X49))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,X49)))
<=> X19 = X49 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [X48,X46] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X48))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X48)))
=> X48 = X46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucE,axiom,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_OSuc,X46)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
=> X48 = X46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_leD,axiom,
! [X31,X33,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X7),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X7),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_card__insert__disjoint,axiom,
! [X8,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X10,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_le__SucE,axiom,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),hAPP(c_Nat_OSuc,X46)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
=> X48 = hAPP(c_Nat_OSuc,X46) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X46] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X46)),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
<=> X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_not__one__less__zero,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),c_Groups_Ozero__class_Ozero(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X33,X31,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X31 != X33
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__cases,axiom,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ( X31 != X33
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( X31 != X33
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X8,X7,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X7),X8))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_not__leE,axiom,
! [X31,X33,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__one__le__zero,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10)),c_Groups_Ozero__class_Ozero(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X33,X31] :
( X31 != X33
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_equalityE,axiom,
! [X10,X11,X12] :
( X12 = X11
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_order__less__irrefl,axiom,
! [X31,X10] :
( class_Orderings_Opreorder(X10)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_linorder__le__cases,axiom,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_less__nat__zero__code,axiom,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),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,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__zeroE,axiom,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__not__refl,axiom,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_less__irrefl__nat,axiom,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(help_c__fequal__1,axiom,
! [X7,X8] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X8),X7))
| X8 = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_card__infinite,axiom,
! [X12,X10] :
( ~ c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ocard(X10,X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
fof(fact__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096,axiom,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096) ).
fof(fact__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096,axiom,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096) ).
fof(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(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_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',conj_0) ).
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,
? [X37] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
& ! [X20] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X37))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X20))),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),X37),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,
! [X19] : hBOOL(hAPP(hAPP(c_member(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____)),X19))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiProf) ).
fof(fact_n_I2_J,axiom,
! [X20] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X20))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I2_J) ).
fof(fact_pred__subset__eq2,axiom,
! [X13,X14,X15,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X15,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X10,c_COMBC(X15,tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X10,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),X10,c_COMBB(tc_prod(X10,X15),tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X10,X15)))),c_Product__Type_OPair(X10,X15)))),X14)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X10,c_COMBC(X15,tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X10,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),X10,c_COMBB(tc_prod(X10,X15),tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X10,X15)))),c_Product__Type_OPair(X10,X15)))),X13)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact__C2_C,axiom,
! [X23,X17,X24,X25,X21,X22] :
( X22 != X21
=> ( X25 != X24
=> ( X22 != X24
=> ( X21 != X25
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X17),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))),X23),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),X22),X21)),hAPP(X17,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),X25),X24)),hAPP(X23,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),X22),X21)),hAPP(v_F,X17)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X24)),hAPP(v_F,X23))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).
fof(fact__C1_C,axiom,
! [X23,X17,X24,X25,X21,X22] :
( X22 != X21
=> ( X25 != X24
=> ( X22 != X24
=> ( X21 != X25
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X17),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))),X23),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),X22),X21)),hAPP(X17,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),X25),X24)),hAPP(X23,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),X22),X21)),hAPP(v_F,X17)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X24)),hAPP(v_F,X23))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_pairwise__neutrality,axiom,
! [X23,X17,X24,X25,X21,X22] :
( X22 != X21
=> ( X25 != X24
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X17),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))),X23),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),X22),X21)),hAPP(X17,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),X25),X24)),hAPP(X23,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),X22),X21)),hAPP(v_F,X17)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X24)),hAPP(v_F,X23))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
fof(fact_pred__equals__eq2,axiom,
! [X13,X14,X15,X10] :
( hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X10,c_COMBC(X15,tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X10,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),X10,c_COMBB(tc_prod(X10,X15),tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X10,X15)))),c_Product__Type_OPair(X10,X15)))),X14) = hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_fun(X15,tc_HOL_Obool)),X10,c_COMBC(X15,tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X15,tc_prod(X10,X15)),tc_fun(X15,tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool)),X10,c_COMBB(tc_prod(X10,X15),tc_fun(tc_fun(tc_prod(X10,X15),tc_HOL_Obool),tc_HOL_Obool),X15,c_member(tc_prod(X10,X15)))),c_Product__Type_OPair(X10,X15)))),X13)
<=> X14 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_Pi__mono,axiom,
! [X42,X11,X15,X12,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),hAPP(X11,X3)),hAPP(X42,X3))) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,X15),tc_HOL_Obool),c_FuncSet_OPi(X10,X15,X12,X11)),c_FuncSet_OPi(X10,X15,X12,X42))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_Pi__I,axiom,
! [X11,X2,X15,X12,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X3)),hAPP(X11,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X15)),X2),c_FuncSet_OPi(X10,X15,X12,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_IIA__def,axiom,
! [X27] :
( c_Arrow__Order__Mirabelle_OIIA(X27)
<=> ! [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))
=> ! [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))),X28),c_Arrow__Order__Mirabelle_OProf))
=> ! [X29,X30] :
( ! [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),X30)),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),X29),X30)),hAPP(X28,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),X30)),hAPP(X27,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),X29),X30)),hAPP(X27,X28))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact__C4_C,axiom,
! [X23,X17,X9,X21,X22] :
( X22 != X21
=> ( X21 != X9
=> ( X22 != X9
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X17),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))),X23),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),X22),X21)),hAPP(X17,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),X21),X9)),hAPP(X23,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),X22),X21)),hAPP(v_F,X17)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X9)),hAPP(v_F,X23))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C4_C) ).
fof(fact_dictatorI,axiom,
! [X45,X27] :
( 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))),X27),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))
=> ! [X29,X30] :
( X29 != X30
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X30)),hAPP(X3,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),X29),X30)),hAPP(X27,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X27,X45) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_in__lex__prod,axiom,
! [X26,X18,X24,X25,X21,X22,X15,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X15),tc_prod(X10,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X15),tc_prod(X10,X15)),hAPP(hAPP(c_Product__Type_OPair(X10,X15),X22),X21)),hAPP(hAPP(c_Product__Type_OPair(X10,X15),X25),X24))),c_Wellfounded_Olex__prod(X10,X15,X18,X26)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X22),X25)),X18))
| ( X22 = X25
& hBOOL(hAPP(hAPP(c_member(tc_prod(X15,X15)),hAPP(hAPP(c_Product__Type_OPair(X15,X15),X21),X24)),X26)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact__C3_C,axiom,
! [X23,X17,X21,X22] :
( X22 != X21
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X17),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))),X23),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),X22),X21)),hAPP(X17,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),X21),X22)),hAPP(X23,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),X22),X21)),hAPP(v_F,X17)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),hAPP(v_F,X23))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C3_C) ).
fof(fact_folding__image__simple_Oeq__fold__g,axiom,
! [X12,X27,X1,X5,X2,X15,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X15,X2,X5,X1,X27)
=> ( c_Finite__Set_Ofinite(X15,X12)
=> hAPP(X27,X12) = c_Finite__Set_Ofold__image(X10,X15,X2,X1,X5,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
fof(fact_subset__image__iff,axiom,
! [X12,X2,X15,X11,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),c_Set_Oimage(X15,X10,X2,X12)))
<=> ? [X68] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),X68),X12))
& X11 = c_Set_Oimage(X15,X10,X2,X68) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_same__fstI,axiom,
! [X10,X14,X7,X16,X15,X8,X17] :
( hBOOL(hAPP(X17,X8))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X15,X15)),hAPP(hAPP(c_Product__Type_OPair(X15,X15),X16),X7)),hAPP(X14,X8)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X15),tc_prod(X10,X15))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X15),tc_prod(X10,X15)),hAPP(hAPP(c_Product__Type_OPair(X10,X15),X8),X16)),hAPP(hAPP(c_Product__Type_OPair(X10,X15),X8),X7))),c_Recdef_Osame__fst(X10,X15,X17,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X10,X15] :
( class_Orderings_Oord(X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X15),X2),X1))
<=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,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,
! [X11,X12,X27,X1,X5,X2,X15,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X15,X2,X5,X1,X27)
=> ( c_Finite__Set_Ofinite(X15,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),X11),X12))
=> hAPP(hAPP(X2,hAPP(X27,X11)),hAPP(X27,X12)) = hAPP(X27,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [X8,X12,X27,X1,X5,X2,X15,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X15,X2,X5,X1,X27)
=> ( c_Finite__Set_Ofinite(X15,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X15),X8),X12))
=> hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X27,X12)) = hAPP(X27,X12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
! [X8,X12,X27,X1,X5,X2,X15,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X15,X2,X5,X1,X27)
=> ( c_Finite__Set_Ofinite(X15,X12)
=> hAPP(X27,c_Set_Oinsert(X15,X8,X12)) = hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X27,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [X8,X27,X1,X5,X2,X15,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X15,X2,X5,X1,X27)
=> hAPP(hAPP(X2,X8),X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_card__bij__eq,axiom,
! [X1,X11,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),c_Set_Oimage(X10,X15,X2,X12)),X11))
=> ( c_Fun_Oinj__on(X15,X10,X1,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oimage(X15,X10,X1,X11)),X12))
=> ( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X15,X11)
=> c_Finite__Set_Ocard(X10,X12) = c_Finite__Set_Ocard(X15,X11) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(fact_unanimity__def,axiom,
! [X27] :
( c_Arrow__Order__Mirabelle_Ounanimity(X27)
<=> ! [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))
=> ! [X29,X30] :
( ! [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),X30)),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),X29),X30)),hAPP(X27,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_card__bij,axiom,
! [X1,X11,X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X15)),X2),c_FuncSet_OPi(X10,X15,X12,hAPP(c_COMBK(tc_fun(X15,tc_HOL_Obool),X10),X11))))
=> ( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X15,X10)),X1),c_FuncSet_OPi(X15,X10,X11,hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X15),X12))))
=> ( c_Fun_Oinj__on(X15,X10,X1,X11)
=> ( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X15,X11)
=> c_Finite__Set_Ocard(X10,X12) = c_Finite__Set_Ocard(X15,X11) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij) ).
fof(fact_pred__subset__eq,axiom,
! [X13,X14,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X14)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X13)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_inj__on__iff__card__le,axiom,
! [X11,X15,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X15,X11)
=> ( ? [X74] :
( c_Fun_Oinj__on(X10,X15,X74,X12)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),c_Set_Oimage(X10,X15,X74,X12)),X11)) )
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X15,X11))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_in__above,axiom,
! [X7,X8,X6,X21,X22] :
( X22 != X21
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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),X8),X7)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X6),X22),X21)))
<=> ( X8 != X7
& ( X8 = X21
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X22),X7)),X6)) )
& ( X8 != X21
=> ( ( X7 = X21
=> ( X8 = X22
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X22)),X6)) ) )
& ( X7 != X21
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X7)),X6)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_in__below,axiom,
! [X7,X8,X6,X21,X22] :
( X22 != X21
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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),X8),X7)),c_Arrow__Order__Mirabelle_Obelow(X6,X22,X21)))
<=> ( X8 != X7
& ( X7 = X22
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X21)),X6)) )
& ( X7 != X22
=> ( ( X8 = X22
=> ( X7 = X21
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X7)),X6)) ) )
& ( X8 != X22
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X7)),X6)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_card_Oeq__fold__g,axiom,
! [X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ocard(X10,X12) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
fof(fact_inv__into__into,axiom,
! [X12,X2,X15,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),c_Set_Oimage(X15,X10,X2,X12)))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(c_Hilbert__Choice_Oinv__into(X15,X10,X12,X2),X8)),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into) ).
fof(fact_inj__image__subset__iff,axiom,
! [X11,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),c_Set_Oimage(X10,X15,X2,X12)),c_Set_Oimage(X10,X15,X2,X11)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_in__finite__psubset,axiom,
! [X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X12),X11)),c_Wellfounded_Ofinite__psubset(X10)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
& c_Finite__Set_Ofinite(X10,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_funcset__image,axiom,
! [X11,X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X15)),X2),c_FuncSet_OPi(X10,X15,X12,hAPP(c_COMBK(tc_fun(X15,tc_HOL_Obool),X10),X11))))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),c_Set_Oimage(X10,X15,X2,X12)),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__image) ).
fof(fact_inv__into__injective,axiom,
! [X7,X8,X2,X12,X15,X10] :
( hAPP(c_Hilbert__Choice_Oinv__into(X10,X15,X12,X2),X8) = hAPP(c_Hilbert__Choice_Oinv__into(X10,X15,X12,X2),X7)
=> ( hBOOL(hAPP(hAPP(c_member(X15),X8),c_Set_Oimage(X10,X15,X2,X12)))
=> ( hBOOL(hAPP(hAPP(c_member(X15),X7),c_Set_Oimage(X10,X15,X2,X12)))
=> X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).
fof(fact_Ints__odd__less__0,axiom,
! [X22,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X22),c_Int_Oring__1__class_OInts(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),X22)),X22)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X22),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_range__ex1__eq,axiom,
! [X21,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X15),X21),c_Set_Oimage(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))))
<=> ? [X3] :
( X21 = hAPP(X2,X3)
& ! [X66] :
( X21 = hAPP(X2,X66)
=> X66 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_card__image__le,axiom,
! [X2,X15,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X15,c_Set_Oimage(X10,X15,X2,X12))),c_Finite__Set_Ocard(X10,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
fof(fact_inj__on__strict__subset,axiom,
! [X12,X11,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X11)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X15,tc_HOL_Obool)),c_Set_Oimage(X10,X15,X2,X12)),c_Set_Oimage(X10,X15,X2,X11))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_endo__inj__surj,axiom,
! [X2,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oimage(X10,X10,X2,X12)),X12))
=> ( c_Fun_Oinj__on(X10,X10,X2,X12)
=> c_Set_Oimage(X10,X10,X2,X12) = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_card__inj__on__le,axiom,
! [X11,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),c_Set_Oimage(X10,X15,X2,X12)),X11))
=> ( c_Finite__Set_Ofinite(X15,X11)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X15,X11))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_image__iff,axiom,
! [X12,X2,X15,X5,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X5),c_Set_Oimage(X15,X10,X2,X12)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X15),X3),X12))
& X5 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_card__inj,axiom,
! [X11,X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X15)),X2),c_FuncSet_OPi(X10,X15,X12,hAPP(c_COMBK(tc_fun(X15,tc_HOL_Obool),X10),X11))))
=> ( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( c_Finite__Set_Ofinite(X15,X11)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X15,X11))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj) ).
fof(fact_Pi__anti__mono,axiom,
! [X11,X15,X12,X43,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X43),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,X15),tc_HOL_Obool),c_FuncSet_OPi(X10,X15,X12,X11)),c_FuncSet_OPi(X10,X15,X43,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_finite__range__imageI,axiom,
! [X2,X44,X1,X15,X10] :
( c_Finite__Set_Ofinite(X10,c_Set_Oimage(X15,X10,X1,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))))
=> c_Finite__Set_Ofinite(X44,c_Set_Oimage(X15,X44,hAPP(c_COMBB(X10,X44,X15,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_const__Lin__Prof,axiom,
! [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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),X6)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_funcset__mem,axiom,
! [X8,X11,X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X15)),X2),c_FuncSet_OPi(X10,X15,X12,hAPP(c_COMBK(tc_fun(X15,tc_HOL_Obool),X10),X11))))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X8)),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_image__mono,axiom,
! [X2,X15,X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),c_Set_Oimage(X10,X15,X2,X12)),c_Set_Oimage(X10,X15,X2,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_mlex__leq,axiom,
! [X14,X10,X7,X8,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X8)),hAPP(X2,X7)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X8),X7)),X14))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X8),X7)),c_Wellfounded_Omlex__prod(X10,X2,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_in__rel__def,axiom,
! [X7,X8,X14,X15,X10] :
( c_FunDef_Oin__rel(X10,X15,X14,X8,X7)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X15)),hAPP(hAPP(c_Product__Type_OPair(X10,X15),X8),X7)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_f__inv__into__f,axiom,
! [X12,X2,X15,X7,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X7),c_Set_Oimage(X15,X10,X2,X12)))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X15,X10,X12,X2),X7)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_surj__iff__all,axiom,
! [X2,X10,X15] :
( c_Set_Oimage(X15,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X15,X10,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)),X2),X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [X18,X10] :
( c_Nitpick_Orefl_H(X10,X18)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_inj__on__inv__into,axiom,
! [X12,X2,X15,X11,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),c_Set_Oimage(X15,X10,X2,X12)))
=> c_Fun_Oinj__on(X10,X15,c_Hilbert__Choice_Oinv__into(X15,X10,X12,X2),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
fof(fact_in__mkbot,axiom,
! [X5,X6,X7,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),X8),X7)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X6),X5)))
<=> ( X7 != X5
& ( X8 = X5
=> X8 != X7 )
& ( X8 != 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),X8),X7)),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X5,X6,X7,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),X8),X7)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X6),X5)))
<=> ( X8 != X5
& ( X7 = X5
=> X8 != X7 )
& ( X7 != 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),X8),X7)),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(help_c__COMBS__1,axiom,
! [X14,X41,X17,X10,X44,X15] : hAPP(c_COMBS(X15,X44,X10,X17,X41),X14) = hAPP(hAPP(X17,X14),hAPP(X41,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_Pi__mem,axiom,
! [X8,X11,X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X15)),X2),c_FuncSet_OPi(X10,X15,X12,X11)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X8)),hAPP(X11,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_inj__image__mem__iff,axiom,
! [X12,X22,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X22)),c_Set_Oimage(X10,X15,X2,X12)))
<=> hBOOL(hAPP(hAPP(c_member(X10),X22),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_image__surj__f__inv__f,axiom,
! [X12,X2,X10,X15] :
( c_Set_Oimage(X15,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> c_Set_Oimage(X15,X10,X2,c_Set_Oimage(X10,X15,c_Hilbert__Choice_Oinv__into(X15,X10,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)),X2),X12)) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
fof(fact_image__inv__into__cancel,axiom,
! [X67,X43,X12,X2,X10,X15] :
( c_Set_Oimage(X15,X10,X2,X12) = X43
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X67),X43))
=> c_Set_Oimage(X15,X10,X2,c_Set_Oimage(X10,X15,c_Hilbert__Choice_Oinv__into(X15,X10,X12,X2),X67)) = X67 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_inj__on__def,axiom,
! [X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
=> ! [X28] :
( hBOOL(hAPP(hAPP(c_member(X10),X28),X12))
=> ( hAPP(X2,X3) = hAPP(X2,X28)
=> X3 = X28 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_above__Lin,axiom,
! [X6,X7,X8] :
( X8 != X7
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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,X6),X8),X7)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_range__composition,axiom,
! [X1,X2,X44,X10,X15] : c_Set_Oimage(X15,X10,hAPP(c_COMBB(X44,X10,X15,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) = c_Set_Oimage(X44,X10,X2,c_Set_Oimage(X15,X44,X1,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
fof(fact_finite__surj__inj,axiom,
! [X2,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),c_Set_Oimage(X10,X10,X2,X12)))
=> c_Fun_Oinj__on(X10,X10,X2,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_dictator__def,axiom,
! [X45,X27] :
( c_Arrow__Order__Mirabelle_Odictator(X27,X45)
<=> ! [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(X27,X3) = hAPP(X3,X45) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_inj__fun,axiom,
! [X44,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X10,tc_fun(X44,X15),hAPP(c_COMBB(X15,tc_fun(X44,X15),X10,c_COMBK(X15,X44)),X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
fof(fact_funcset__id,axiom,
! [X12,X10] : hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X10)),c_COMBI(X10)),c_FuncSet_OPi(X10,X10,X12,hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_image__image,axiom,
! [X12,X1,X44,X2,X10,X15] : c_Set_Oimage(X15,X10,X2,c_Set_Oimage(X44,X15,X1,X12)) = c_Set_Oimage(X44,X10,hAPP(c_COMBB(X15,X10,X44,X2),X1),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_below__Lin,axiom,
! [X6,X7,X8] :
( X8 != X7
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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(X6,X8,X7)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_in__measure,axiom,
! [X2,X7,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X8),X7)),c_Wellfounded_Omeasure(X10,X2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X8)),hAPP(X2,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_inv__into__image__cancel,axiom,
! [X13,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X13),X12))
=> c_Set_Oimage(X15,X10,c_Hilbert__Choice_Oinv__into(X10,X15,X12,X2),c_Set_Oimage(X10,X15,X2,X13)) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
fof(fact_finite__surj,axiom,
! [X2,X11,X15,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X15,tc_HOL_Obool),X11),c_Set_Oimage(X10,X15,X2,X12)))
=> c_Finite__Set_Ofinite(X15,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(fact_mkbot__Lin,axiom,
! [X8,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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,X6),X8)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_mktop__Lin,axiom,
! [X8,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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,X6),X8)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_inv__image__comp,axiom,
! [X72,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Set_Oimage(X15,X10,c_Hilbert__Choice_Oinv__into(X10,X15,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),c_Set_Oimage(X10,X15,X2,X72)) = X72 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).
fof(fact_image__inv__f__f,axiom,
! [X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Set_Oimage(X15,X10,c_Hilbert__Choice_Oinv__into(X10,X15,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),c_Set_Oimage(X10,X15,X2,X12)) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
fof(fact_surj__f__inv__f,axiom,
! [X7,X2,X10,X15] :
( c_Set_Oimage(X15,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X15,X10,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)),X2),X7)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
fof(fact_mlex__less,axiom,
! [X14,X10,X7,X8,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X8)),hAPP(X2,X7)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X8),X7)),c_Wellfounded_Omlex__prod(X10,X2,X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_surj__imp__inj__inv,axiom,
! [X2,X10,X15] :
( c_Set_Oimage(X15,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> c_Fun_Oinj__on(X10,X15,c_Hilbert__Choice_Oinv__into(X15,X10,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
fof(fact_rangeI,axiom,
! [X15,X8,X2,X10] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X8)),c_Set_Oimage(X15,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_inj__imp__surj__inv,axiom,
! [X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Set_Oimage(X15,X10,c_Hilbert__Choice_Oinv__into(X10,X15,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
fof(fact_imageI,axiom,
! [X2,X15,X12,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X8)),c_Set_Oimage(X10,X15,X2,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
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__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_range__eqI,axiom,
! [X15,X10,X8,X2,X21] :
( X21 = hAPP(X2,X8)
=> hBOOL(hAPP(hAPP(c_member(X10),X21),c_Set_Oimage(X15,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_image__eqI,axiom,
! [X10,X12,X15,X8,X2,X21] :
( X21 = hAPP(X2,X8)
=> ( hBOOL(hAPP(hAPP(c_member(X15),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X10),X21),c_Set_Oimage(X15,X10,X2,X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X15,X2,X21,X12,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( X21 = hAPP(X2,X8)
=> hBOOL(hAPP(hAPP(c_member(X15),X21),c_Set_Oimage(X10,X15,X2,X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__image__eq__iff,axiom,
! [X11,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( c_Set_Oimage(X10,X15,X2,X12) = c_Set_Oimage(X10,X15,X2,X11)
<=> X12 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_add__less__imp__less__right,axiom,
! [X36,X34,X35,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X34)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X21,X9,X22,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X21),X9)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X22),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X36,X35,X34,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X36)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X21,X22,X9,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X9),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X9),X21)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X22),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_finite__imageD,axiom,
! [X12,X2,X15,X10] :
( c_Finite__Set_Ofinite(X10,c_Set_Oimage(X15,X10,X2,X12))
=> ( c_Fun_Oinj__on(X15,X10,X2,X12)
=> c_Finite__Set_Ofinite(X15,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_psubset__trans,axiom,
! [X42,X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X11),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_add__le__cancel__right,axiom,
! [X21,X9,X22,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X21),X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X22),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__right,axiom,
! [X36,X34,X35,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X34)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__left,axiom,
! [X21,X22,X9,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X9),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X9),X21)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X22),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [X36,X35,X34,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X36)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_insert__subset,axiom,
! [X11,X12,X8,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X8,X12)),X11))
<=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X11))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_inv__f__f,axiom,
! [X8,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hAPP(c_Hilbert__Choice_Oinv__into(X10,X15,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),hAPP(X2,X8)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f) ).
fof(fact_inv__f__eq,axiom,
! [X7,X8,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(X2,X8) = X7
=> hAPP(c_Hilbert__Choice_Oinv__into(X10,X15,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),X7) = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq) ).
fof(fact_pred__equals__eq,axiom,
! [X13,X14,X10] :
( hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X14) = hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X13)
<=> X14 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X19,X49,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X49)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X19)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_inv__into__f__f,axiom,
! [X8,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hAPP(c_Hilbert__Choice_Oinv__into(X10,X15,X12,X2),hAPP(X2,X8)) = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
fof(fact_inv__into__f__eq,axiom,
! [X7,X8,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( hAPP(X2,X8) = X7
=> hAPP(c_Hilbert__Choice_Oinv__into(X10,X15,X12,X2),X7) = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [X2,X15,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ocard(X15,c_Set_Oimage(X10,X15,X2,X12)) = c_Finite__Set_Ocard(X10,X12)
=> c_Fun_Oinj__on(X10,X15,X2,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X15,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Fun_Oinj__on(X10,X15,X2,X12)
<=> c_Finite__Set_Ocard(X15,c_Set_Oimage(X10,X15,X2,X12)) = c_Finite__Set_Ocard(X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_insert__mono,axiom,
! [X22,X58,X42,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X42),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X22,X42)),c_Set_Oinsert(X10,X22,X58))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(help_c__COMBB__1,axiom,
! [X14,X41,X17,X44,X10,X15] : hAPP(hAPP(c_COMBB(X15,X10,X44,X17),X41),X14) = hAPP(X17,hAPP(X41,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__strict__mono,axiom,
! [X40,X34,X36,X35,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X34),X40))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X40))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_image__add__atLeastLessThan,axiom,
! [X77,X45,X52] : 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)),X52),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45,X77)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X52),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X52)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X19,X49,X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X49)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X19)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_add__le__less__mono,axiom,
! [X40,X34,X36,X35,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X36))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X34),X40))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X40))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X40,X34,X36,X35,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X34),X40))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X40))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_subset__psubset__trans,axiom,
! [X42,X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X11),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X42,X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),X42))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [X19,X49] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X49)),X19))
<=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_insert__image,axiom,
! [X2,X15,X12,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Set_Oinsert(X15,hAPP(X2,X8),c_Set_Oimage(X10,X15,X2,X12)) = c_Set_Oimage(X10,X15,X2,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
fof(fact_card__psubset,axiom,
! [X12,X11,X10] :
( c_Finite__Set_Ofinite(X10,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X10,X11)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(fact_add__mono,axiom,
! [X40,X34,X36,X35,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X36))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X34),X40))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X40))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X22,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X22)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X22),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X22,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X22)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X22),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_add__less__mono,axiom,
! [X56,X47,X53,X54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),X53))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),X56))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X56))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_image__insert,axiom,
! [X11,X22,X2,X10,X15] : c_Set_Oimage(X15,X10,X2,c_Set_Oinsert(X15,X22,X11)) = c_Set_Oinsert(X10,hAPP(X2,X22),c_Set_Oimage(X15,X10,X2,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [X2,X10] :
( c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( c_Set_Oimage(X10,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> c_Fun_Oinj__on(X10,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_subset__inj__on,axiom,
! [X12,X11,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> c_Fun_Oinj__on(X10,X15,X2,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_card__image,axiom,
! [X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> c_Finite__Set_Ocard(X15,c_Set_Oimage(X10,X15,X2,X12)) = c_Finite__Set_Ocard(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_add__neg__neg,axiom,
! [X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36)),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_Ints__add,axiom,
! [X21,X22,X10] :
( class_Rings_Oring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X22),c_Int_Oring__1__class_OInts(X10)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X21),c_Int_Oring__1__class_OInts(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X21)),c_Int_Oring__1__class_OInts(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X10] :
( c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X10,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Set_Oimage(X10,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_add__strict__right__mono,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X34))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X36))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X22,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X22)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X22),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_add__nonpos__neg,axiom,
! [X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36)),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36)),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__le__mono,axiom,
! [X56,X47,X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54),X53))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X47),X56))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X56))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_finite__Plus__iff,axiom,
! [X11,X12,X15,X10] :
( c_Finite__Set_Ofinite(tc_sum(X10,X15),c_Sum__Type_OPlus(X10,X15,X12,X11))
<=> ( c_Finite__Set_Ofinite(X10,X12)
& c_Finite__Set_Ofinite(X15,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X11,X12,X15,X10] :
( c_Finite__Set_Ofinite(tc_sum(X10,X15),c_Sum__Type_OPlus(X10,X15,X12,X11))
=> c_Finite__Set_Ofinite(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [X11,X12,X15,X10] :
( c_Finite__Set_Ofinite(tc_sum(X10,X15),c_Sum__Type_OPlus(X10,X15,X12,X11))
=> c_Finite__Set_Ofinite(X15,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_add__right__mono,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X36))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X34))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X36))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X36))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__lessD1,axiom,
! [X47,X53,X54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X53)),X47))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),c_Groups_Ozero__class_Ozero(X10)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),c_Groups_Ozero__class_Ozero(X10)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36)),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_predicate2D,axiom,
! [X7,X8,X41,X17,X15,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X15,tc_HOL_Obool)),X17),X41))
=> ( hBOOL(hAPP(hAPP(X17,X8),X7))
=> hBOOL(hAPP(hAPP(X41,X8),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X41,X15,X10,X7,X8,X17] :
( hBOOL(hAPP(hAPP(X17,X8),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X15,tc_HOL_Obool)),X17),X41))
=> hBOOL(hAPP(hAPP(X41,X8),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_add__less__mono1,axiom,
! [X47,X53,X54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),X53))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X47))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_inj__on__iff,axiom,
! [X7,X8,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X7),X12))
=> ( hAPP(X2,X8) = hAPP(X2,X7)
<=> X8 = X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__on__contraD,axiom,
! [X7,X8,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( X8 != X7
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X7),X12))
=> hAPP(X2,X8) != hAPP(X2,X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_inj__onD,axiom,
! [X7,X8,X12,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,X12)
=> ( hAPP(X2,X8) = hAPP(X2,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X7),X12))
=> X8 = X7 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_add__leD1,axiom,
! [X46,X47,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X47)),X46))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X46,X47,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X47)),X46))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X47),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__pos__pos,axiom,
! [X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__le__mono1,axiom,
! [X47,X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54),X53))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X47))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_psubsetD,axiom,
! [X9,X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X9),X12))
=> hBOOL(hAPP(hAPP(c_member(X10),X9),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_psubset__card__mono,axiom,
! [X12,X11,X10] :
( c_Finite__Set_Ofinite(X10,X11)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X10,X11))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_inj__on__add__nat,axiom,
! [X55,X52] : 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)),X52),X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X40,X34,X36,X35,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X40)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_subset__trans,axiom,
! [X42,X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),X42))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_add__nonneg__pos,axiom,
! [X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_card__Plus__conv__if,axiom,
! [X11,X15,X12,X10] :
( ( ( c_Finite__Set_Ofinite(X10,X12)
& c_Finite__Set_Ofinite(X15,X11) )
=> c_Finite__Set_Ocard(tc_sum(X10,X15),c_Sum__Type_OPlus(X10,X15,X12,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X15,X11)) )
& ( ~ ( c_Finite__Set_Ofinite(X10,X12)
& c_Finite__Set_Ofinite(X15,X11) )
=> c_Finite__Set_Ocard(tc_sum(X10,X15),c_Sum__Type_OPlus(X10,X15,X12,X11)) = 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,
! [X11,X15,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X15,X11)
=> c_Finite__Set_Ocard(tc_sum(X10,X15),c_Sum__Type_OPlus(X10,X15,X12,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X15,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_pos__add__strict,axiom,
! [X34,X36,X35,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_card__insert__le,axiom,
! [X8,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
fof(fact_Ints__odd__nonzero,axiom,
! [X22,X10] :
( class_Int_Oring__char__0(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X22),c_Int_Oring__1__class_OInts(X10)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),X22)),X22) != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X22,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X22)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_add__gr__0,axiom,
! [X19,X49] :
( 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),X49),X19)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X49))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_card__seteq,axiom,
! [X12,X11,X10] :
( c_Finite__Set_Ofinite(X10,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X11)),c_Finite__Set_Ocard(X10,X12)))
=> X12 = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_subset__insertI2,axiom,
! [X21,X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),c_Set_Oinsert(X10,X21,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_add__strict__increasing2,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X36))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_psubset__imp__subset,axiom,
! [X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
| X12 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__eq,axiom,
! [X11,X12,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X11))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
& X12 != X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_insert__iff,axiom,
! [X12,X21,X22,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oinsert(X10,X21,X12)))
<=> ( X22 = X21
| hBOOL(hAPP(hAPP(c_member(X10),X22),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X12,X21,X22,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oinsert(X10,X21,X12)))
=> ( X22 != X21
=> hBOOL(hAPP(hAPP(c_member(X10),X22),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X22,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_Pi__UNIV,axiom,
! [X12,X15,X10] : c_FuncSet_OPi(X10,X15,X12,hAPP(c_COMBK(tc_fun(X15,tc_HOL_Obool),X10),c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X15),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
fof(fact_add__increasing,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X35,X36,X34,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X34))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),X35))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_finite__Plus,axiom,
! [X11,X15,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X15,X11)
=> c_Finite__Set_Ofinite(tc_sum(X10,X15),c_Sum__Type_OPlus(X10,X15,X12,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(help_c__COMBC__1,axiom,
! [X14,X41,X17,X10,X44,X15] : hAPP(hAPP(hAPP(c_COMBC(X15,X44,X10),X17),X41),X14) = hAPP(hAPP(X17,X14),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_set__eq__subset,axiom,
! [X10,X11,X12] :
( X12 = X11
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),X12))
=> X12 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_set__rev__mp,axiom,
! [X11,X12,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> hBOOL(hAPP(hAPP(c_member(X10),X8),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_in__mono,axiom,
! [X8,X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X10),X8),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_set__mp,axiom,
! [X8,X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X10),X8),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_subsetD,axiom,
! [X9,X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X9),X12))
=> hBOOL(hAPP(hAPP(c_member(X10),X9),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_le__funD,axiom,
! [X8,X1,X2,X10,X15] :
( class_Orderings_Oord(X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X15),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,hAPP(X2,X8)),hAPP(X1,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X8,X1,X2,X10,X15] :
( class_Orderings_Oord(X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X15),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X15,hAPP(X2,X8)),hAPP(X1,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_finite__imageI,axiom,
! [X65,X15,X27,X10] :
( c_Finite__Set_Ofinite(X10,X27)
=> c_Finite__Set_Ofinite(X15,c_Set_Oimage(X10,X15,X65,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_card__mono,axiom,
! [X12,X11,X10] :
( c_Finite__Set_Ofinite(X10,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X10,X11))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X34,X36,X35,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36)),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),X36) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_inj__eq,axiom,
! [X7,X8,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(X2,X8) = hAPP(X2,X7)
<=> X8 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [X7,X8,X2,X15,X10] :
( c_Fun_Oinj__on(X10,X15,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(X2,X8) = hAPP(X2,X7)
=> X8 = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
fof(fact_less__add__Suc1,axiom,
! [X48,X54] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X48)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X48,X54] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X54)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_insertI2,axiom,
! [X21,X11,X22,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X22),X11))
=> hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oinsert(X10,X21,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_less__trans__Suc,axiom,
! [X47,X53,X54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),X53))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X53),X47))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X54)),X47)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [X10] :
( c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,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(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,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,
! [X19,X49] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X49)),hAPP(c_Nat_OSuc,X19)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__less__SucD,axiom,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)),hAPP(c_Nat_OSuc,X46)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [X15,X10] :
( c_Finite__Set_Ofinite(tc_fun(X10,X15),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X15),tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X15,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_order__less__trans,axiom,
! [X32,X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X32))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X32,X31,X33,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_image__Suc__atLeastLessThan,axiom,
! [X77,X45] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X45,X77)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X45),hAPP(c_Nat_OSuc,X77)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X7,X8,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X8))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X7))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X8),X7) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X8 = c_Groups_Ozero__class_Ozero(X10)
& X7 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [X15,X10] : c_Sum__Type_OPlus(X10,X15,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X10,X15),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_trans__less__add1,axiom,
! [X48,X53,X54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),X53))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X48))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X32,X33,X31] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add2,axiom,
! [X48,X53,X54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),X53))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X53))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X33,X32,X31] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X32))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X19,X49] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),hAPP(c_Nat_OSuc,X19)))
<=> ( X49 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X63] :
( X49 = hAPP(c_Nat_OSuc,X63)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X63),X19)) ) ) ),
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,
! [X34,X36,X35,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36)),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X34)) ),
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,
! [X34,X36,X35,X10] :
( class_Groups_Oab__semigroup__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36)),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X34)) ),
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,
! [X40,X34,X35,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X40)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_insert__code,axiom,
! [X8,X12,X7,X10] :
( hBOOL(hAPP(c_Set_Oinsert(X10,X7,X12),X8))
<=> ( X7 = X8
| hBOOL(hAPP(X12,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_zero__less__two,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),c_Groups_Oone__class_Oone(X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_Suc__le__mono,axiom,
! [X49,X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19)),hAPP(c_Nat_OSuc,X49)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_order__le__less__trans,axiom,
! [X32,X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X32))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X32,X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X32))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I8_J,axiom,
! [X32,X31,X33,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X32,X31,X33,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X15,X10] :
( c_Finite__Set_Ofinite(tc_sum(X10,X15),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X10,X15),tc_HOL_Obool)))
<=> ( c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
& c_Finite__Set_Ofinite(X15,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X15,X10] :
( c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( c_Finite__Set_Ofinite(X15,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(tc_prod(X10,X15),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10,X15),tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_less__add__eq__less,axiom,
! [X46,X48,X56,X47] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),X56))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X46)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_subset__insertI,axiom,
! [X22,X11,X10] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),c_Set_Oinsert(X10,X22,X11))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_Suc__lessD,axiom,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__mono,axiom,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)),hAPP(c_Nat_OSuc,X46))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_trans__le__add1,axiom,
! [X48,X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54),X53))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X48))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X32,X33,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add2,axiom,
! [X48,X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54),X53))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X53))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X33,X32,X31] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X32))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X15,X10] :
( c_Finite__Set_Ofinite(tc_fun(X10,X15),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X15),tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(X15,c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_nat__add__assoc,axiom,
! [X47,X46,X48] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X46)),X47) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X47)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_less__eq__Suc__le,axiom,
! [X49,X19] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X49))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19)),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X19,X49] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X49)),X19))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X48)),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_predicate1D,axiom,
! [X8,X41,X17,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X17),X41))
=> ( hBOOL(hAPP(X17,X8))
=> hBOOL(hAPP(X41,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X41,X10,X8,X17] :
( hBOOL(hAPP(X17,X8))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X17),X41))
=> hBOOL(hAPP(X41,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_order__trans,axiom,
! [X32,X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X32))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X32,X31,X33,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_Suc__lessI,axiom,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
=> ( hAPP(c_Nat_OSuc,X48) != X46
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__add__one,axiom,
! [X35,X10] :
( class_Rings_Olinordered__semidom(X10)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),c_Groups_Oone__class_Oone(X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_le__less__Suc__eq,axiom,
! [X19,X49] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,X49)))
<=> X19 = X49 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__leD,axiom,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X48)),X46))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X55] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X55)
<=> ? [X20] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X55))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_insert__commute,axiom,
! [X12,X7,X8,X10] : c_Set_Oinsert(X10,X8,c_Set_Oinsert(X10,X7,X12)) = c_Set_Oinsert(X10,X7,c_Set_Oinsert(X10,X8,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_insertI1,axiom,
! [X11,X22,X10] : hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oinsert(X10,X22,X11))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_less__Suc__eq,axiom,
! [X19,X49] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),hAPP(c_Nat_OSuc,X19)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19))
| X49 = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__leI,axiom,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X48)),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X40,X34,X35,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X40)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_le__trans,axiom,
! [X47,X53,X54] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54),X53))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53),X47))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54),X47)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_finite__subset,axiom,
! [X11,X12,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ( c_Finite__Set_Ofinite(X10,X11)
=> c_Finite__Set_Ofinite(X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [X12,X11,X10] :
( c_Finite__Set_Ofinite(X10,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> c_Finite__Set_Ofinite(X10,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_less__iff__Suc__add,axiom,
! [X19,X49] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19))
<=> ? [X57] : X19 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__Suc__eq__le,axiom,
! [X19,X49] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),hAPP(c_Nat_OSuc,X19)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X55] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X55)
<=> ? [X20] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X55))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_less__SucI,axiom,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_OSuc,X46))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [X22,X10] :
( class_Int_Oring__char__0(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X22),c_Int_Oring__1__class_OInts(X10)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X22) = c_Groups_Ozero__class_Ozero(X10)
<=> X22 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_nat__case__Suc,axiom,
! [X62,X70,X71,X10] : c_Nat_Onat_Onat__case(X10,X71,X70,hAPP(c_Nat_OSuc,X62)) = hAPP(X70,X62),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_le__Suc__eq,axiom,
! [X19,X49] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),hAPP(c_Nat_OSuc,X19)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19))
| X49 = hAPP(c_Nat_OSuc,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_subset__UNIV,axiom,
! [X12,X10] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_nat__less__cases,axiom,
! [X17,X19,X49] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19))
=> hBOOL(hAPP(hAPP(X17,X19),X49)) )
=> ( ( X49 = X19
=> hBOOL(hAPP(hAPP(X17,X19),X49)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X49))
=> hBOOL(hAPP(hAPP(X17,X19),X49)) )
=> hBOOL(hAPP(hAPP(X17,X19),X49)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_nat__add__left__commute,axiom,
! [X32,X33,X31] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X32)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_order__eq__iff,axiom,
! [X7,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( X8 = X7
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X7),X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X8,X7,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X7),X8))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
<=> X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X33,X31,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31))
=> X31 = X33 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X31,X33,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
=> X31 = X33 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_card__ge__0__finite,axiom,
! [X12,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X10,X12)))
=> c_Finite__Set_Ofinite(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_le__imp__less__Suc,axiom,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_OSuc,X46))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X12,X10] :
( c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X10,X12) = c_Finite__Set_Ocard(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> X12 = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_order__le__less,axiom,
! [X7,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
| X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X7,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
& X8 != X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__less__imp__le,axiom,
! [X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_le__add1,axiom,
! [X48,X46] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X48))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X48,X46] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X46))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_image__ident,axiom,
! [X69,X10] : c_Set_Oimage(X10,X10,c_COMBI(X10),X69) = X69,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_inj__on__id2,axiom,
! [X12,X10] : c_Fun_Oinj__on(X10,X10,c_COMBI(X10),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(fact_nat__case__0,axiom,
! [X70,X71,X10] : c_Nat_Onat_Onat__case(X10,X71,X70,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X71,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
fof(fact_xt1_I11_J,axiom,
! [X35,X36,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),X35))
=> ( X35 != X36
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),X35)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X36,X35,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X36))
=> ( X35 != X36
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X33,X31,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
| X31 = X33 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X36,X35,X10] :
( class_Orderings_Oorder(X10)
=> ( X35 != X36
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_xt1_I12_J,axiom,
! [X36,X35,X10] :
( class_Orderings_Oorder(X10)
=> ( X35 != X36
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X36),X35))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),X35)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_less__Suc0,axiom,
! [X19] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_inj__Suc,axiom,
! [X55] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_le__antisym,axiom,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X48))
=> X48 = X46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_eq__mem,axiom,
! [X7,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),hAPP(c_fequal,X7)))
<=> X8 = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__SucI,axiom,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),hAPP(c_Nat_OSuc,X46))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_nat__less__le,axiom,
! [X19,X49] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19))
& X49 != X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X19,X49] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19))
| X49 = X19 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_less__imp__le__nat,axiom,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X46,X48] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
| X48 = X46 )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X33,X31] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X31),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_insert__absorb,axiom,
! [X12,X22,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X22),X12))
=> c_Set_Oinsert(X10,X22,X12) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_linorder__neq__iff,axiom,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( X8 != X7
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X7),X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
| X31 = X33
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_finite__option__UNIV,axiom,
! [X10] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X10),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X10),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_le__neq__implies__less,axiom,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
=> ( X48 != X46
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_insert__absorb2,axiom,
! [X12,X8,X10] : c_Set_Oinsert(X10,X8,c_Set_Oinsert(X10,X8,X12)) = c_Set_Oinsert(X10,X8,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [X8,X10] : hBOOL(hAPP(hAPP(c_member(X10),X8),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_UNIV__I,axiom,
! [X8,X10] : hBOOL(hAPP(hAPP(c_member(X10),X8),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_finite__insert,axiom,
! [X12,X22,X10] :
( c_Finite__Set_Ofinite(X10,c_Set_Oinsert(X10,X22,X12))
<=> c_Finite__Set_Ofinite(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
fof(fact_mem__def,axiom,
! [X12,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
<=> hBOOL(hAPP(X12,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_linorder__le__less__linear,axiom,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_add__Suc,axiom,
! [X46,X48] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)),X46) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_le__iff__add,axiom,
! [X19,X49] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19))
<=> ? [X57] : X19 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_nat__neq__iff,axiom,
! [X19,X49] :
( X49 != X19
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X49)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_gr0__conv__Suc,axiom,
! [X19] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19))
<=> ? [X20] : X19 = hAPP(c_Nat_OSuc,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X33,X31,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> X33 != X31 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X33,X31,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> X31 != X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X33,X31,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> X31 != X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_equalityD1,axiom,
! [X10,X11,X12] :
( X12 = X11
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X10,X11,X12] :
( X12 = X11
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_subset__refl,axiom,
! [X12,X10] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_neq0__conv,axiom,
! [X19] :
( X19 != 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)),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_add__right__cancel,axiom,
! [X9,X22,X21,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X21),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X9),X22)
<=> X21 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__right__imp__eq,axiom,
! [X34,X35,X36,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35)
=> X36 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Ocancel__ab__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)
=> X36 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X9,X21,X22,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X9)
<=> X21 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [X34,X36,X35,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)
=> X36 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_linorder__linear,axiom,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_add__Suc__right,axiom,
! [X46,X48] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),hAPP(c_Nat_OSuc,X46)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_add__Suc__shift,axiom,
! [X46,X48] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)),X46) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),hAPP(c_Nat_OSuc,X46)),
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,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
=> X46 != 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,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zero__less__Suc,axiom,
! [X46] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X46))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_less__not__refl2,axiom,
! [X48,X46] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X48))
=> X48 != X46 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [X50,X51] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X50))
=> X51 != X50 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_zero__less__one,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),c_Groups_Oone__class_Oone(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_Ints__0,axiom,
! [X10] :
( class_Rings_Oring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Ozero__class_Ozero(X10)),c_Int_Oring__1__class_OInts(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(fact_Ints__1,axiom,
! [X10] :
( class_Rings_Oring__1(X10)
=> hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Oone__class_Oone(X10)),c_Int_Oring__1__class_OInts(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(fact_nat__add__right__cancel,axiom,
! [X19,X52,X49] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X52) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X19),X52)
<=> X49 = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X19,X49,X52] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X49) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X19)
<=> X49 = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_finite_OinsertI,axiom,
! [X22,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ofinite(X10,c_Set_Oinsert(X10,X22,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_lessI,axiom,
! [X46] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X46))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_top1I,axiom,
! [X8,X10] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_le__0__eq,axiom,
! [X19] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X19 = 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,
! [X19,X49] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X19) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X49 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X49 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X19 = 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,
! [X19,X49] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X19)
<=> ( ( X49 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X49 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X19 = 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,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),c_Groups_Oone__class_Oone(X10))) ),
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,
! [X34,X35,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_gr0I,axiom,
! [X46] :
( X46 != 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)),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_top__greatest,axiom,
! [X31,X10] :
( class_Orderings_Otop(X10)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),c_Orderings_Otop__class_Otop(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_double__eq__0__iff,axiom,
! [X22,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X22) = c_Groups_Ozero__class_Ozero(X10)
<=> X22 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X22,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X22)
<=> X22 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__iff,axiom,
! [X22,X21,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( X21 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X21),X22)
<=> X22 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_order__eq__refl,axiom,
! [X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( X31 = X33
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(help_c__COMBK__1,axiom,
! [X81,X80,X15,X10] : hAPP(hAPP(c_COMBK(X10,X15),X80),X81) = X80,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_nat__add__commute,axiom,
! [X46,X48] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X46) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),X48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_order__refl,axiom,
! [X31,X10] :
( class_Orderings_Opreorder(X10)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X46] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X46] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_top__apply,axiom,
! [X8,X15,X10] :
( class_Orderings_Otop(X10)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X15,X10)),X8) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_add__is__0,axiom,
! [X19,X49] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X49 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X19 = 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,
! [X46,X48] :
( X48 = X46
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(help_c__fequal__2,axiom,
! [X7,X8] :
( X8 != X7
| hBOOL(hAPP(hAPP(c_fequal,X8),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_add__eq__self__zero,axiom,
! [X46,X48] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X46) = X48
=> X46 = 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,
! [X46] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X46),X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_finite__UNIV,axiom,
! [X10] :
( class_Finite__Set_Ofinite(X10)
=> c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,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,
! [X35,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X35) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0,axiom,
! [X35,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X35) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [X35,X10] :
( class_Groups_Omonoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X35) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X35,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),c_Groups_Ozero__class_Ozero(X10)) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X35,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),c_Groups_Ozero__class_Ozero(X10)) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [X35,X10] :
( class_Groups_Omonoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),c_Groups_Ozero__class_Ozero(X10)) = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X46] : hAPP(c_Nat_OSuc,X46) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_Suc__eq__plus1,axiom,
! [X46] : hAPP(c_Nat_OSuc,X46) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X46),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,
! [X46] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X46) = X46,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X19] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X48] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X48,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [X79,X78] :
( ( class_Finite__Set_Ofinite(X78)
& class_Finite__Set_Ofinite(X79) )
=> class_Finite__Set_Ofinite(tc_sum(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [X79,X78] :
( ( class_Finite__Set_Ofinite(X78)
& class_Finite__Set_Ofinite(X79) )
=> class_Finite__Set_Ofinite(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X79,X78] :
( ( class_Finite__Set_Ofinite(X78)
& class_Finite__Set_Ofinite(X79) )
=> class_Finite__Set_Ofinite(tc_prod(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(fact_Suc__inject,axiom,
! [X33,X31] :
( hAPP(c_Nat_OSuc,X31) = hAPP(c_Nat_OSuc,X33)
=> X31 = X33 ),
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,
! [X78,X79] :
( class_Orderings_Oorder(X79)
=> class_Orderings_Oorder(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X78,X79] :
( class_Orderings_Oord(X79)
=> class_Orderings_Oord(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X78,X79] :
( class_Orderings_Opreorder(X79)
=> class_Orderings_Opreorder(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Otop,axiom,
! [X78,X79] :
( class_Orderings_Otop(X79)
=> class_Orderings_Otop(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(fact_Suc__not__Zero,axiom,
! [X48] : hAPP(c_Nat_OSuc,X48) != 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,
! [X48] : hAPP(c_Nat_OSuc,X48) != 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,
! [X48] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X48),
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,
! [X48] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_finite__code,axiom,
! [X12,X10] :
( class_Finite__Set_Ofinite(X10)
=> c_Finite__Set_Ofinite(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_finite,axiom,
! [X12,X10] :
( class_Finite__Set_Ofinite(X10)
=> c_Finite__Set_Ofinite(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_Suc__n__not__n,axiom,
! [X46] : hAPP(c_Nat_OSuc,X46) != X46,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X46] : X46 != hAPP(c_Nat_OSuc,X46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(help_c__COMBI__1,axiom,
! [X80,X10] : hAPP(c_COMBI(X10),X80) = X80,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_zero__neq__one,axiom,
! [X10] :
( class_Rings_Ozero__neq__one(X10)
=> c_Groups_Ozero__class_Ozero(X10) != c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X10] :
( class_Rings_Ozero__neq__one(X10)
=> c_Groups_Oone__class_Oone(X10) != c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [X79] :
( class_Finite__Set_Ofinite(X79)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(fact_nat__size,axiom,
! [X46] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X46) = X46,
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__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_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_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_096) ).
fof(fact__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_096) ).
fof(fact_n_I3_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
file('/export/starexec/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__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__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__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_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_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_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(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_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_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_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_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
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_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_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
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__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(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(i_0_519,plain,
! [X4] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> ( ( hAPP(v_h____,X4) = v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
& ( hAPP(v_h____,X4) != v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) )
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ) ) ),
inference(fof_simplification,[status(thm)],[fact__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_A_Ib_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096]) ).
fof(i_0_520,plain,
~ ! [X37] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> ( ! [X20] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X37))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X20))),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),X37),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_521,plain,
! [X8,X12,X27,X1,X5,X2,X15,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X15,X2,X5,X1,X27)
=> ( c_Finite__Set_Ofinite(X15,X12)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X15),X8),X12))
=> hAPP(X27,c_Set_Oinsert(X15,X8,X12)) = hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X27,X12)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(i_0_522,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_523,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_524,plain,
! [X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X10,c_Set_Oimage(X15,X10,X2,X12))),c_Finite__Set_Ocard(X15,X12)))
=> ~ c_Fun_Oinj__on(X15,X10,X2,X12) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).
fof(i_0_525,plain,
! [X12,X10] :
( ( c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ocard(X10,X12) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X12) )
& ( ~ c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ocard(X10,X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_card__def]) ).
fof(i_0_526,plain,
! [X1623] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,X1623) != v_n____
| hAPP(v_h____,X1623) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,X1623) != v_n____
| hAPP(v_h____,X1623) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| hAPP(v_h____,X1623) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| hAPP(v_h____,X1623) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,X1623) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,X1623) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,X1623) != v_n____
| hAPP(v_h____,X1623) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,X1623) != v_n____
| hAPP(v_h____,X1623) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| hAPP(v_h____,X1623) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| hAPP(v_h____,X1623) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,X1623) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,X1623) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hAPP(v_h____,X1623) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hAPP(v_h____,X1623) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hAPP(v_h____,X1623) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( hAPP(v_h____,X1623) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
& ( hAPP(v_h____,X1623) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
& ( hAPP(v_h____,X1623) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1623)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
& ( hAPP(v_h____,X1623) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1623)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) )
& ( hAPP(v_h____,X1623) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1623)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1623)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_519])])]) ).
fof(i_0_527,plain,
! [X7,X8,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),c_Arrow__Order__Mirabelle_OLin))
=> ( 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),X7)),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),X7),X8)),X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_528,plain,
! [X21,X22,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X6),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),X22),X21)),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),X21),X22)),X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_529,plain,
! [X8,X11,X12,X2,X15,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X15)),X2),c_FuncSet_OPi(X10,X15,X12,X11)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X15),hAPP(X2,X8)),hAPP(X11,X8)))
=> ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_530,plain,
! [X11,X12,X8,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),c_Set_Oinsert(X10,X8,X11)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_531,plain,
~ ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X38))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X38),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_532,plain,
~ ! [X39] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X39))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X39),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_533,plain,
! [X1,X2,X10,X15] :
( class_Orderings_Oord(X15)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X15)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X15),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X15),X1),X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_534,plain,
! [X46,X47,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X47)),X46))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X47),X46)) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_535,plain,
! [X53,X54] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X53)),X54)),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_536,plain,
! [X54,X53] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X54)),X54)),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_537,plain,
! [X19,X17] :
( ~ hBOOL(hAPP(X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X17,X19))
=> ? [X57] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X19))
& ! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X57))
=> ~ hBOOL(hAPP(X17,X4)) )
& hBOOL(hAPP(X17,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X57),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_538,plain,
! [X21,X11,X22,X10] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X22),X11))
=> X22 = X21 )
=> hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oinsert(X10,X21,X11))) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_539,plain,
! [X11,X12,X8,X10] :
( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X11))
=> ( c_Set_Oinsert(X10,X8,X12) = c_Set_Oinsert(X10,X8,X11)
<=> X12 = X11 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_540,plain,
! [X19,X49] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X19))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X19)),X49)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_541,plain,
! [X19,X49] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X19))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,X49))) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_542,plain,
! [X35,X36,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),X35))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36)) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_543,plain,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X7),X8))
| X8 = X7 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_544,plain,
! [X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_545,plain,
! [X36,X35,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X36))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X36),X35)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_546,plain,
! [X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_547,plain,
! [X33,X31,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_548,plain,
! [X8,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X10,X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).
fof(i_0_549,plain,
! [X7,X8,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X7),X8)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_550,plain,
! [X8,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)) = c_Finite__Set_Ocard(X10,X12) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X10,X12)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).
fof(i_0_551,plain,
! [X49,X19] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X49))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),hAPP(c_Nat_OSuc,X49)))
<=> X19 = X49 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_552,plain,
! [X48,X46] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X48))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X48)))
=> X48 = X46 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_553,plain,
! [X46,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),hAPP(c_Nat_OSuc,X46)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X48),X46))
=> X48 = X46 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_554,plain,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> X8 = X7 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_555,plain,
! [X31,X33,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33)) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_556,plain,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X7),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_557,plain,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X7),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_558,plain,
! [X8,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Finite__Set_Ocard(X10,c_Set_Oinsert(X10,X8,X12)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X10,X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).
fof(i_0_559,plain,
! [X46,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),hAPP(c_Nat_OSuc,X46)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X48),X46))
=> X48 = hAPP(c_Nat_OSuc,X46) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_560,plain,
! [X46] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X46)),X46)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_561,plain,
! [X7,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X8),X7))
<=> X8 = X7 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_562,plain,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),c_Groups_Ozero__class_Ozero(X10))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_563,plain,
! [X33,X31,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X31 != X33
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_564,plain,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> ( X31 != X33
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_565,plain,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( X31 != X33
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X33),X31)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_566,plain,
! [X8,X7,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X7),X8))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X8),X7))
<=> X8 = X7 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_567,plain,
! [X31,X33,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_568,plain,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_569,plain,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10)),c_Groups_Ozero__class_Ozero(X10))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_570,plain,
! [X33,X31] :
( X31 != X33
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X31)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_571,plain,
! [X10,X11,X12] :
( X12 = X11
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),X12)) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_572,plain,
! [X31,X10] :
( class_Orderings_Opreorder(X10)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X31)) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_573,plain,
! [X33,X31,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X31),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X33),X31)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_574,plain,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_575,plain,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_576,plain,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_577,plain,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X46)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_578,plain,
! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X46)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_579,plain,
! [X7,X8] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X8),X7))
| X8 = X7 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_580,plain,
! [X12,X10] :
( ~ c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ocard(X10,X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
fof(i_0_581,plain,
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ) ),
inference(fof_nnf,[status(thm)],[fact__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_J_A_061_Ia_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_J_096]) ).
fof(i_0_582,plain,
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ) ),
inference(fof_nnf,[status(thm)],[fact__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_A_061_Ib_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_096]) ).
fof(i_0_583,plain,
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_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_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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_585,plain,
! [X1978] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk17_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,X1978),esk17_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____)),X1978))),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),esk17_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_520])])])]) ).
fof(i_0_586,plain,
! [X1974] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk14_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,X1974),esk14_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____)),X1974))),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),esk14_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_587,plain,
! [X1658] : hBOOL(hAPP(hAPP(c_member(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____)),X1658))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
inference(variable_rename,[status(thm)],[fact_PiProf]) ).
fof(i_0_588,plain,
! [X1659] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1659),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X1659))),v_Lab____)),v_Lba____)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n_I2_J])]) ).
fof(i_0_589,plain,
! [X2016,X2017,X2018,X2019] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2019,tc_fun(X2018,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2019,tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_fun(X2018,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2018,tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_fun(X2018,tc_HOL_Obool)),X2019,c_COMBC(X2018,tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2018,tc_prod(X2019,X2018)),tc_fun(X2018,tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),X2019,c_COMBB(tc_prod(X2019,X2018),tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool),X2018,c_member(tc_prod(X2019,X2018)))),c_Product__Type_OPair(X2019,X2018)))),X2017)),hAPP(hAPP(c_COMBC(X2019,tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_fun(X2018,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2018,tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_fun(X2018,tc_HOL_Obool)),X2019,c_COMBC(X2018,tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2018,tc_prod(X2019,X2018)),tc_fun(X2018,tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),X2019,c_COMBB(tc_prod(X2019,X2018),tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool),X2018,c_member(tc_prod(X2019,X2018)))),c_Product__Type_OPair(X2019,X2018)))),X2016)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),X2017),X2016)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),X2017),X2016))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2019,tc_fun(X2018,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2019,tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_fun(X2018,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2018,tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_fun(X2018,tc_HOL_Obool)),X2019,c_COMBC(X2018,tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2018,tc_prod(X2019,X2018)),tc_fun(X2018,tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),X2019,c_COMBB(tc_prod(X2019,X2018),tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool),X2018,c_member(tc_prod(X2019,X2018)))),c_Product__Type_OPair(X2019,X2018)))),X2017)),hAPP(hAPP(c_COMBC(X2019,tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_fun(X2018,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2018,tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_fun(X2018,tc_HOL_Obool)),X2019,c_COMBC(X2018,tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2018,tc_prod(X2019,X2018)),tc_fun(X2018,tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool)),X2019,c_COMBB(tc_prod(X2019,X2018),tc_fun(tc_fun(tc_prod(X2019,X2018),tc_HOL_Obool),tc_HOL_Obool),X2018,c_member(tc_prod(X2019,X2018)))),c_Product__Type_OPair(X2019,X2018)))),X2016))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_590,plain,
! [X1703,X1704,X1705,X1706,X1707,X1708] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1708),X1707)),hAPP(v_F,X1704)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1706),X1705)),hAPP(v_F,X1703)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1708),X1707)),hAPP(X1704,esk7_6(X1703,X1704,X1705,X1706,X1707,X1708))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1706),X1705)),hAPP(X1703,esk7_6(X1703,X1704,X1705,X1706,X1707,X1708))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1703),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))),X1704),c_Arrow__Order__Mirabelle_OProf))
| X1707 = X1706
| X1708 = X1705
| X1706 = X1705
| X1708 = X1707 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1706),X1705)),hAPP(v_F,X1703)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1708),X1707)),hAPP(v_F,X1704)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1708),X1707)),hAPP(X1704,esk7_6(X1703,X1704,X1705,X1706,X1707,X1708))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1706),X1705)),hAPP(X1703,esk7_6(X1703,X1704,X1705,X1706,X1707,X1708))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1703),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))),X1704),c_Arrow__Order__Mirabelle_OProf))
| X1707 = X1706
| X1708 = X1705
| X1706 = X1705
| X1708 = X1707 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1708),X1707)),hAPP(v_F,X1704)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1706),X1705)),hAPP(v_F,X1703)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1708),X1707)),hAPP(X1704,esk7_6(X1703,X1704,X1705,X1706,X1707,X1708))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1706),X1705)),hAPP(X1703,esk7_6(X1703,X1704,X1705,X1706,X1707,X1708))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1703),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))),X1704),c_Arrow__Order__Mirabelle_OProf))
| X1707 = X1706
| X1708 = X1705
| X1706 = X1705
| X1708 = X1707 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1706),X1705)),hAPP(v_F,X1703)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1708),X1707)),hAPP(v_F,X1704)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1708),X1707)),hAPP(X1704,esk7_6(X1703,X1704,X1705,X1706,X1707,X1708))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1706),X1705)),hAPP(X1703,esk7_6(X1703,X1704,X1705,X1706,X1707,X1708))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1703),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))),X1704),c_Arrow__Order__Mirabelle_OProf))
| X1707 = X1706
| X1708 = X1705
| X1706 = X1705
| X1708 = X1707 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).
fof(i_0_591,plain,
! [X1696,X1697,X1698,X1699,X1700,X1701] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1701),X1700)),hAPP(X1697,esk6_6(X1696,X1697,X1698,X1699,X1700,X1701))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1699),X1698)),hAPP(X1696,esk6_6(X1696,X1697,X1698,X1699,X1700,X1701))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1701),X1700)),hAPP(v_F,X1697)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1699),X1698)),hAPP(v_F,X1696)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1696),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))),X1697),c_Arrow__Order__Mirabelle_OProf))
| X1700 = X1699
| X1701 = X1698
| X1699 = X1698
| X1701 = X1700 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1701),X1700)),hAPP(X1697,esk6_6(X1696,X1697,X1698,X1699,X1700,X1701))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1699),X1698)),hAPP(X1696,esk6_6(X1696,X1697,X1698,X1699,X1700,X1701))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1701),X1700)),hAPP(v_F,X1697)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1699),X1698)),hAPP(v_F,X1696)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1696),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))),X1697),c_Arrow__Order__Mirabelle_OProf))
| X1700 = X1699
| X1701 = X1698
| X1699 = X1698
| X1701 = X1700 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).
fof(i_0_592,plain,
! [X1683,X1684,X1685,X1686,X1687,X1688] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(v_F,X1684)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),X1685)),hAPP(v_F,X1683)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(X1684,esk4_6(X1683,X1684,X1685,X1686,X1687,X1688))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),X1685)),hAPP(X1683,esk4_6(X1683,X1684,X1685,X1686,X1687,X1688))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1683),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))),X1684),c_Arrow__Order__Mirabelle_OProf))
| X1686 = X1685
| X1688 = X1687 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),X1685)),hAPP(v_F,X1683)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(v_F,X1684)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(X1684,esk4_6(X1683,X1684,X1685,X1686,X1687,X1688))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),X1685)),hAPP(X1683,esk4_6(X1683,X1684,X1685,X1686,X1687,X1688))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1683),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))),X1684),c_Arrow__Order__Mirabelle_OProf))
| X1686 = X1685
| X1688 = X1687 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(v_F,X1684)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),X1685)),hAPP(v_F,X1683)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(X1684,esk4_6(X1683,X1684,X1685,X1686,X1687,X1688))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),X1685)),hAPP(X1683,esk4_6(X1683,X1684,X1685,X1686,X1687,X1688))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1683),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))),X1684),c_Arrow__Order__Mirabelle_OProf))
| X1686 = X1685
| X1688 = X1687 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),X1685)),hAPP(v_F,X1683)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(v_F,X1684)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1688),X1687)),hAPP(X1684,esk4_6(X1683,X1684,X1685,X1686,X1687,X1688))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),X1685)),hAPP(X1683,esk4_6(X1683,X1684,X1685,X1686,X1687,X1688))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1683),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))),X1684),c_Arrow__Order__Mirabelle_OProf))
| X1686 = X1685
| X1688 = X1687 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pairwise__neutrality])])])]) ).
fof(i_0_593,plain,
! [X1619,X1620,X1621,X1622] :
( ( hAPP(hAPP(c_COMBC(X1622,tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_fun(X1621,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1621,tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_fun(X1621,tc_HOL_Obool)),X1622,c_COMBC(X1621,tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1621,tc_prod(X1622,X1621)),tc_fun(X1621,tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),X1622,c_COMBB(tc_prod(X1622,X1621),tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool),X1621,c_member(tc_prod(X1622,X1621)))),c_Product__Type_OPair(X1622,X1621)))),X1620) != hAPP(hAPP(c_COMBC(X1622,tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_fun(X1621,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1621,tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_fun(X1621,tc_HOL_Obool)),X1622,c_COMBC(X1621,tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1621,tc_prod(X1622,X1621)),tc_fun(X1621,tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),X1622,c_COMBB(tc_prod(X1622,X1621),tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool),X1621,c_member(tc_prod(X1622,X1621)))),c_Product__Type_OPair(X1622,X1621)))),X1619)
| X1620 = X1619 )
& ( X1620 != X1619
| hAPP(hAPP(c_COMBC(X1622,tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_fun(X1621,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1621,tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_fun(X1621,tc_HOL_Obool)),X1622,c_COMBC(X1621,tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1621,tc_prod(X1622,X1621)),tc_fun(X1621,tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),X1622,c_COMBB(tc_prod(X1622,X1621),tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool),X1621,c_member(tc_prod(X1622,X1621)))),c_Product__Type_OPair(X1622,X1621)))),X1620) = hAPP(hAPP(c_COMBC(X1622,tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_fun(X1621,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1621,tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_fun(X1621,tc_HOL_Obool)),X1622,c_COMBC(X1621,tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1621,tc_prod(X1622,X1621)),tc_fun(X1621,tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool)),X1622,c_COMBB(tc_prod(X1622,X1621),tc_fun(tc_fun(tc_prod(X1622,X1621),tc_HOL_Obool),tc_HOL_Obool),X1621,c_member(tc_prod(X1622,X1621)))),c_Product__Type_OPair(X1622,X1621)))),X1619) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_594,plain,
! [X2419,X2420,X2421,X2422,X2423] :
( ( hBOOL(hAPP(hAPP(c_member(X2423),esk29_5(X2419,X2420,X2421,X2422,X2423)),X2422))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2423,X2421),tc_HOL_Obool),c_FuncSet_OPi(X2423,X2421,X2422,X2420)),c_FuncSet_OPi(X2423,X2421,X2422,X2419))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2421,tc_HOL_Obool),hAPP(X2420,esk29_5(X2419,X2420,X2421,X2422,X2423))),hAPP(X2419,esk29_5(X2419,X2420,X2421,X2422,X2423))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2423,X2421),tc_HOL_Obool),c_FuncSet_OPi(X2423,X2421,X2422,X2420)),c_FuncSet_OPi(X2423,X2421,X2422,X2419))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_595,plain,
! [X2425,X2426,X2427,X2428,X2429] :
( ( hBOOL(hAPP(hAPP(c_member(X2429),esk30_5(X2425,X2426,X2427,X2428,X2429)),X2428))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2429,X2427)),X2426),c_FuncSet_OPi(X2429,X2427,X2428,X2425))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2427),hAPP(X2426,esk30_5(X2425,X2426,X2427,X2428,X2429))),hAPP(X2425,esk30_5(X2425,X2426,X2427,X2428,X2429))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2429,X2427)),X2426),c_FuncSet_OPi(X2429,X2427,X2428,X2425))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_596,plain,
! [X1722,X1723,X1724,X1725,X1726,X1728,X1733,X1734] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1722,X1723)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1722,X1724)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1723,esk8_5(X1722,X1723,X1724,X1725,X1726))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1724,esk8_5(X1722,X1723,X1724,X1725,X1726))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1724),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))),X1723),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1722) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1722,X1724)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1722,X1723)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1723,esk8_5(X1722,X1723,X1724,X1725,X1726))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1724,esk8_5(X1722,X1723,X1724,X1725,X1726))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1724),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))),X1723),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1722) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1722,X1723)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1722,X1724)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1723,esk8_5(X1722,X1723,X1724,X1725,X1726))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1724,esk8_5(X1722,X1723,X1724,X1725,X1726))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1724),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))),X1723),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1722) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1722,X1724)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1722,X1723)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1723,esk8_5(X1722,X1723,X1724,X1725,X1726))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1725),X1726)),hAPP(X1724,esk8_5(X1722,X1723,X1724,X1725,X1726))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1724),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))),X1723),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1722) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk9_1(X1728)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1728) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk10_1(X1728)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1728) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1728)),esk12_1(X1728))),hAPP(esk9_1(X1728),X1733)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1728)),esk12_1(X1728))),hAPP(esk10_1(X1728),X1733)))
| c_Arrow__Order__Mirabelle_OIIA(X1728) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1728)),esk12_1(X1728))),hAPP(esk10_1(X1728),X1734)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1728)),esk12_1(X1728))),hAPP(esk9_1(X1728),X1734)))
| c_Arrow__Order__Mirabelle_OIIA(X1728) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1728)),esk12_1(X1728))),hAPP(X1728,esk9_1(X1728))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1728)),esk12_1(X1728))),hAPP(X1728,esk10_1(X1728))))
| c_Arrow__Order__Mirabelle_OIIA(X1728) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1728)),esk12_1(X1728))),hAPP(X1728,esk9_1(X1728))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1728)),esk12_1(X1728))),hAPP(X1728,esk10_1(X1728))))
| c_Arrow__Order__Mirabelle_OIIA(X1728) ) ),
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_597,plain,
! [X1690,X1691,X1692,X1693,X1694] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1694),X1693)),hAPP(v_F,X1691)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(v_F,X1690)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1694),X1693)),hAPP(X1691,esk5_5(X1690,X1691,X1692,X1693,X1694))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(X1690,esk5_5(X1690,X1691,X1692,X1693,X1694))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1690),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1691),c_Arrow__Order__Mirabelle_OProf))
| X1694 = X1692
| X1693 = X1692
| X1694 = X1693 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(v_F,X1690)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1694),X1693)),hAPP(v_F,X1691)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1694),X1693)),hAPP(X1691,esk5_5(X1690,X1691,X1692,X1693,X1694))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(X1690,esk5_5(X1690,X1691,X1692,X1693,X1694))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1690),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1691),c_Arrow__Order__Mirabelle_OProf))
| X1694 = X1692
| X1693 = X1692
| X1694 = X1693 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1694),X1693)),hAPP(v_F,X1691)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(v_F,X1690)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1694),X1693)),hAPP(X1691,esk5_5(X1690,X1691,X1692,X1693,X1694))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(X1690,esk5_5(X1690,X1691,X1692,X1693,X1694))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1690),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1691),c_Arrow__Order__Mirabelle_OProf))
| X1694 = X1692
| X1693 = X1692
| X1694 = X1693 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(v_F,X1690)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1694),X1693)),hAPP(v_F,X1691)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1694),X1693)),hAPP(X1691,esk5_5(X1690,X1691,X1692,X1693,X1694))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1693),X1692)),hAPP(X1690,esk5_5(X1690,X1691,X1692,X1693,X1694))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1690),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1691),c_Arrow__Order__Mirabelle_OProf))
| X1694 = X1692
| X1693 = X1692
| X1694 = X1693 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C4_C])])])]) ).
fof(i_0_598,plain,
! [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))),esk18_2(X2233,X2234)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2234,X2233)
| ~ 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))),X2234),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)))) )
& ( esk19_2(X2233,X2234) != esk20_2(X2233,X2234)
| c_Arrow__Order__Mirabelle_Odictator(X2234,X2233)
| ~ 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))),X2234),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),esk19_2(X2233,X2234)),esk20_2(X2233,X2234))),hAPP(esk18_2(X2233,X2234),X2233)))
| c_Arrow__Order__Mirabelle_Odictator(X2234,X2233)
| ~ 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))),X2234),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),esk19_2(X2233,X2234)),esk20_2(X2233,X2234))),hAPP(X2234,esk18_2(X2233,X2234))))
| c_Arrow__Order__Mirabelle_Odictator(X2234,X2233)
| ~ 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))),X2234),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_599,plain,
! [X1711,X1712,X1713,X1714,X1715,X1716,X1717,X1718] :
( ( X1716 = X1714
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1718,X1718)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1718),X1716),X1714)),X1712))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1718,X1717),tc_prod(X1718,X1717))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1718,X1717),tc_prod(X1718,X1717)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1717),X1716),X1715)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1717),X1714),X1713))),c_Wellfounded_Olex__prod(X1718,X1717,X1712,X1711))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1717,X1717)),hAPP(hAPP(c_Product__Type_OPair(X1717,X1717),X1715),X1713)),X1711))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1718,X1718)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1718),X1716),X1714)),X1712))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1718,X1717),tc_prod(X1718,X1717))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1718,X1717),tc_prod(X1718,X1717)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1717),X1716),X1715)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1717),X1714),X1713))),c_Wellfounded_Olex__prod(X1718,X1717,X1712,X1711))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1718,X1718)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1718),X1716),X1714)),X1712))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1718,X1717),tc_prod(X1718,X1717))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1718,X1717),tc_prod(X1718,X1717)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1717),X1716),X1715)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1717),X1714),X1713))),c_Wellfounded_Olex__prod(X1718,X1717,X1712,X1711))) )
& ( X1716 != X1714
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1717,X1717)),hAPP(hAPP(c_Product__Type_OPair(X1717,X1717),X1715),X1713)),X1711))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1718,X1717),tc_prod(X1718,X1717))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1718,X1717),tc_prod(X1718,X1717)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1717),X1716),X1715)),hAPP(hAPP(c_Product__Type_OPair(X1718,X1717),X1714),X1713))),c_Wellfounded_Olex__prod(X1718,X1717,X1712,X1711))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_600,plain,
! [X1678,X1679,X1680,X1681] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1681),X1680)),hAPP(v_F,X1679)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1681)),hAPP(v_F,X1678)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1681),X1680)),hAPP(X1679,esk3_4(X1678,X1679,X1680,X1681))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1681)),hAPP(X1678,esk3_4(X1678,X1679,X1680,X1681))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1678),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1679),c_Arrow__Order__Mirabelle_OProf))
| X1681 = X1680 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1681)),hAPP(v_F,X1678)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1681),X1680)),hAPP(v_F,X1679)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1681),X1680)),hAPP(X1679,esk3_4(X1678,X1679,X1680,X1681))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1681)),hAPP(X1678,esk3_4(X1678,X1679,X1680,X1681))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1678),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1679),c_Arrow__Order__Mirabelle_OProf))
| X1681 = X1680 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1681),X1680)),hAPP(v_F,X1679)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1681)),hAPP(v_F,X1678)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1681),X1680)),hAPP(X1679,esk3_4(X1678,X1679,X1680,X1681))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1681)),hAPP(X1678,esk3_4(X1678,X1679,X1680,X1681))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1678),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1679),c_Arrow__Order__Mirabelle_OProf))
| X1681 = X1680 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1681)),hAPP(v_F,X1678)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1681),X1680)),hAPP(v_F,X1679)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1681),X1680)),hAPP(X1679,esk3_4(X1678,X1679,X1680,X1681))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1680),X1681)),hAPP(X1678,esk3_4(X1678,X1679,X1680,X1681))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1678),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1679),c_Arrow__Order__Mirabelle_OProf))
| X1681 = X1680 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C3_C])])])]) ).
fof(i_0_601,plain,
! [X2868,X2869,X2870,X2871,X2872,X2873,X2874] :
( ~ c_Finite__Set_Ofolding__image__simple(X2874,X2873,X2872,X2871,X2870,X2869)
| ~ c_Finite__Set_Ofinite(X2873,X2868)
| hAPP(X2869,X2868) = c_Finite__Set_Ofold__image(X2874,X2873,X2872,X2870,X2871,X2868) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).
fof(i_0_602,plain,
! [X3018,X3019,X3020,X3021,X3022,X3024,X3025,X3026,X3027,X3028,X3029] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3020,tc_HOL_Obool),esk39_5(X3018,X3019,X3020,X3021,X3022)),X3018))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3022,tc_HOL_Obool),X3021),c_Set_Oimage(X3020,X3022,X3019,X3018))) )
& ( X3021 = c_Set_Oimage(X3020,X3022,X3019,esk39_5(X3018,X3019,X3020,X3021,X3022))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3022,tc_HOL_Obool),X3021),c_Set_Oimage(X3020,X3022,X3019,X3018))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3026,tc_HOL_Obool),X3029),X3024))
| X3027 != c_Set_Oimage(X3026,X3028,X3025,X3029)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3028,tc_HOL_Obool),X3027),c_Set_Oimage(X3026,X3028,X3025,X3024))) ) ),
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_603,plain,
! [X1629,X1630,X1631,X1632,X1633,X1634,X1635] :
( ~ hBOOL(hAPP(X1635,X1634))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1633,X1633)),hAPP(hAPP(c_Product__Type_OPair(X1633,X1633),X1632),X1631)),hAPP(X1630,X1634)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1629,X1633),tc_prod(X1629,X1633))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1629,X1633),tc_prod(X1629,X1633)),hAPP(hAPP(c_Product__Type_OPair(X1629,X1633),X1634),X1632)),hAPP(hAPP(c_Product__Type_OPair(X1629,X1633),X1634),X1631))),c_Recdef_Osame__fst(X1629,X1633,X1635,X1630))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_604,plain,
! [X1798,X1799,X1800,X1801,X1802] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1800,X1801),X1799),X1798))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1801,hAPP(X1799,X1802)),hAPP(X1798,X1802)))
| ~ class_Orderings_Oord(X1801) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1801,hAPP(X1799,esk13_4(X1798,X1799,X1800,X1801))),hAPP(X1798,esk13_4(X1798,X1799,X1800,X1801))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1800,X1801),X1799),X1798))
| ~ class_Orderings_Oord(X1801) ) ),
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_605,plain,
! [X2479,X2480,X2481,X2482,X2483,X2484,X2485,X2486] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2486,X2485,X2484,X2483,X2482,X2481)
| ~ c_Finite__Set_Ofinite(X2485,X2480)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2485,tc_HOL_Obool),X2479),X2480))
| hAPP(hAPP(X2484,hAPP(X2481,X2479)),hAPP(X2481,X2480)) = hAPP(X2481,X2480) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_606,plain,
! [X2597,X2598,X2599,X2600,X2601,X2602,X2603,X2604] :
( ~ c_Finite__Set_Ofolding__image__simple(X2604,X2603,X2602,X2601,X2600,X2599)
| ~ c_Finite__Set_Ofinite(X2603,X2598)
| hBOOL(hAPP(hAPP(c_member(X2603),X2597),X2598))
| hAPP(X2599,c_Set_Oinsert(X2603,X2597,X2598)) = hAPP(hAPP(X2602,hAPP(X2600,X2597)),hAPP(X2599,X2598)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_521])]) ).
fof(i_0_607,plain,
! [X2583,X2584,X2585,X2586,X2587,X2588,X2589,X2590] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2590,X2589,X2588,X2587,X2586,X2585)
| ~ c_Finite__Set_Ofinite(X2589,X2584)
| ~ hBOOL(hAPP(hAPP(c_member(X2589),X2583),X2584))
| hAPP(hAPP(X2588,hAPP(X2586,X2583)),hAPP(X2585,X2584)) = hAPP(X2585,X2584) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_608,plain,
! [X2498,X2499,X2500,X2501,X2502,X2503,X2504,X2505] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2505,X2504,X2503,X2502,X2501,X2500)
| ~ c_Finite__Set_Ofinite(X2504,X2499)
| hAPP(X2500,c_Set_Oinsert(X2504,X2498,X2499)) = hAPP(hAPP(X2503,hAPP(X2501,X2498)),hAPP(X2500,X2499)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).
fof(i_0_609,plain,
! [X2509,X2510,X2511,X2512,X2513,X2514,X2515] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2515,X2514,X2513,X2512,X2511,X2510)
| hAPP(hAPP(X2513,X2509),X2509) = X2509 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).
fof(i_0_610,plain,
! [X3105,X3106,X3107,X3108,X3109,X3110] :
( ~ c_Fun_Oinj__on(X3110,X3109,X3108,X3107)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3109,tc_HOL_Obool),c_Set_Oimage(X3110,X3109,X3108,X3107)),X3106))
| ~ c_Fun_Oinj__on(X3109,X3110,X3105,X3106)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3110,tc_HOL_Obool),c_Set_Oimage(X3109,X3110,X3105,X3106)),X3107))
| ~ c_Finite__Set_Ofinite(X3110,X3107)
| ~ c_Finite__Set_Ofinite(X3109,X3106)
| c_Finite__Set_Ocard(X3110,X3107) = c_Finite__Set_Ocard(X3109,X3106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).
fof(i_0_611,plain,
! [X2402,X2403,X2404,X2405,X2407,X2411] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2402)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2403),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),X2404),X2405)),hAPP(X2403,esk25_4(X2402,X2403,X2404,X2405))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2404),X2405)),hAPP(X2402,X2403))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk26_1(X2407)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X2407) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk27_1(X2407)),esk28_1(X2407))),hAPP(esk26_1(X2407),X2411)))
| c_Arrow__Order__Mirabelle_Ounanimity(X2407) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk27_1(X2407)),esk28_1(X2407))),hAPP(X2407,esk26_1(X2407))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2407) ) ),
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_612,plain,
! [X1710] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| hAPP(v_h____,X1710) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| hAPP(v_h____,X1710) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_e____)))
| hAPP(v_h____,X1710) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_e____)))
| hAPP(v_h____,X1710) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| hAPP(v_h____,X1710) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| hAPP(v_h____,X1710) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_e____)))
| hAPP(v_h____,X1710) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_e____)))
| hAPP(v_h____,X1710) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),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____,X1710)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),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____,X1710)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),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____,X1710)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),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____,X1710)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( hAPP(v_h____,X1710) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( hAPP(v_h____,X1710) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),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____,X1710)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1710)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( hAPP(v_h____,X1710) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1710)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( hAPP(v_h____,X1710) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1710)),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____,X1710)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),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____,X1710)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1710) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1710) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1710)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1710)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_522])])]) ).
fof(i_0_613,plain,
! [X2431,X2432,X2433,X2434,X2435,X2436] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2436,X2435)),X2434),c_FuncSet_OPi(X2436,X2435,X2433,hAPP(c_COMBK(tc_fun(X2435,tc_HOL_Obool),X2436),X2432))))
| ~ c_Fun_Oinj__on(X2436,X2435,X2434,X2433)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2435,X2436)),X2431),c_FuncSet_OPi(X2435,X2436,X2432,hAPP(c_COMBK(tc_fun(X2436,tc_HOL_Obool),X2435),X2433))))
| ~ c_Fun_Oinj__on(X2435,X2436,X2431,X2432)
| ~ c_Finite__Set_Ofinite(X2436,X2433)
| ~ c_Finite__Set_Ofinite(X2435,X2432)
| c_Finite__Set_Ocard(X2436,X2433) = c_Finite__Set_Ocard(X2435,X2432) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij])]) ).
fof(i_0_614,plain,
! [X2034,X2035,X2036] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2036,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2036,tc_fun(X2036,tc_HOL_Obool),tc_HOL_Obool),c_member(X2036)),X2035)),hAPP(hAPP(c_COMBC(X2036,tc_fun(X2036,tc_HOL_Obool),tc_HOL_Obool),c_member(X2036)),X2034)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2036,tc_HOL_Obool),X2035),X2034)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2036,tc_HOL_Obool),X2035),X2034))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2036,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2036,tc_fun(X2036,tc_HOL_Obool),tc_HOL_Obool),c_member(X2036)),X2035)),hAPP(hAPP(c_COMBC(X2036,tc_fun(X2036,tc_HOL_Obool),tc_HOL_Obool),c_member(X2036)),X2034))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_615,plain,
! [X1606] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( hAPP(v_h____,X1606) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( hAPP(v_h____,X1606) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( hAPP(v_h____,X1606) != v_n____
| hAPP(v_h____,X1606) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| hAPP(v_h____,X1606) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( hAPP(v_h____,X1606) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1606)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( hAPP(v_h____,X1606) != v_n____
| hAPP(v_h____,X1606) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| hAPP(v_h____,X1606) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( hAPP(v_h____,X1606) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),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____,X1606)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606)),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____,X1606)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1606))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])])]) ).
fof(i_0_616,plain,
! [X2887,X2888,X2889,X2890] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2890,c_Set_Oimage(X2889,X2890,X2888,X2887))),c_Finite__Set_Ocard(X2889,X2887)))
| ~ c_Fun_Oinj__on(X2889,X2890,X2888,X2887) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])]) ).
fof(i_0_617,plain,
! [X3117,X3118,X3119,X3120,X3121] :
( ( ~ c_Fun_Oinj__on(X3120,X3118,X3121,X3119)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3118,tc_HOL_Obool),c_Set_Oimage(X3120,X3118,X3121,X3119)),X3117))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3120,X3119)),c_Finite__Set_Ocard(X3118,X3117)))
| ~ c_Finite__Set_Ofinite(X3118,X3117)
| ~ c_Finite__Set_Ofinite(X3120,X3119) )
& ( c_Fun_Oinj__on(X3120,X3118,esk41_4(X3117,X3118,X3119,X3120),X3119)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3120,X3119)),c_Finite__Set_Ocard(X3118,X3117)))
| ~ c_Finite__Set_Ofinite(X3118,X3117)
| ~ c_Finite__Set_Ofinite(X3120,X3119) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3118,tc_HOL_Obool),c_Set_Oimage(X3120,X3118,esk41_4(X3117,X3118,X3119,X3120),X3119)),X3117))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3120,X3119)),c_Finite__Set_Ocard(X3118,X3117)))
| ~ c_Finite__Set_Ofinite(X3118,X3117)
| ~ c_Finite__Set_Ofinite(X3120,X3119) ) ),
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_618,plain,
! [X1968,X1969,X1970,X1971,X1972] :
( ( X1969 != X1968
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1969 != X1971
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1972),X1968)),X1970))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1968 != X1971
| X1969 = X1972
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1972)),X1970))
| X1969 = X1971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1968 = X1971
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),X1970))
| X1969 = X1971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1969 != X1971
| X1969 = X1971
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1968 != X1971
| X1968 = X1971
| X1969 = X1971
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),X1970))
| X1968 = X1971
| X1969 = X1971
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1968 != X1971
| X1969 != X1972
| X1969 = X1971
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),X1970))
| X1969 != X1972
| X1969 = X1971
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1968 != X1971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1972)),X1970))
| X1969 = X1971
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),X1970))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1972)),X1970))
| X1969 = X1971
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1969 != X1971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1972),X1968)),X1970))
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1968 != X1971
| X1968 = X1971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1972),X1968)),X1970))
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),X1970))
| X1968 = X1971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1972),X1968)),X1970))
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1968 != X1971
| X1969 != X1972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1972),X1968)),X1970))
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),X1970))
| X1969 != X1972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1972),X1968)),X1970))
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( X1968 != X1971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1972)),X1970))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1972),X1968)),X1970))
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),X1970))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1972)),X1970))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1972),X1968)),X1970))
| X1969 = X1968
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1969),X1968)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1970),X1972),X1971)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1970),c_Arrow__Order__Mirabelle_OLin))
| X1972 = X1971 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_619,plain,
! [X1979,X1980,X1981,X1982,X1983] :
( ( X1980 != X1979
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1979 != X1983
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1982)),X1981))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1980 != X1983
| X1979 = X1982
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1982),X1979)),X1981))
| X1979 = X1983
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1980 = X1983
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1981))
| X1979 = X1983
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1979 != X1983
| X1979 = X1983
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1980 != X1983
| X1980 = X1983
| X1979 = X1983
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1981))
| X1980 = X1983
| X1979 = X1983
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1980 != X1983
| X1979 != X1982
| X1979 = X1983
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1981))
| X1979 != X1982
| X1979 = X1983
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1980 != X1983
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1982),X1979)),X1981))
| X1979 = X1983
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1981))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1982),X1979)),X1981))
| X1979 = X1983
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1979 != X1983
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1982)),X1981))
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1980 != X1983
| X1980 = X1983
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1982)),X1981))
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1981))
| X1980 = X1983
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1982)),X1981))
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1980 != X1983
| X1979 != X1982
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1982)),X1981))
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1981))
| X1979 != X1982
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1982)),X1981))
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( X1980 != X1983
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1982),X1979)),X1981))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1982)),X1981))
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1981))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1982),X1979)),X1981))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1982)),X1981))
| X1980 = X1979
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Obelow(X1981,X1983,X1982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1981),c_Arrow__Order__Mirabelle_OLin))
| X1983 = X1982 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_620,plain,
! [X2866,X2867] :
( ( ~ c_Finite__Set_Ofinite(X2867,X2866)
| c_Finite__Set_Ocard(X2867,X2866) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2867,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2867),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2866) )
& ( c_Finite__Set_Ofinite(X2867,X2866)
| c_Finite__Set_Ocard(X2867,X2866) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])]) ).
fof(i_0_621,plain,
! [X2864,X2865] :
( ~ c_Finite__Set_Ofinite(X2865,X2864)
| c_Finite__Set_Ocard(X2865,X2864) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2865,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2865),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2864) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).
fof(i_0_622,plain,
! [X2942,X2943,X2944,X2945,X2946] :
( ~ hBOOL(hAPP(hAPP(c_member(X2946),X2945),c_Set_Oimage(X2944,X2946,X2943,X2942)))
| hBOOL(hAPP(hAPP(c_member(X2944),hAPP(c_Hilbert__Choice_Oinv__into(X2944,X2946,X2942,X2943),X2945)),X2942)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).
fof(i_0_623,plain,
! [X3061,X3062,X3063,X3064,X3065] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),c_Set_Oimage(X3065,X3064,X3063,X3062)),c_Set_Oimage(X3065,X3064,X3063,X3061)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3065,tc_HOL_Obool),X3062),X3061))
| ~ c_Fun_Oinj__on(X3065,X3064,X3063,c_Orderings_Otop__class_Otop(tc_fun(X3065,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3065,tc_HOL_Obool),X3062),X3061))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),c_Set_Oimage(X3065,X3064,X3063,X3062)),c_Set_Oimage(X3065,X3064,X3063,X3061)))
| ~ c_Fun_Oinj__on(X3065,X3064,X3063,c_Orderings_Otop__class_Otop(tc_fun(X3065,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_624,plain,
! [X2469,X2470,X2471] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2471,tc_HOL_Obool)),X2470),X2469))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2471,tc_HOL_Obool),tc_fun(X2471,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2471,tc_HOL_Obool),tc_fun(X2471,tc_HOL_Obool)),X2470),X2469)),c_Wellfounded_Ofinite__psubset(X2471))) )
& ( c_Finite__Set_Ofinite(X2471,X2469)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2471,tc_HOL_Obool),tc_fun(X2471,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2471,tc_HOL_Obool),tc_fun(X2471,tc_HOL_Obool)),X2470),X2469)),c_Wellfounded_Ofinite__psubset(X2471))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2471,tc_HOL_Obool)),X2470),X2469))
| ~ c_Finite__Set_Ofinite(X2471,X2469)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2471,tc_HOL_Obool),tc_fun(X2471,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2471,tc_HOL_Obool),tc_fun(X2471,tc_HOL_Obool)),X2470),X2469)),c_Wellfounded_Ofinite__psubset(X2471))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).
cnf(i_0_625,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_626,plain,
! [X3100,X3101,X3102,X3103,X3104] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3104,X3103)),X3102),c_FuncSet_OPi(X3104,X3103,X3101,hAPP(c_COMBK(tc_fun(X3103,tc_HOL_Obool),X3104),X3100))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3103,tc_HOL_Obool),c_Set_Oimage(X3104,X3103,X3102,X3101)),X3100)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_627,plain,
! [X2936,X2937,X2938,X2939,X2940,X2941] :
( hAPP(c_Hilbert__Choice_Oinv__into(X2941,X2940,X2939,X2938),X2937) != hAPP(c_Hilbert__Choice_Oinv__into(X2941,X2940,X2939,X2938),X2936)
| ~ hBOOL(hAPP(hAPP(c_member(X2940),X2937),c_Set_Oimage(X2941,X2940,X2938,X2939)))
| ~ hBOOL(hAPP(hAPP(c_member(X2940),X2936),c_Set_Oimage(X2941,X2940,X2938,X2939)))
| X2937 = X2936 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).
fof(i_0_628,plain,
! [X2849,X2850] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2850),c_Groups_Oone__class_Oone(X2850)),X2849)),X2849)),c_Groups_Ozero__class_Ozero(X2850)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2850),X2849),c_Groups_Ozero__class_Ozero(X2850)))
| ~ hBOOL(hAPP(hAPP(c_member(X2850),X2849),c_Int_Oring__1__class_OInts(X2850)))
| ~ class_Rings_Olinordered__idom(X2850) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2850),X2849),c_Groups_Ozero__class_Ozero(X2850)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2850),c_Groups_Oone__class_Oone(X2850)),X2849)),X2849)),c_Groups_Ozero__class_Ozero(X2850)))
| ~ hBOOL(hAPP(hAPP(c_member(X2850),X2849),c_Int_Oring__1__class_OInts(X2850)))
| ~ class_Rings_Olinordered__idom(X2850) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).
fof(i_0_629,plain,
! [X2896,X2897,X2898,X2899,X2901,X2902] :
( ( X2896 = hAPP(X2897,esk35_4(X2896,X2897,X2898,X2899))
| ~ hBOOL(hAPP(hAPP(c_member(X2898),X2896),c_Set_Oimage(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,tc_HOL_Obool))) )
& ( X2896 != hAPP(X2897,X2901)
| X2901 = esk35_4(X2896,X2897,X2898,X2899)
| ~ hBOOL(hAPP(hAPP(c_member(X2898),X2896),c_Set_Oimage(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,tc_HOL_Obool))) )
& ( X2896 = hAPP(X2897,esk36_5(X2896,X2897,X2898,X2899,X2902))
| X2896 != hAPP(X2897,X2902)
| hBOOL(hAPP(hAPP(c_member(X2898),X2896),c_Set_Oimage(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,tc_HOL_Obool))) )
& ( esk36_5(X2896,X2897,X2898,X2899,X2902) != X2902
| X2896 != hAPP(X2897,X2902)
| hBOOL(hAPP(hAPP(c_member(X2898),X2896),c_Set_Oimage(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,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_630,plain,
! [X3057,X3058,X3059,X3060] :
( ~ c_Finite__Set_Ofinite(X3060,X3059)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3058,c_Set_Oimage(X3060,X3058,X3057,X3059))),c_Finite__Set_Ocard(X3060,X3059))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_631,plain,
! [X2974,X2975,X2976,X2977,X2978] :
( ~ c_Fun_Oinj__on(X2978,X2977,X2976,X2975)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2978,tc_HOL_Obool)),X2974),X2975))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2977,tc_HOL_Obool)),c_Set_Oimage(X2978,X2977,X2976,X2974)),c_Set_Oimage(X2978,X2977,X2976,X2975))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_632,plain,
! [X3070,X3071,X3072] :
( ~ c_Finite__Set_Ofinite(X3072,X3071)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3072,tc_HOL_Obool),c_Set_Oimage(X3072,X3072,X3070,X3071)),X3071))
| ~ c_Fun_Oinj__on(X3072,X3072,X3070,X3071)
| c_Set_Oimage(X3072,X3072,X3070,X3071) = X3071 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_633,plain,
! [X3111,X3112,X3113,X3114,X3115] :
( ~ c_Fun_Oinj__on(X3115,X3114,X3113,X3112)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3114,tc_HOL_Obool),c_Set_Oimage(X3115,X3114,X3113,X3112)),X3111))
| ~ c_Finite__Set_Ofinite(X3114,X3111)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3115,X3112)),c_Finite__Set_Ocard(X3114,X3111))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).
fof(i_0_634,plain,
! [X2990,X2991,X2992,X2993,X2994,X2996,X2997,X2998,X2999,X3000,X3001] :
( ( hBOOL(hAPP(hAPP(c_member(X2992),esk38_4(X2990,X2991,X2992,X2993)),X2990))
| ~ hBOOL(hAPP(hAPP(c_member(X2994),X2993),c_Set_Oimage(X2992,X2994,X2991,X2990))) )
& ( X2993 = hAPP(X2991,esk38_4(X2990,X2991,X2992,X2993))
| ~ hBOOL(hAPP(hAPP(c_member(X2994),X2993),c_Set_Oimage(X2992,X2994,X2991,X2990))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2998),X3000),X2996))
| X2999 != hAPP(X2997,X3000)
| hBOOL(hAPP(hAPP(c_member(X3001),X2999),c_Set_Oimage(X2998,X3001,X2997,X2996))) ) ),
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_635,plain,
! [X1888,X1889,X1890] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1889),X1888)),X1890))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1889)),X1890))
| X1889 = X1888
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1890),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),X1888),X1889)),X1890))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1889),X1888)),X1890))
| X1889 = X1888
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1890),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])])]) ).
fof(i_0_636,plain,
! [X1891,X1892,X1893] :
( ~ 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_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1892),X1891)),X1893))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1891),X1892)),X1893)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])]) ).
fof(i_0_637,plain,
! [X2414,X2415,X2416,X2417,X2418] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2418,X2417)),X2416),c_FuncSet_OPi(X2418,X2417,X2415,hAPP(c_COMBK(tc_fun(X2417,tc_HOL_Obool),X2418),X2414))))
| ~ c_Fun_Oinj__on(X2418,X2417,X2416,X2415)
| ~ c_Finite__Set_Ofinite(X2417,X2414)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2418,X2415)),c_Finite__Set_Ocard(X2417,X2414))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj])]) ).
fof(i_0_638,plain,
! [X2161,X2162,X2163,X2164,X2165] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2165,tc_HOL_Obool),X2164),X2163))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2165,X2162),tc_HOL_Obool),c_FuncSet_OPi(X2165,X2162,X2163,X2161)),c_FuncSet_OPi(X2165,X2162,X2164,X2161))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_639,plain,
! [X3044,X3045,X3046,X3047,X3048] :
( ~ c_Finite__Set_Ofinite(X3048,c_Set_Oimage(X3047,X3048,X3046,c_Orderings_Otop__class_Otop(tc_fun(X3047,tc_HOL_Obool))))
| c_Finite__Set_Ofinite(X3045,c_Set_Oimage(X3047,X3045,hAPP(c_COMBB(X3048,X3045,X3047,X3044),X3046),c_Orderings_Otop__class_Otop(tc_fun(X3047,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).
fof(i_0_640,plain,
! [X1967] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1967),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),X1967)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_641,plain,
! [X2046,X2047,X2048,X2049,X2050,X2051] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2051,X2050)),X2049),c_FuncSet_OPi(X2051,X2050,X2048,hAPP(c_COMBK(tc_fun(X2050,tc_HOL_Obool),X2051),X2047))))
| ~ hBOOL(hAPP(hAPP(c_member(X2051),X2046),X2048))
| hBOOL(hAPP(hAPP(c_member(X2050),hAPP(X2049,X2046)),X2047)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
cnf(i_0_642,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hAPP(v_h____,X1) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_643,plain,
! [X3030,X3031,X3032,X3033,X3034] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3034,tc_HOL_Obool),X3033),X3032))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3031,tc_HOL_Obool),c_Set_Oimage(X3034,X3031,X3030,X3033)),c_Set_Oimage(X3034,X3031,X3030,X3032))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_644,plain,
! [X1962,X1963,X1964,X1965,X1966] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1966,X1965)),hAPP(X1966,X1964)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1963,X1963)),hAPP(hAPP(c_Product__Type_OPair(X1963,X1963),X1965),X1964)),X1962))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1963,X1963)),hAPP(hAPP(c_Product__Type_OPair(X1963,X1963),X1965),X1964)),c_Wellfounded_Omlex__prod(X1963,X1966,X1962))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
cnf(i_0_645,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hAPP(v_h____,X1) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
cnf(i_0_646,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_647,plain,
! [X1624,X1625,X1626,X1627,X1628] :
( ( ~ c_FunDef_Oin__rel(X1628,X1627,X1626,X1625,X1624)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1628,X1627)),hAPP(hAPP(c_Product__Type_OPair(X1628,X1627),X1625),X1624)),X1626)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1628,X1627)),hAPP(hAPP(c_Product__Type_OPair(X1628,X1627),X1625),X1624)),X1626))
| c_FunDef_Oin__rel(X1628,X1627,X1626,X1625,X1624) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
cnf(i_0_648,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,X1) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
cnf(i_0_649,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_650,plain,
! [X2947,X2948,X2949,X2950,X2951] :
( ~ hBOOL(hAPP(hAPP(c_member(X2951),X2950),c_Set_Oimage(X2949,X2951,X2948,X2947)))
| hAPP(X2948,hAPP(c_Hilbert__Choice_Oinv__into(X2949,X2951,X2947,X2948),X2950)) = X2950 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).
cnf(i_0_651,plain,
( hAPP(v_h____,X1) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_652,plain,
! [X2966,X2967,X2968,X2969,X2970,X2971,X2972] :
( ( c_Set_Oimage(X2968,X2967,X2966,c_Orderings_Otop__class_Otop(tc_fun(X2968,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2967,tc_HOL_Obool))
| hAPP(X2966,hAPP(c_Hilbert__Choice_Oinv__into(X2968,X2967,c_Orderings_Otop__class_Otop(tc_fun(X2968,tc_HOL_Obool)),X2966),X2969)) = X2969 )
& ( hAPP(X2970,hAPP(c_Hilbert__Choice_Oinv__into(X2972,X2971,c_Orderings_Otop__class_Otop(tc_fun(X2972,tc_HOL_Obool)),X2970),esk37_3(X2970,X2971,X2972))) != esk37_3(X2970,X2971,X2972)
| c_Set_Oimage(X2972,X2971,X2970,c_Orderings_Otop__class_Otop(tc_fun(X2972,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2971,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_653,plain,
! [X1643,X1644,X1645,X1646,X1647] :
( ( ~ c_Nitpick_Orefl_H(X1644,X1643)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1644,X1644)),hAPP(hAPP(c_Product__Type_OPair(X1644,X1644),X1645),X1645)),X1643)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1647,X1647)),hAPP(hAPP(c_Product__Type_OPair(X1647,X1647),esk2_2(X1646,X1647)),esk2_2(X1646,X1647))),X1646))
| c_Nitpick_Orefl_H(X1647,X1646) ) ),
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_Nitpick_Orefl_H__def])])])])]) ).
fof(i_0_654,plain,
! [X3076,X3077,X3078,X3079,X3080] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3080,tc_HOL_Obool),X3079),c_Set_Oimage(X3078,X3080,X3077,X3076)))
| c_Fun_Oinj__on(X3080,X3078,c_Hilbert__Choice_Oinv__into(X3078,X3080,X3076,X3077),X3079) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).
fof(i_0_655,plain,
! [X1607,X1608,X1609,X1610] :
( ( X1609 != X1607
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1608),X1607))) )
& ( X1610 != X1607
| X1610 != X1609
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1608),X1607))) )
& ( X1610 = X1607
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),X1608))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1608),X1607))) )
& ( X1610 != X1607
| X1610 = X1607
| X1609 = X1607
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1608),X1607))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),X1608))
| X1610 = X1607
| X1609 = X1607
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1608),X1607))) )
& ( X1610 != X1607
| X1610 = X1609
| X1609 = X1607
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1608),X1607))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),X1608))
| X1610 = X1609
| X1609 = X1607
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1610),X1609)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1608),X1607))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_656,plain,
! [X1611,X1612,X1613,X1614] :
( ( X1614 != X1611
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1612),X1611))) )
& ( X1613 != X1611
| X1614 != X1613
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1612),X1611))) )
& ( X1613 = X1611
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),X1612))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1612),X1611))) )
& ( X1613 != X1611
| X1613 = X1611
| X1614 = X1611
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1612),X1611))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),X1612))
| X1613 = X1611
| X1614 = X1611
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1612),X1611))) )
& ( X1613 != X1611
| X1614 = X1613
| X1614 = X1611
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1612),X1611))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),X1612))
| X1614 = X1613
| X1614 = X1611
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1614),X1613)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1612),X1611))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_657,plain,
! [X3175,X3176,X3177,X3178,X3179,X3180] : hAPP(c_COMBS(X3180,X3179,X3178,X3177,X3176),X3175) = hAPP(hAPP(X3177,X3175),hAPP(X3176,X3175)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_658,plain,
! [X2052,X2053,X2054,X2055,X2056,X2057] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2057,X2056)),X2055),c_FuncSet_OPi(X2057,X2056,X2054,X2053)))
| ~ hBOOL(hAPP(hAPP(c_member(X2057),X2052),X2054))
| hBOOL(hAPP(hAPP(c_member(X2056),hAPP(X2055,X2052)),hAPP(X2053,X2052))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_659,plain,
! [X2040,X2041,X2042,X2043,X2044,X2045] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2045,X2044)),X2043),c_FuncSet_OPi(X2045,X2044,X2042,X2041)))
| hBOOL(hAPP(hAPP(c_member(X2044),hAPP(X2043,X2040)),hAPP(X2041,X2040)))
| ~ hBOOL(hAPP(hAPP(c_member(X2045),X2040),X2042)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])]) ).
fof(i_0_660,plain,
! [X2891,X2892,X2893,X2894,X2895] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2894),hAPP(X2893,X2892)),c_Set_Oimage(X2895,X2894,X2893,X2891)))
| hBOOL(hAPP(hAPP(c_member(X2895),X2892),X2891))
| ~ c_Fun_Oinj__on(X2895,X2894,X2893,c_Orderings_Otop__class_Otop(tc_fun(X2895,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2895),X2892),X2891))
| hBOOL(hAPP(hAPP(c_member(X2894),hAPP(X2893,X2892)),c_Set_Oimage(X2895,X2894,X2893,X2891)))
| ~ c_Fun_Oinj__on(X2895,X2894,X2893,c_Orderings_Otop__class_Otop(tc_fun(X2895,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_661,plain,
! [X2958,X2959,X2960,X2961] :
( c_Set_Oimage(X2961,X2960,X2959,c_Orderings_Otop__class_Otop(tc_fun(X2961,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2960,tc_HOL_Obool))
| c_Set_Oimage(X2961,X2960,X2959,c_Set_Oimage(X2960,X2961,c_Hilbert__Choice_Oinv__into(X2961,X2960,c_Orderings_Otop__class_Otop(tc_fun(X2961,tc_HOL_Obool)),X2959),X2958)) = X2958 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).
fof(i_0_662,plain,
! [X2952,X2953,X2954,X2955,X2956,X2957] :
( c_Set_Oimage(X2957,X2956,X2955,X2954) != X2953
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2956,tc_HOL_Obool),X2952),X2953))
| c_Set_Oimage(X2957,X2956,X2955,c_Set_Oimage(X2956,X2957,c_Hilbert__Choice_Oinv__into(X2957,X2956,X2954,X2955),X2952)) = X2952 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).
fof(i_0_663,plain,
! [X2293,X2294,X2295,X2296,X2297,X2298,X2299,X2300,X2301,X2302] :
( ( ~ c_Fun_Oinj__on(X2296,X2295,X2294,X2293)
| ~ hBOOL(hAPP(hAPP(c_member(X2296),X2297),X2293))
| ~ hBOOL(hAPP(hAPP(c_member(X2296),X2298),X2293))
| hAPP(X2294,X2297) != hAPP(X2294,X2298)
| X2297 = X2298 )
& ( hBOOL(hAPP(hAPP(c_member(X2302),esk21_4(X2299,X2300,X2301,X2302)),X2299))
| c_Fun_Oinj__on(X2302,X2301,X2300,X2299) )
& ( hBOOL(hAPP(hAPP(c_member(X2302),esk22_4(X2299,X2300,X2301,X2302)),X2299))
| c_Fun_Oinj__on(X2302,X2301,X2300,X2299) )
& ( hAPP(X2300,esk21_4(X2299,X2300,X2301,X2302)) = hAPP(X2300,esk22_4(X2299,X2300,X2301,X2302))
| c_Fun_Oinj__on(X2302,X2301,X2300,X2299) )
& ( esk21_4(X2299,X2300,X2301,X2302) != esk22_4(X2299,X2300,X2301,X2302)
| c_Fun_Oinj__on(X2302,X2301,X2300,X2299) ) ),
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_664,plain,
! [X1881,X1882,X1883] :
( X1883 = X1882
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1881),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,X1881),X1883),X1882)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_665,plain,
! [X3007,X3008,X3009,X3010,X3011] : c_Set_Oimage(X3011,X3010,hAPP(c_COMBB(X3009,X3010,X3011,X3008),X3007),c_Orderings_Otop__class_Otop(tc_fun(X3011,tc_HOL_Obool))) = c_Set_Oimage(X3009,X3010,X3008,c_Set_Oimage(X3011,X3009,X3007,c_Orderings_Otop__class_Otop(tc_fun(X3011,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_range__composition]) ).
fof(i_0_666,plain,
! [X3073,X3074,X3075] :
( ~ c_Finite__Set_Ofinite(X3075,X3074)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3075,tc_HOL_Obool),X3074),c_Set_Oimage(X3075,X3075,X3073,X3074)))
| c_Fun_Oinj__on(X3075,X3075,X3073,X3074) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_667,plain,
! [X2309,X2310,X2311,X2312,X2313] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2310,X2309)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2311),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2310,X2311) = hAPP(X2311,X2309) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk23_2(X2312,X2313)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2313,X2312) )
& ( hAPP(X2313,esk23_2(X2312,X2313)) != hAPP(esk23_2(X2312,X2313),X2312)
| c_Arrow__Order__Mirabelle_Odictator(X2313,X2312) ) ),
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_668,plain,
! [X2229,X2230,X2231,X2232] :
( ~ c_Fun_Oinj__on(X2232,X2231,X2230,c_Orderings_Otop__class_Otop(tc_fun(X2232,tc_HOL_Obool)))
| c_Fun_Oinj__on(X2232,tc_fun(X2229,X2231),hAPP(c_COMBB(X2231,tc_fun(X2229,X2231),X2232,c_COMBK(X2231,X2229)),X2230),c_Orderings_Otop__class_Otop(tc_fun(X2232,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).
fof(i_0_669,plain,
! [X2224,X2225] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2225,X2225)),c_COMBI(X2225)),c_FuncSet_OPi(X2225,X2225,X2224,hAPP(c_COMBK(tc_fun(X2225,tc_HOL_Obool),X2225),X2224)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_670,plain,
! [X3012,X3013,X3014,X3015,X3016,X3017] : c_Set_Oimage(X3017,X3016,X3015,c_Set_Oimage(X3014,X3017,X3013,X3012)) = c_Set_Oimage(X3014,X3016,hAPP(c_COMBB(X3017,X3016,X3014,X3015),X3013),X3012),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_671,plain,
! [X2037,X2038,X2039] :
( X2039 = X2038
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2037),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(X2037,X2039,X2038)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_672,plain,
! [X1639,X1640,X1641,X1642] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1642,X1642)),hAPP(hAPP(c_Product__Type_OPair(X1642,X1642),X1641),X1640)),c_Wellfounded_Omeasure(X1642,X1639)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1639,X1641)),hAPP(X1639,X1640))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1639,X1641)),hAPP(X1639,X1640)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1642,X1642)),hAPP(hAPP(c_Product__Type_OPair(X1642,X1642),X1641),X1640)),c_Wellfounded_Omeasure(X1642,X1639))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_673,plain,
! [X3081,X3082,X3083,X3084,X3085] :
( ~ c_Fun_Oinj__on(X3085,X3084,X3083,X3082)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3085,tc_HOL_Obool),X3081),X3082))
| c_Set_Oimage(X3084,X3085,c_Hilbert__Choice_Oinv__into(X3085,X3084,X3082,X3083),c_Set_Oimage(X3085,X3084,X3083,X3081)) = X3081 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).
fof(i_0_674,plain,
! [X2918,X2919,X2920,X2921,X2922] :
( ~ c_Finite__Set_Ofinite(X2922,X2921)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2920,tc_HOL_Obool),X2919),c_Set_Oimage(X2922,X2920,X2918,X2921)))
| c_Finite__Set_Ofinite(X2920,X2919) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
fof(i_0_675,plain,
! [X1884,X1885] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1885),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,X1885),X1884)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_676,plain,
! [X1886,X1887] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1887),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,X1887),X1886)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_677,plain,
! [X3093,X3094,X3095,X3096] :
( ~ c_Fun_Oinj__on(X3096,X3095,X3094,c_Orderings_Otop__class_Otop(tc_fun(X3096,tc_HOL_Obool)))
| c_Set_Oimage(X3095,X3096,c_Hilbert__Choice_Oinv__into(X3096,X3095,c_Orderings_Otop__class_Otop(tc_fun(X3096,tc_HOL_Obool)),X3094),c_Set_Oimage(X3096,X3095,X3094,X3093)) = X3093 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).
fof(i_0_678,plain,
! [X3089,X3090,X3091,X3092] :
( ~ c_Fun_Oinj__on(X3092,X3091,X3090,c_Orderings_Otop__class_Otop(tc_fun(X3092,tc_HOL_Obool)))
| c_Set_Oimage(X3091,X3092,c_Hilbert__Choice_Oinv__into(X3092,X3091,c_Orderings_Otop__class_Otop(tc_fun(X3092,tc_HOL_Obool)),X3090),c_Set_Oimage(X3092,X3091,X3090,X3089)) = X3089 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).
fof(i_0_679,plain,
! [X2962,X2963,X2964,X2965] :
( c_Set_Oimage(X2965,X2964,X2963,c_Orderings_Otop__class_Otop(tc_fun(X2965,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2964,tc_HOL_Obool))
| hAPP(X2963,hAPP(c_Hilbert__Choice_Oinv__into(X2965,X2964,c_Orderings_Otop__class_Otop(tc_fun(X2965,tc_HOL_Obool)),X2963),X2962)) = X2962 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).
fof(i_0_680,plain,
! [X1649,X1650,X1651,X1652,X1653] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1653,X1652)),hAPP(X1653,X1651)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1650,X1650)),hAPP(hAPP(c_Product__Type_OPair(X1650,X1650),X1652),X1651)),c_Wellfounded_Omlex__prod(X1650,X1653,X1649))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_681,plain,
! [X3097,X3098,X3099] :
( c_Set_Oimage(X3099,X3098,X3097,c_Orderings_Otop__class_Otop(tc_fun(X3099,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3098,tc_HOL_Obool))
| c_Fun_Oinj__on(X3098,X3099,c_Hilbert__Choice_Oinv__into(X3099,X3098,c_Orderings_Otop__class_Otop(tc_fun(X3099,tc_HOL_Obool)),X3097),c_Orderings_Otop__class_Otop(tc_fun(X3098,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).
fof(i_0_682,plain,
! [X2914,X2915,X2916,X2917] : hBOOL(hAPP(hAPP(c_member(X2917),hAPP(X2916,X2915)),c_Set_Oimage(X2914,X2917,X2916,c_Orderings_Otop__class_Otop(tc_fun(X2914,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_683,plain,
! [X3086,X3087,X3088] :
( ~ c_Fun_Oinj__on(X3088,X3087,X3086,c_Orderings_Otop__class_Otop(tc_fun(X3088,tc_HOL_Obool)))
| c_Set_Oimage(X3087,X3088,c_Hilbert__Choice_Oinv__into(X3088,X3087,c_Orderings_Otop__class_Otop(tc_fun(X3088,tc_HOL_Obool)),X3086),c_Orderings_Otop__class_Otop(tc_fun(X3087,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3088,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).
fof(i_0_684,plain,
! [X2985,X2986,X2987,X2988,X2989] :
( ~ hBOOL(hAPP(hAPP(c_member(X2989),X2988),X2987))
| hBOOL(hAPP(hAPP(c_member(X2986),hAPP(X2985,X2988)),c_Set_Oimage(X2989,X2986,X2985,X2987))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_685,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_686,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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_687,plain,
! [X2909,X2910,X2911,X2912,X2913] :
( X2913 != hAPP(X2912,X2911)
| hBOOL(hAPP(hAPP(c_member(X2910),X2913),c_Set_Oimage(X2909,X2910,X2912,c_Orderings_Otop__class_Otop(tc_fun(X2909,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_688,plain,
! [X2877,X2878,X2879,X2880,X2881,X2882] :
( X2882 != hAPP(X2881,X2880)
| ~ hBOOL(hAPP(hAPP(c_member(X2879),X2880),X2878))
| hBOOL(hAPP(hAPP(c_member(X2877),X2882),c_Set_Oimage(X2879,X2877,X2881,X2878))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_689,plain,
! [X2979,X2980,X2981,X2982,X2983,X2984] :
( ~ hBOOL(hAPP(hAPP(c_member(X2984),X2983),X2982))
| X2981 != hAPP(X2980,X2983)
| hBOOL(hAPP(hAPP(c_member(X2979),X2981),c_Set_Oimage(X2984,X2979,X2980,X2982))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_690,plain,
! [X2927,X2928,X2929,X2930,X2931] :
( ( c_Set_Oimage(X2931,X2930,X2929,X2928) != c_Set_Oimage(X2931,X2930,X2929,X2927)
| X2928 = X2927
| ~ c_Fun_Oinj__on(X2931,X2930,X2929,c_Orderings_Otop__class_Otop(tc_fun(X2931,tc_HOL_Obool))) )
& ( X2928 != X2927
| c_Set_Oimage(X2931,X2930,X2929,X2928) = c_Set_Oimage(X2931,X2930,X2929,X2927)
| ~ c_Fun_Oinj__on(X2931,X2930,X2929,c_Orderings_Otop__class_Otop(tc_fun(X2931,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_691,plain,
! [X2216,X2217,X2218,X2219] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2219),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2219),X2218),X2217)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2219),X2216),X2217)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2219),X2218),X2216)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_692,plain,
! [X2195,X2196,X2197,X2198] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2198),X2197),X2196)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2198),X2195),X2196)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2198),X2197),X2195))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2198) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2198),X2197),X2195))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2198),X2197),X2196)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2198),X2195),X2196)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2198) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_693,plain,
! [X2220,X2221,X2222,X2223] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2223)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2223),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2223),X2222),X2221)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2223),X2222),X2220)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2223),X2221),X2220)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_694,plain,
! [X2199,X2200,X2201,X2202] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2202),X2201),X2200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2202),X2201),X2199)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2202),X2200),X2199))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2202) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2202),X2200),X2199))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2202),X2201),X2200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2202),X2201),X2199)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2202) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_695,plain,
! [X2923,X2924,X2925,X2926] :
( ~ c_Finite__Set_Ofinite(X2926,c_Set_Oimage(X2925,X2926,X2924,X2923))
| ~ c_Fun_Oinj__on(X2925,X2926,X2924,X2923)
| c_Finite__Set_Ofinite(X2925,X2923) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_696,plain,
! [X2128,X2129,X2130,X2131] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2131,tc_HOL_Obool)),X2130),X2129))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2131,tc_HOL_Obool)),X2129),X2128))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2131,tc_HOL_Obool)),X2130),X2128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_697,plain,
! [X2191,X2192,X2193,X2194] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2194,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2194),X2193),X2192)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2194),X2191),X2192)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2194,X2193),X2191))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2194) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2194,X2193),X2191))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2194,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2194),X2193),X2192)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2194),X2191),X2192)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2194) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_698,plain,
! [X2170,X2171,X2172,X2173] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2173)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2173,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2173),X2172),X2171)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2173),X2170),X2171)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2173,X2172),X2170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_699,plain,
! [X2187,X2188,X2189,X2190] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2190,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2190),X2189),X2188)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2190),X2189),X2187)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2190,X2188),X2187))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2190) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2190,X2188),X2187))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2190,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2190),X2189),X2188)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2190),X2189),X2187)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2190) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_700,plain,
! [X2166,X2167,X2168,X2169] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2169)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2169,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2169),X2168),X2167)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2169),X2168),X2166)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2169,X2167),X2166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_701,plain,
! [X2572,X2573,X2574,X2575] :
( ( hBOOL(hAPP(hAPP(c_member(X2575),X2574),X2572))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2575,tc_HOL_Obool),c_Set_Oinsert(X2575,X2574,X2573)),X2572)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2575,tc_HOL_Obool),X2573),X2572))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2575,tc_HOL_Obool),c_Set_Oinsert(X2575,X2574,X2573)),X2572)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2575),X2574),X2572))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2575,tc_HOL_Obool),X2573),X2572))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2575,tc_HOL_Obool),c_Set_Oinsert(X2575,X2574,X2573)),X2572)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_702,plain,
! [X1989,X1990,X1991,X1992] :
( ~ c_Fun_Oinj__on(X1992,X1991,X1990,c_Orderings_Otop__class_Otop(tc_fun(X1992,tc_HOL_Obool)))
| hAPP(c_Hilbert__Choice_Oinv__into(X1992,X1991,c_Orderings_Otop__class_Otop(tc_fun(X1992,tc_HOL_Obool)),X1990),hAPP(X1990,X1989)) = X1989 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).
fof(i_0_703,plain,
! [X1984,X1985,X1986,X1987,X1988] :
( ~ c_Fun_Oinj__on(X1988,X1987,X1986,c_Orderings_Otop__class_Otop(tc_fun(X1988,tc_HOL_Obool)))
| hAPP(X1986,X1985) != X1984
| hAPP(c_Hilbert__Choice_Oinv__into(X1988,X1987,c_Orderings_Otop__class_Otop(tc_fun(X1988,tc_HOL_Obool)),X1986),X1984) = X1985 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).
fof(i_0_704,plain,
! [X1636,X1637,X1638] :
( ( hAPP(hAPP(c_COMBC(X1638,tc_fun(X1638,tc_HOL_Obool),tc_HOL_Obool),c_member(X1638)),X1637) != hAPP(hAPP(c_COMBC(X1638,tc_fun(X1638,tc_HOL_Obool),tc_HOL_Obool),c_member(X1638)),X1636)
| X1637 = X1636 )
& ( X1637 != X1636
| hAPP(hAPP(c_COMBC(X1638,tc_fun(X1638,tc_HOL_Obool),tc_HOL_Obool),c_member(X1638)),X1637) = hAPP(hAPP(c_COMBC(X1638,tc_fun(X1638,tc_HOL_Obool),tc_HOL_Obool),c_member(X1638)),X1636) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_705,plain,
! [X2353,X2354,X2355] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2355),X2354)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2355),X2353)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2354),X2353)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2354),X2353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2355),X2354)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2355),X2353))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_706,plain,
! [X1999,X2000,X2001,X2002,X2003] :
( ~ c_Fun_Oinj__on(X2003,X2002,X2001,X2000)
| ~ hBOOL(hAPP(hAPP(c_member(X2003),X1999),X2000))
| hAPP(c_Hilbert__Choice_Oinv__into(X2003,X2002,X2000,X2001),hAPP(X2001,X1999)) = X1999 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).
fof(i_0_707,plain,
! [X1993,X1994,X1995,X1996,X1997,X1998] :
( ~ c_Fun_Oinj__on(X1998,X1997,X1996,X1995)
| ~ hBOOL(hAPP(hAPP(c_member(X1998),X1994),X1995))
| hAPP(X1996,X1994) != X1993
| hAPP(c_Hilbert__Choice_Oinv__into(X1998,X1997,X1995,X1996),X1993) = X1994 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).
fof(i_0_708,plain,
! [X3049,X3050,X3051,X3052] :
( ~ c_Finite__Set_Ofinite(X3052,X3051)
| c_Finite__Set_Ocard(X3050,c_Set_Oimage(X3052,X3050,X3049,X3051)) != c_Finite__Set_Ocard(X3052,X3051)
| c_Fun_Oinj__on(X3052,X3050,X3049,X3051) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_709,plain,
! [X3053,X3054,X3055,X3056] :
( ( ~ c_Fun_Oinj__on(X3056,X3054,X3053,X3055)
| c_Finite__Set_Ocard(X3054,c_Set_Oimage(X3056,X3054,X3053,X3055)) = c_Finite__Set_Ocard(X3056,X3055)
| ~ c_Finite__Set_Ofinite(X3056,X3055) )
& ( c_Finite__Set_Ocard(X3054,c_Set_Oimage(X3056,X3054,X3053,X3055)) != c_Finite__Set_Ocard(X3056,X3055)
| c_Fun_Oinj__on(X3056,X3054,X3053,X3055)
| ~ c_Finite__Set_Ofinite(X3056,X3055) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).
fof(i_0_710,plain,
! [X2534,X2535,X2536,X2537] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2537,tc_HOL_Obool),X2536),X2535))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2537,tc_HOL_Obool),c_Set_Oinsert(X2537,X2534,X2536)),c_Set_Oinsert(X2537,X2534,X2535))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(i_0_711,plain,
! [X3163,X3164,X3165,X3166,X3167,X3168] : hAPP(hAPP(c_COMBB(X3168,X3167,X3166,X3165),X3164),X3163) = hAPP(X3165,hAPP(X3164,X3163)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_712,plain,
! [X2211,X2212,X2213,X2214,X2215] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2215),X2214),X2213))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2215),X2212),X2211))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2215),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2215),X2214),X2212)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2215),X2213),X2211))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_713,plain,
! [X3127,X3128,X3129] : 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)),X3129),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3128,X3127)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3128),X3129),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3127),X3129)),
inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).
fof(i_0_714,plain,
! [X2380,X2381,X2382] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2382),X2381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2382),X2380)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2381),X2380)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2381),X2380))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2382),X2381)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2382),X2380))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_715,plain,
! [X2065,X2066,X2067,X2068,X2069] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2069)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2069,X2068),X2067))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2069),X2066),X2065))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2069),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2069),X2068),X2066)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2069),X2067),X2065))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_716,plain,
! [X2060,X2061,X2062,X2063,X2064] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2064)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2064),X2063),X2062))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2064,X2061),X2060))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2064),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2064),X2063),X2061)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2064),X2062),X2060))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_717,plain,
! [X2105,X2106,X2107,X2108] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2108,tc_HOL_Obool),X2107),X2106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2108,tc_HOL_Obool)),X2106),X2105))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2108,tc_HOL_Obool)),X2107),X2105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_718,plain,
! [X2101,X2102,X2103,X2104] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2104,tc_HOL_Obool)),X2103),X2102))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2104,tc_HOL_Obool),X2102),X2101))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2104,tc_HOL_Obool)),X2103),X2101)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_719,plain,
! [X2875,X2876] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2876)),X2875))
| hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2876),X2875)) )
& ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2876),X2875))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2876)),X2875)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_720,plain,
! [X2904,X2905,X2906,X2907,X2908] :
( ~ hBOOL(hAPP(hAPP(c_member(X2908),X2907),X2906))
| c_Set_Oinsert(X2905,hAPP(X2904,X2907),c_Set_Oimage(X2908,X2905,X2904,X2906)) = c_Set_Oimage(X2908,X2905,X2904,X2906) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
fof(i_0_721,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))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2439,X2437)),c_Finite__Set_Ocard(X2439,X2438)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2439,tc_HOL_Obool)),X2437),X2438)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_722,plain,
! [X2174,X2175,X2176,X2177,X2178] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2178)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2178,X2177),X2176))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2178,X2175),X2174))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2178,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2178),X2177),X2175)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2178),X2176),X2174))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_723,plain,
! [X2658,X2659] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2659),X2658),X2658)),c_Groups_Ozero__class_Ozero(X2659)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2659),X2658),c_Groups_Ozero__class_Ozero(X2659)))
| ~ class_Groups_Olinordered__ab__group__add(X2659) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2659),X2658),c_Groups_Ozero__class_Ozero(X2659)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2659),X2658),X2658)),c_Groups_Ozero__class_Ozero(X2659)))
| ~ class_Groups_Olinordered__ab__group__add(X2659) ) ),
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_724,plain,
! [X2702,X2703] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2703),X2702),X2702)),c_Groups_Ozero__class_Ozero(X2703)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2703),X2702),c_Groups_Ozero__class_Ozero(X2703)))
| ~ class_Rings_Olinordered__idom(X2703) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2703),X2702),c_Groups_Ozero__class_Ozero(X2703)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2703),X2702),X2702)),c_Groups_Ozero__class_Ozero(X2703)))
| ~ class_Rings_Olinordered__idom(X2703) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_725,plain,
! [X2340,X2341,X2342,X2343] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2343),X2342))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2341),X2340))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2343),X2341)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2342),X2340))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_726,plain,
! [X3002,X3003,X3004,X3005,X3006] : c_Set_Oimage(X3006,X3005,X3004,c_Set_Oinsert(X3006,X3003,X3002)) = c_Set_Oinsert(X3005,hAPP(X3004,X3003),c_Set_Oimage(X3006,X3005,X3004,X3002)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
fof(i_0_727,plain,
! [X3068,X3069] :
( ~ c_Finite__Set_Ofinite(X3069,c_Orderings_Otop__class_Otop(tc_fun(X3069,tc_HOL_Obool)))
| c_Set_Oimage(X3069,X3069,X3068,c_Orderings_Otop__class_Otop(tc_fun(X3069,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3069,tc_HOL_Obool))
| c_Fun_Oinj__on(X3069,X3069,X3068,c_Orderings_Otop__class_Otop(tc_fun(X3069,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_728,plain,
! [X2248,X2249,X2250,X2251,X2252] :
( ~ c_Fun_Oinj__on(X2252,X2251,X2250,X2249)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2252,tc_HOL_Obool),X2248),X2249))
| c_Fun_Oinj__on(X2252,X2251,X2250,X2248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_729,plain,
! [X2932,X2933,X2934,X2935] :
( ~ c_Fun_Oinj__on(X2935,X2934,X2933,X2932)
| c_Finite__Set_Ocard(X2934,c_Set_Oimage(X2935,X2934,X2933,X2932)) = c_Finite__Set_Ocard(X2935,X2932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_730,plain,
! [X2667,X2668,X2669] :
( ~ class_Groups_Oordered__comm__monoid__add(X2669)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2669),X2668),c_Groups_Ozero__class_Ozero(X2669)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2669),X2667),c_Groups_Ozero__class_Ozero(X2669)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2669),X2668),X2667)),c_Groups_Ozero__class_Ozero(X2669))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_731,plain,
! [X2856,X2857,X2858] :
( ~ class_Rings_Oring__1(X2858)
| ~ hBOOL(hAPP(hAPP(c_member(X2858),X2857),c_Int_Oring__1__class_OInts(X2858)))
| ~ hBOOL(hAPP(hAPP(c_member(X2858),X2856),c_Int_Oring__1__class_OInts(X2858)))
| hBOOL(hAPP(hAPP(c_member(X2858),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2858),X2857),X2856)),c_Int_Oring__1__class_OInts(X2858))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).
fof(i_0_732,plain,
! [X3066,X3067] :
( ~ c_Finite__Set_Ofinite(X3067,c_Orderings_Otop__class_Otop(tc_fun(X3067,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X3067,X3067,X3066,c_Orderings_Otop__class_Otop(tc_fun(X3067,tc_HOL_Obool)))
| c_Set_Oimage(X3067,X3067,X3066,c_Orderings_Otop__class_Otop(tc_fun(X3067,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3067,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_733,plain,
! [X2203,X2204,X2205,X2206] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2206)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2206),X2205),X2204))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2206),X2205),X2203)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2206),X2204),X2203))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_734,plain,
! [X2207,X2208,X2209,X2210] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2210),X2209),X2208))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2210),X2207),X2209)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2210),X2207),X2208))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_735,plain,
! [X2637,X2638] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2638,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2638),X2637),X2637)),c_Groups_Ozero__class_Ozero(X2638)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2638,X2637),c_Groups_Ozero__class_Ozero(X2638)))
| ~ class_Groups_Olinordered__ab__group__add(X2638) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2638,X2637),c_Groups_Ozero__class_Ozero(X2638)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2638,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2638),X2637),X2637)),c_Groups_Ozero__class_Ozero(X2638)))
| ~ class_Groups_Olinordered__ab__group__add(X2638) ) ),
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_736,plain,
! [X2576,X2577,X2578,X2579] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2579,tc_HOL_Obool),X2577),c_Set_Oinsert(X2579,X2578,X2576)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2579,tc_HOL_Obool),X2577),X2576))
| hBOOL(hAPP(hAPP(c_member(X2579),X2578),X2577)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2579,tc_HOL_Obool),X2577),X2576))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2579,tc_HOL_Obool),X2577),c_Set_Oinsert(X2579,X2578,X2576)))
| hBOOL(hAPP(hAPP(c_member(X2579),X2578),X2577)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])])]) ).
fof(i_0_737,plain,
! [X2695,X2696,X2697] :
( ~ class_Groups_Oordered__comm__monoid__add(X2697)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2697,X2696),c_Groups_Ozero__class_Ozero(X2697)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2697),X2695),c_Groups_Ozero__class_Ozero(X2697)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2697),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2697),X2696),X2695)),c_Groups_Ozero__class_Ozero(X2697))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_738,plain,
! [X2692,X2693,X2694] :
( ~ class_Groups_Oordered__comm__monoid__add(X2694)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2694),X2693),c_Groups_Ozero__class_Ozero(X2694)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2694,X2692),c_Groups_Ozero__class_Ozero(X2694)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2694),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2694),X2693),X2692)),c_Groups_Ozero__class_Ozero(X2694))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_739,plain,
! [X2392,X2393,X2394,X2395] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2395),X2394))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2393),X2392))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2395),X2393)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2394),X2392))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_740,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk15_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk15_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_531])])]) ).
fof(i_0_741,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk16_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk16_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_532])])]) ).
fof(i_0_742,plain,
! [X2556,X2557,X2558,X2559] :
( ( c_Finite__Set_Ofinite(X2559,X2557)
| ~ c_Finite__Set_Ofinite(tc_sum(X2559,X2558),c_Sum__Type_OPlus(X2559,X2558,X2557,X2556)) )
& ( c_Finite__Set_Ofinite(X2558,X2556)
| ~ c_Finite__Set_Ofinite(tc_sum(X2559,X2558),c_Sum__Type_OPlus(X2559,X2558,X2557,X2556)) )
& ( ~ c_Finite__Set_Ofinite(X2559,X2557)
| ~ c_Finite__Set_Ofinite(X2558,X2556)
| c_Finite__Set_Ofinite(tc_sum(X2559,X2558),c_Sum__Type_OPlus(X2559,X2558,X2557,X2556)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_743,plain,
! [X2564,X2565,X2566,X2567] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2567,X2566),c_Sum__Type_OPlus(X2567,X2566,X2565,X2564))
| c_Finite__Set_Ofinite(X2567,X2565) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_744,plain,
! [X2568,X2569,X2570,X2571] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2571,X2570),c_Sum__Type_OPlus(X2571,X2570,X2569,X2568))
| c_Finite__Set_Ofinite(X2570,X2568) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_745,plain,
! [X2183,X2184,X2185,X2186] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2186)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2186,X2185),X2184))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2186,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2186),X2185),X2183)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2186),X2184),X2183))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_746,plain,
! [X2179,X2180,X2181,X2182] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2182)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2182,X2181),X2180))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2182,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2182),X2179),X2181)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2182),X2179),X2180))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_747,plain,
! [X2333,X2334,X2335] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2335),X2334)),X2333))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2335),X2333)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_748,plain,
! [X2653,X2654,X2655] :
( ~ class_Groups_Oordered__comm__monoid__add(X2655)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2655,X2654),c_Groups_Ozero__class_Ozero(X2655)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2655,X2653),c_Groups_Ozero__class_Ozero(X2655)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2655,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2655),X2654),X2653)),c_Groups_Ozero__class_Ozero(X2655))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_749,plain,
! [X2008,X2009,X2010,X2011] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2010,X2011),X2009),X2008))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2010,X2011)),X2009),X2008))
| ~ class_Orderings_Oord(X2011) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2010,X2011),X2008),X2009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2010,X2011)),X2009),X2008))
| ~ class_Orderings_Oord(X2011) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2010,X2011),X2009),X2008))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2010,X2011),X2008),X2009))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2010,X2011)),X2009),X2008))
| ~ class_Orderings_Oord(X2011) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_533])])]) ).
fof(i_0_750,plain,
! [X2113,X2114,X2115,X2116,X2117,X2118] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2118,tc_fun(X2117,tc_HOL_Obool)),X2116),X2115))
| ~ hBOOL(hAPP(hAPP(X2116,X2114),X2113))
| hBOOL(hAPP(hAPP(X2115,X2114),X2113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_751,plain,
! [X2122,X2123,X2124,X2125,X2126,X2127] :
( ~ hBOOL(hAPP(hAPP(X2127,X2126),X2125))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2124,tc_fun(X2123,tc_HOL_Obool)),X2127),X2122))
| hBOOL(hAPP(hAPP(X2122,X2126),X2125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_752,plain,
! [X2344,X2345,X2346] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2346),X2345))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2346),X2344)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2345),X2344))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_753,plain,
! [X2321,X2322,X2323,X2324,X2325,X2326] :
( ( hAPP(X2324,X2322) != hAPP(X2324,X2321)
| X2322 = X2321
| ~ hBOOL(hAPP(hAPP(c_member(X2326),X2321),X2323))
| ~ hBOOL(hAPP(hAPP(c_member(X2326),X2322),X2323))
| ~ c_Fun_Oinj__on(X2326,X2325,X2324,X2323) )
& ( X2322 != X2321
| hAPP(X2324,X2322) = hAPP(X2324,X2321)
| ~ hBOOL(hAPP(hAPP(c_member(X2326),X2321),X2323))
| ~ hBOOL(hAPP(hAPP(c_member(X2326),X2322),X2323))
| ~ c_Fun_Oinj__on(X2326,X2325,X2324,X2323) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_754,plain,
! [X2327,X2328,X2329,X2330,X2331,X2332] :
( ~ c_Fun_Oinj__on(X2332,X2331,X2330,X2329)
| X2328 = X2327
| ~ hBOOL(hAPP(hAPP(c_member(X2332),X2328),X2329))
| ~ hBOOL(hAPP(hAPP(c_member(X2332),X2327),X2329))
| hAPP(X2330,X2328) != hAPP(X2330,X2327) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_755,plain,
! [X2315,X2316,X2317,X2318,X2319,X2320] :
( ~ c_Fun_Oinj__on(X2320,X2319,X2318,X2317)
| hAPP(X2318,X2316) != hAPP(X2318,X2315)
| ~ hBOOL(hAPP(hAPP(c_member(X2320),X2316),X2317))
| ~ hBOOL(hAPP(hAPP(c_member(X2320),X2315),X2317))
| X2316 = X2315 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_756,plain,
! [X2253,X2254,X2255] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2255),X2253))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2255),X2254)),X2253)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2254),X2253))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2255),X2254)),X2253)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_534])])]) ).
fof(i_0_757,plain,
! [X2399,X2400,X2401] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2401),X2400)),X2399))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2401),X2399)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_758,plain,
! [X2396,X2397,X2398] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2398),X2397)),X2396))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2397),X2396)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_759,plain,
! [X2660,X2661,X2662] :
( ~ class_Groups_Oordered__comm__monoid__add(X2662)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2662),c_Groups_Ozero__class_Ozero(X2662)),X2661))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2662),c_Groups_Ozero__class_Ozero(X2662)),X2660))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2662),c_Groups_Ozero__class_Ozero(X2662)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2662),X2661),X2660))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_760,plain,
! [X2389,X2390,X2391] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2391),X2390))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2391),X2389)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2390),X2389))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_761,plain,
! [X2012,X2013,X2014,X2015] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2015,tc_HOL_Obool)),X2014),X2013))
| ~ hBOOL(hAPP(hAPP(c_member(X2015),X2012),X2014))
| hBOOL(hAPP(hAPP(c_member(X2015),X2012),X2013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_762,plain,
! [X2440,X2441,X2442] :
( ~ c_Finite__Set_Ofinite(X2442,X2441)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2442,tc_HOL_Obool)),X2440),X2441))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2442,X2440)),c_Finite__Set_Ocard(X2442,X2441))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_763,plain,
! [X2305,X2306] : 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)),X2306),X2305),
inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).
fof(i_0_764,plain,
! [X2807,X2808,X2809,X2810,X2811] :
( ~ class_Rings_Ocomm__semiring__1(X2811)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2811),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2811),X2810),X2809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2811),X2808),X2807)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2811),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2811),X2810),X2808)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2811),X2809),X2807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_765,plain,
! [X2109,X2110,X2111,X2112] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2112,tc_HOL_Obool),X2111),X2110))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2112,tc_HOL_Obool),X2110),X2109))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2112,tc_HOL_Obool),X2111),X2109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_766,plain,
! [X2681,X2682,X2683] :
( ~ class_Groups_Oordered__comm__monoid__add(X2683)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2683,c_Groups_Ozero__class_Ozero(X2683)),X2682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2683),c_Groups_Ozero__class_Ozero(X2683)),X2681))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2683),c_Groups_Ozero__class_Ozero(X2683)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2683),X2682),X2681))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_767,plain,
! [X2678,X2679,X2680] :
( ~ class_Groups_Oordered__comm__monoid__add(X2680)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2680),c_Groups_Ozero__class_Ozero(X2680)),X2679))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2680,c_Groups_Ozero__class_Ozero(X2680)),X2678))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2680),c_Groups_Ozero__class_Ozero(X2680)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2680),X2679),X2678))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_768,plain,
! [X2358,X2359] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2359),X2358)),X2359)),
inference(variable_rename,[status(thm)],[i_0_535]) ).
fof(i_0_769,plain,
! [X2356,X2357] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2357),X2356)),X2356)),
inference(variable_rename,[status(thm)],[i_0_536]) ).
fof(i_0_770,plain,
! [X2593,X2594,X2595,X2596] :
( ( ~ c_Finite__Set_Ofinite(X2596,X2595)
| ~ c_Finite__Set_Ofinite(X2594,X2593)
| c_Finite__Set_Ocard(tc_sum(X2596,X2594),c_Sum__Type_OPlus(X2596,X2594,X2595,X2593)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2596,X2595)),c_Finite__Set_Ocard(X2594,X2593)) )
& ( c_Finite__Set_Ofinite(X2596,X2595)
| c_Finite__Set_Ocard(tc_sum(X2596,X2594),c_Sum__Type_OPlus(X2596,X2594,X2595,X2593)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X2594,X2593)
| c_Finite__Set_Ocard(tc_sum(X2596,X2594),c_Sum__Type_OPlus(X2596,X2594,X2595,X2593)) = 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_771,plain,
! [X2472,X2473,X2474,X2475] :
( ~ c_Finite__Set_Ofinite(X2475,X2474)
| ~ c_Finite__Set_Ofinite(X2473,X2472)
| c_Finite__Set_Ocard(tc_sum(X2475,X2473),c_Sum__Type_OPlus(X2475,X2473,X2474,X2472)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2475,X2474)),c_Finite__Set_Ocard(X2473,X2472)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_772,plain,
! [X2663,X2664,X2665,X2666] :
( ~ class_Rings_Olinordered__semidom(X2666)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2666),c_Groups_Ozero__class_Ozero(X2666)),X2665))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2666),X2664),X2663))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2666),X2664),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2666),X2665),X2663))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_773,plain,
! [X2580,X2581,X2582] :
( ~ c_Finite__Set_Ofinite(X2582,X2581)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2582,X2581)),c_Finite__Set_Ocard(X2582,c_Set_Oinsert(X2582,X2580,X2581)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).
fof(i_0_774,plain,
! [X2862,X2863] :
( ~ class_Int_Oring__char__0(X2863)
| ~ hBOOL(hAPP(hAPP(c_member(X2863),X2862),c_Int_Oring__1__class_OInts(X2863)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2863),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2863),c_Groups_Oone__class_Oone(X2863)),X2862)),X2862) != c_Groups_Ozero__class_Ozero(X2863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).
fof(i_0_775,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_776,plain,
! [X2674,X2675] :
( ( ~ 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),X2675),X2674)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2675))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2674)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2675))
| 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),X2675),X2674))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2674))
| 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),X2675),X2674))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_777,plain,
! [X2443,X2444,X2445] :
( ~ c_Finite__Set_Ofinite(X2445,X2444)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2445,tc_HOL_Obool),X2443),X2444))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2445,X2444)),c_Finite__Set_Ocard(X2445,X2443)))
| X2443 = X2444 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_778,plain,
! [X2538,X2539,X2540,X2541] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2541,tc_HOL_Obool),X2540),X2539))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2541,tc_HOL_Obool),X2540),c_Set_Oinsert(X2541,X2538,X2539))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_779,plain,
! [X2688,X2689,X2690,X2691] :
( ~ class_Groups_Oordered__comm__monoid__add(X2691)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2691,c_Groups_Ozero__class_Ozero(X2691)),X2690))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2691),X2689),X2688))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2691),X2689),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2691),X2690),X2688))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_780,plain,
! [X2684,X2685,X2686,X2687] :
( ~ class_Groups_Oordered__comm__monoid__add(X2687)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2687),c_Groups_Ozero__class_Ozero(X2687)),X2686))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2687,X2685),X2684))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2687),X2685),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2687),X2686),X2684))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_781,plain,
! [X2639,X2640,X2641] :
( ~ class_Groups_Oordered__comm__monoid__add(X2641)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2641,c_Groups_Ozero__class_Ozero(X2641)),X2640))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2641,c_Groups_Ozero__class_Ozero(X2641)),X2639))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2641,c_Groups_Ozero__class_Ozero(X2641)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2641),X2640),X2639))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_782,plain,
! [X2094,X2095,X2096] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2096,tc_HOL_Obool)),X2095),X2094))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2096,tc_HOL_Obool),X2095),X2094)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_783,plain,
! [X2081,X2082,X2083] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2083,tc_HOL_Obool),X2082),X2081))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2083,tc_HOL_Obool)),X2082),X2081))
| X2082 = X2081 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2083,tc_HOL_Obool)),X2082),X2081))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2083,tc_HOL_Obool),X2082),X2081)) )
& ( X2082 != X2081
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2083,tc_HOL_Obool),X2082),X2081)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_784,plain,
! [X2075,X2076,X2077] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2077,tc_HOL_Obool),X2076),X2075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2077,tc_HOL_Obool)),X2076),X2075)) )
& ( X2076 != X2075
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2077,tc_HOL_Obool)),X2076),X2075)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2077,tc_HOL_Obool),X2076),X2075))
| X2076 = X2075
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2077,tc_HOL_Obool)),X2076),X2075)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_785,plain,
! [X2527,X2528,X2529,X2530] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2530),X2529),c_Set_Oinsert(X2530,X2528,X2527)))
| X2529 = X2528
| hBOOL(hAPP(hAPP(c_member(X2530),X2529),X2527)) )
& ( X2529 != X2528
| hBOOL(hAPP(hAPP(c_member(X2530),X2529),c_Set_Oinsert(X2530,X2528,X2527))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2530),X2529),X2527))
| hBOOL(hAPP(hAPP(c_member(X2530),X2529),c_Set_Oinsert(X2530,X2528,X2527))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_786,plain,
! [X2491,X2492,X2493,X2494] :
( ~ hBOOL(hAPP(hAPP(c_member(X2494),X2493),c_Set_Oinsert(X2494,X2492,X2491)))
| X2493 = X2492
| hBOOL(hAPP(hAPP(c_member(X2494),X2493),X2491)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
fof(i_0_787,plain,
! [X2635,X2636] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2636),X2635),X2635)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),X2635))
| ~ class_Groups_Olinordered__ab__group__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,c_Groups_Ozero__class_Ozero(X2636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2636),X2635),X2635)))
| ~ class_Groups_Olinordered__ab__group__add(X2636) ) ),
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_788,plain,
! [X2226,X2227,X2228] : c_FuncSet_OPi(X2228,X2227,X2226,hAPP(c_COMBK(tc_fun(X2227,tc_HOL_Obool),X2228),c_Orderings_Otop__class_Otop(tc_fun(X2227,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2228,X2227),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pi__UNIV]) ).
fof(i_0_789,plain,
! [X2645,X2646,X2647,X2648] :
( ~ class_Groups_Oordered__comm__monoid__add(X2648)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2648,c_Groups_Ozero__class_Ozero(X2648)),X2647))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2648,X2646),X2645))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2648,X2646),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2648),X2647),X2645))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_790,plain,
! [X2649,X2650,X2651,X2652] :
( ~ class_Groups_Oordered__comm__monoid__add(X2652)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2652,c_Groups_Ozero__class_Ozero(X2652)),X2651))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2652,X2650),X2649))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2652,X2650),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2652),X2649),X2651))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_791,plain,
! [X2560,X2561,X2562,X2563] :
( ~ c_Finite__Set_Ofinite(X2563,X2562)
| ~ c_Finite__Set_Ofinite(X2561,X2560)
| c_Finite__Set_Ofinite(tc_sum(X2563,X2561),c_Sum__Type_OPlus(X2563,X2561,X2562,X2560)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_792,plain,
! [X3169,X3170,X3171,X3172,X3173,X3174] : hAPP(hAPP(hAPP(c_COMBC(X3174,X3173,X3172),X3171),X3170),X3169) = hAPP(hAPP(X3171,X3169),X3170),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_793,plain,
! [X2078,X2079,X2080] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2078,tc_HOL_Obool),X2080),X2079))
| X2080 != X2079 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2078,tc_HOL_Obool),X2079),X2080))
| X2080 != X2079 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2078,tc_HOL_Obool),X2080),X2079))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2078,tc_HOL_Obool),X2079),X2080))
| X2080 = X2079 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_794,plain,
! [X2070,X2071,X2072] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2072,tc_HOL_Obool),X2071),X2070))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2072,tc_HOL_Obool),X2070),X2071))
| X2071 = X2070 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_795,plain,
! [X2024,X2025,X2026,X2027] :
( ~ hBOOL(hAPP(hAPP(c_member(X2027),X2026),X2025))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2027,tc_HOL_Obool),X2025),X2024))
| hBOOL(hAPP(hAPP(c_member(X2027),X2026),X2024)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_796,plain,
! [X2028,X2029,X2030,X2031] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2031,tc_HOL_Obool),X2030),X2029))
| ~ hBOOL(hAPP(hAPP(c_member(X2031),X2028),X2030))
| hBOOL(hAPP(hAPP(c_member(X2031),X2028),X2029)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_797,plain,
! [X2020,X2021,X2022,X2023] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2023,tc_HOL_Obool),X2022),X2021))
| ~ hBOOL(hAPP(hAPP(c_member(X2023),X2020),X2022))
| hBOOL(hAPP(hAPP(c_member(X2023),X2020),X2021)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_798,plain,
! [X2004,X2005,X2006,X2007] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2007,tc_HOL_Obool),X2006),X2005))
| ~ hBOOL(hAPP(hAPP(c_member(X2007),X2004),X2006))
| hBOOL(hAPP(hAPP(c_member(X2007),X2004),X2005)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_799,plain,
! [X1784,X1785,X1786,X1787,X1788] :
( ~ class_Orderings_Oord(X1788)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1787,X1788),X1786),X1785))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1788,hAPP(X1786,X1784)),hAPP(X1785,X1784))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_800,plain,
! [X1746,X1747,X1748,X1749,X1750] :
( ~ class_Orderings_Oord(X1750)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1749,X1750),X1748),X1747))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1750,hAPP(X1748,X1746)),hAPP(X1747,X1746))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_801,plain,
! [X2883,X2884,X2885,X2886] :
( ~ c_Finite__Set_Ofinite(X2886,X2885)
| c_Finite__Set_Ofinite(X2884,c_Set_Oimage(X2886,X2884,X2883,X2885)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
fof(i_0_802,plain,
! [X2446,X2447,X2448] :
( ~ c_Finite__Set_Ofinite(X2448,X2447)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2448,tc_HOL_Obool),X2446),X2447))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2448,X2446)),c_Finite__Set_Ocard(X2448,X2447))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_803,plain,
! [X2812,X2813,X2814,X2815] :
( ~ class_Rings_Ocomm__semiring__1(X2815)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2815),X2814),X2813)),X2812) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2815),X2814),X2812)),X2813) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_804,plain,
! [X2243,X2244,X2245,X2246,X2247] :
( ( hAPP(X2245,X2244) != hAPP(X2245,X2243)
| X2244 = X2243
| ~ c_Fun_Oinj__on(X2247,X2246,X2245,c_Orderings_Otop__class_Otop(tc_fun(X2247,tc_HOL_Obool))) )
& ( X2244 != X2243
| hAPP(X2245,X2244) = hAPP(X2245,X2243)
| ~ c_Fun_Oinj__on(X2247,X2246,X2245,c_Orderings_Otop__class_Otop(tc_fun(X2247,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_805,plain,
! [X2238,X2239,X2240,X2241,X2242] :
( ~ c_Fun_Oinj__on(X2242,X2241,X2240,c_Orderings_Otop__class_Otop(tc_fun(X2242,tc_HOL_Obool)))
| hAPP(X2240,X2239) != hAPP(X2240,X2238)
| X2239 = X2238 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_806,plain,
! [X2851,X2852,X2854] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk34_2(X2851,X2852)),X2851))
| ~ hBOOL(hAPP(X2852,X2851))
| hBOOL(hAPP(X2852,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2854),esk34_2(X2851,X2852)))
| ~ hBOOL(hAPP(X2852,X2854))
| ~ hBOOL(hAPP(X2852,X2851))
| hBOOL(hAPP(X2852,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X2852,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk34_2(X2851,X2852)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X2852,X2851))
| hBOOL(hAPP(X2852,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_537])])])])]) ).
fof(i_0_807,plain,
! [X2790,X2791] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2791),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2791),X2790)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_808,plain,
! [X2788,X2789] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2789),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2788),X2789)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_809,plain,
! [X2519,X2520,X2521,X2522] :
( ~ hBOOL(hAPP(hAPP(c_member(X2522),X2521),X2520))
| hBOOL(hAPP(hAPP(c_member(X2522),X2521),c_Set_Oinsert(X2522,X2519,X2520))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_810,plain,
! [X2487,X2488,X2489,X2490] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2490),X2489),X2488))
| hBOOL(hAPP(hAPP(c_member(X2490),X2489),c_Set_Oinsert(X2490,X2487,X2488))) )
& ( X2489 != X2487
| hBOOL(hAPP(hAPP(c_member(X2490),X2489),c_Set_Oinsert(X2490,X2487,X2488))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])])]) ).
fof(i_0_811,plain,
! [X2724,X2725,X2726] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2726),X2725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2725),X2724))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2726)),X2724)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_812,plain,
! [X2701] :
( ~ c_Finite__Set_Ofinite(X2701,c_Orderings_Otop__class_Otop(tc_fun(X2701,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(X2701,c_Orderings_Otop__class_Otop(tc_fun(X2701,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_813,plain,
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk40_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,esk40_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_814,plain,
! [X2735,X2736] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2736)),hAPP(c_Nat_OSuc,X2735)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2736),X2735)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2736),X2735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2736)),hAPP(c_Nat_OSuc,X2735))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_815,plain,
! [X2718,X2719] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2719)),hAPP(c_Nat_OSuc,X2718)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2719),X2718)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_816,plain,
! [X2704,X2705] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2705,X2704),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2705,X2704),tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2704,c_Orderings_Otop__class_Otop(tc_fun(X2704,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Finite__Set_Ofinite(X2705,c_Orderings_Otop__class_Otop(tc_fun(X2705,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_817,plain,
! [X1948,X1949,X1950,X1951] :
( ~ class_Orderings_Opreorder(X1951)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1951),X1950),X1949))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1951),X1949),X1948))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1951),X1950),X1948)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_818,plain,
! [X1952,X1953,X1954,X1955] :
( ~ class_Orderings_Oorder(X1955)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1955),X1954),X1953))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1955),X1952),X1954))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1955),X1952),X1953)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_819,plain,
! [X3125,X3126] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3126,X3125)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3126),hAPP(c_Nat_OSuc,X3125)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).
fof(i_0_820,plain,
! [X2642,X2643,X2644] :
( ( X2643 = c_Groups_Ozero__class_Ozero(X2644)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2644),X2643),X2642) != c_Groups_Ozero__class_Ozero(X2644)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,c_Groups_Ozero__class_Ozero(X2644)),X2642))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,c_Groups_Ozero__class_Ozero(X2644)),X2643))
| ~ class_Groups_Oordered__comm__monoid__add(X2644) )
& ( X2642 = c_Groups_Ozero__class_Ozero(X2644)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2644),X2643),X2642) != c_Groups_Ozero__class_Ozero(X2644)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,c_Groups_Ozero__class_Ozero(X2644)),X2642))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,c_Groups_Ozero__class_Ozero(X2644)),X2643))
| ~ class_Groups_Oordered__comm__monoid__add(X2644) )
& ( X2643 != c_Groups_Ozero__class_Ozero(X2644)
| X2642 != c_Groups_Ozero__class_Ozero(X2644)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2644),X2643),X2642) = c_Groups_Ozero__class_Ozero(X2644)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,c_Groups_Ozero__class_Ozero(X2644)),X2642))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,c_Groups_Ozero__class_Ozero(X2644)),X2643))
| ~ class_Groups_Oordered__comm__monoid__add(X2644) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_821,plain,
! [X2591,X2592] : c_Sum__Type_OPlus(X2592,X2591,c_Orderings_Otop__class_Otop(tc_fun(X2592,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2591,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2592,X2591),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_822,plain,
! [X2350,X2351,X2352] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2352),X2351))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2352),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2351),X2350))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_823,plain,
! [X1873,X1874,X1875] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1875),X1874))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1874),X1873))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_824,plain,
! [X2347,X2348,X2349] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2349),X2348))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2349),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2347),X2348))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_825,plain,
! [X1876,X1877,X1878] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1878),X1877))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1876),X1877))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_826,plain,
! [X2772,X2773,X2775,X2776,X2777] :
( ( X2773 = hAPP(c_Nat_OSuc,esk32_2(X2772,X2773))
| X2773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2773),hAPP(c_Nat_OSuc,X2772))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_2(X2772,X2773)),X2772))
| X2773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2773),hAPP(c_Nat_OSuc,X2772))) )
& ( X2776 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2776),hAPP(c_Nat_OSuc,X2775))) )
& ( X2776 != hAPP(c_Nat_OSuc,X2777)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2777),X2775))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2776),hAPP(c_Nat_OSuc,X2775))) ) ),
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_827,plain,
! [X2816,X2817,X2818,X2819] :
( ~ class_Rings_Ocomm__semiring__1(X2819)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2819),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2819),X2818),X2817)),X2816) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2819),X2818),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2819),X2817),X2816)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_828,plain,
! [X2155,X2156,X2157,X2158] :
( ~ class_Groups_Oab__semigroup__add(X2158)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2158),X2157),X2156)),X2155) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2158),X2157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2158),X2156),X2155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_829,plain,
! [X2820,X2821,X2822,X2823] :
( ~ class_Rings_Ocomm__semiring__1(X2823)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2823),X2822),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2823),X2821),X2820)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2823),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2823),X2822),X2821)),X2820) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_830,plain,
! [X2552,X2553,X2554,X2555] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2555,X2554,X2553),X2552))
| X2554 = X2552
| hBOOL(hAPP(X2553,X2552)) )
& ( X2554 != X2552
| hBOOL(hAPP(c_Set_Oinsert(X2555,X2554,X2553),X2552)) )
& ( ~ hBOOL(hAPP(X2553,X2552))
| hBOOL(hAPP(c_Set_Oinsert(X2555,X2554,X2553),X2552)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_831,plain,
! [X2698] :
( ~ class_Rings_Olinordered__semidom(X2698)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2698),c_Groups_Ozero__class_Ozero(X2698)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2698),c_Groups_Oone__class_Oone(X2698)),c_Groups_Oone__class_Oone(X2698)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_832,plain,
! [X2752,X2753] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2753)),hAPP(c_Nat_OSuc,X2752)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2753),X2752)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2753),X2752))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2753)),hAPP(c_Nat_OSuc,X2752))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_833,plain,
! [X1863,X1864,X1865,X1866] :
( ~ class_Orderings_Opreorder(X1866)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1866,X1865),X1864))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1866),X1864),X1863))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1866),X1865),X1863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_834,plain,
! [X1855,X1856,X1857,X1858] :
( ~ class_Orderings_Opreorder(X1858)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1858),X1857),X1856))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1858,X1856),X1855))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1858),X1857),X1855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_835,plain,
! [X1867,X1868,X1869,X1870] :
( ~ class_Orderings_Oorder(X1870)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1870,X1869),X1868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1870),X1867),X1869))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1870),X1867),X1868)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_836,plain,
! [X1859,X1860,X1861,X1862] :
( ~ class_Orderings_Oorder(X1862)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1862),X1861),X1860))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1862,X1859),X1861))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1862),X1859),X1860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_837,plain,
! [X2462,X2463] :
( ( c_Finite__Set_Ofinite(X2463,c_Orderings_Otop__class_Otop(tc_fun(X2463,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2463,X2462),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2463,X2462),tc_HOL_Obool))) )
& ( c_Finite__Set_Ofinite(X2462,c_Orderings_Otop__class_Otop(tc_fun(X2462,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2463,X2462),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2463,X2462),tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2463,c_Orderings_Otop__class_Otop(tc_fun(X2463,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2462,c_Orderings_Otop__class_Otop(tc_fun(X2462,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_sum(X2463,X2462),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2463,X2462),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_838,plain,
! [X2460,X2461] :
( ~ c_Finite__Set_Ofinite(X2461,c_Orderings_Otop__class_Otop(tc_fun(X2461,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2460,c_Orderings_Otop__class_Otop(tc_fun(X2460,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_prod(X2461,X2460),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2461,X2460),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_839,plain,
! [X2336,X2337,X2338,X2339] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2339),X2338))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2337),X2338) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2339),X2336)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2337),X2336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_840,plain,
! [X2542,X2543,X2544] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2544,tc_HOL_Obool),X2543),c_Set_Oinsert(X2544,X2542,X2543))),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_841,plain,
! [X2523,X2524,X2525,X2526] :
( ( c_Set_Oinsert(X2526,X2525,X2524) != c_Set_Oinsert(X2526,X2525,X2523)
| X2524 = X2523
| hBOOL(hAPP(hAPP(c_member(X2526),X2525),X2523))
| hBOOL(hAPP(hAPP(c_member(X2526),X2525),X2524)) )
& ( X2524 != X2523
| c_Set_Oinsert(X2526,X2525,X2524) = c_Set_Oinsert(X2526,X2525,X2523)
| hBOOL(hAPP(hAPP(c_member(X2526),X2525),X2523))
| hBOOL(hAPP(hAPP(c_member(X2526),X2525),X2524)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])])]) ).
fof(i_0_842,plain,
! [X2720,X2721] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2721)),X2720))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2721),X2720)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_843,plain,
! [X2748,X2749] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2749),X2748))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2748)),X2749)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2748)),X2749))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2749),X2748)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])]) ).
fof(i_0_844,plain,
! [X2708,X2709] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2709),X2708))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2709)),hAPP(c_Nat_OSuc,X2708))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_845,plain,
! [X2383,X2384,X2385] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2385),X2384))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2385),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2384),X2383))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_846,plain,
! [X1737,X1738,X1739] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1739),X1738))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1738),X1737))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_847,plain,
! [X2386,X2387,X2388] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2388),X2387))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2386),X2387))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_848,plain,
! [X1740,X1741,X1742] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1742),X1741))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1740),X1741))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_849,plain,
! [X2467,X2468] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2468,X2467),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2468,X2467),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2467,c_Orderings_Otop__class_Otop(tc_fun(X2467,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_850,plain,
! [X2739,X2740] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2740),X2739))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2739),hAPP(c_Nat_OSuc,X2740))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2739),hAPP(c_Nat_OSuc,X2740)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2740),X2739)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])]) ).
fof(i_0_851,plain,
! [X2274,X2275,X2276] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2276),X2275)),X2274) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2275),X2274)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_852,plain,
! [X2804,X2805] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2805),X2804))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2805)),X2804)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2805)),X2804))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2805),X2804)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_853,plain,
! [X2800,X2801] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2801)),X2800))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2801),X2800)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2801),X2800))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2801)),X2800)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_854,plain,
! [X2792,X2793] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2793)),X2792))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2793),X2792)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_855,plain,
! [X2097,X2098,X2099,X2100] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2100,tc_HOL_Obool),X2099),X2098))
| ~ hBOOL(hAPP(X2099,X2097))
| hBOOL(hAPP(X2098,X2097)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_856,plain,
! [X2084,X2085,X2086,X2087] :
( ~ hBOOL(hAPP(X2087,X2086))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2085,tc_HOL_Obool),X2087),X2084))
| hBOOL(hAPP(X2084,X2086)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_857,plain,
! [X1758,X1759,X1760,X1761] :
( ~ class_Orderings_Opreorder(X1761)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1761,X1760),X1759))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1761,X1759),X1758))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1761,X1760),X1758)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_858,plain,
! [X1751,X1752,X1753,X1754] :
( ~ class_Orderings_Oorder(X1754)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1754,X1753),X1752))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1754,X1751),X1753))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1754,X1751),X1752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_859,plain,
! [X2727,X2728] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2728),X2727))
| hAPP(c_Nat_OSuc,X2728) = X2727
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2728)),X2727)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_860,plain,
! [X1929,X1930,X1931] :
( ~ class_Orderings_Oorder(X1931)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1931),X1930),X1929))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1931),X1929),X1930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])]) ).
fof(i_0_861,plain,
! [X1899,X1900,X1901] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1901),X1900),X1899))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1901),X1899),X1900))
| X1900 = X1899
| ~ class_Orderings_Olinorder(X1901) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1901),X1899),X1900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1901),X1900),X1899))
| ~ class_Orderings_Olinorder(X1901) )
& ( X1900 != X1899
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1901),X1900),X1899))
| ~ class_Orderings_Olinorder(X1901) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])])]) ).
fof(i_0_862,plain,
! [X1956,X1957,X1958] :
( ~ class_Orderings_Opreorder(X1958)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1958),X1957),X1956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1958),X1956),X1957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])]) ).
fof(i_0_863,plain,
! [X1926,X1927,X1928] :
( ~ class_Orderings_Opreorder(X1928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1928),X1927),X1926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1928),X1926),X1927)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])]) ).
fof(i_0_864,plain,
! [X1917,X1918,X1919] :
( ~ class_Orderings_Opreorder(X1919)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1919),X1918),X1917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1919),X1917),X1918)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])]) ).
fof(i_0_865,plain,
! [X1914,X1915,X1916] :
( ~ class_Orderings_Opreorder(X1916)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1916),X1915),X1914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1916),X1914),X1915)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])]) ).
fof(i_0_866,plain,
! [X2058,X2059] :
( ~ class_Rings_Olinordered__semidom(X2059)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2059),X2058),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2059),X2058),c_Groups_Oone__class_Oone(X2059)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_867,plain,
! [X2794,X2795] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2794),hAPP(c_Nat_OSuc,X2795)))
| X2794 = X2795
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2795),X2794)) )
& ( X2794 != X2795
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2794),hAPP(c_Nat_OSuc,X2795)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2795),X2794)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_868,plain,
! [X2758,X2759] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2759)),X2758))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2759),X2758)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_869,plain,
! [X2476,X2477,X2478] :
( ~ c_Finite__Set_Ofinite(X2478,X2477)
| hBOOL(hAPP(hAPP(c_member(X2478),X2476),X2477))
| c_Finite__Set_Ocard(X2478,c_Set_Oinsert(X2478,X2476,X2477)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X2478,X2477)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])]) ).
fof(i_0_870,plain,
! [X1816,X1817,X1818] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1818,X1817),X1816))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1818),X1817),X1816))
| ~ class_Orderings_Opreorder(X1818) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1818,X1816),X1817))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1818),X1817),X1816))
| ~ class_Orderings_Opreorder(X1818) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1818,X1817),X1816))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1818,X1816),X1817))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1818),X1817),X1816))
| ~ class_Orderings_Opreorder(X1818) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])])]) ).
fof(i_0_871,plain,
! [X2834,X2835,X2836] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2836),X2834),X2835))
| c_Finite__Set_Ocard(X2836,c_Set_Oinsert(X2836,X2834,X2835)) = c_Finite__Set_Ocard(X2836,X2835)
| ~ c_Finite__Set_Ofinite(X2836,X2835) )
& ( hBOOL(hAPP(hAPP(c_member(X2836),X2834),X2835))
| c_Finite__Set_Ocard(X2836,c_Set_Oinsert(X2836,X2834,X2835)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2836,X2835))
| ~ c_Finite__Set_Ofinite(X2836,X2835) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])])]) ).
fof(i_0_872,plain,
! [X3130,X3132,X3133,X3134] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3130)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3132),X3130))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3132),esk42_1(X3130))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk43_2(X3133,X3134)),X3133))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3133) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk43_2(X3133,X3134)),X3134))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3133) ) ),
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_873,plain,
! [X2548,X2549,X2550,X2551] : c_Set_Oinsert(X2551,X2550,c_Set_Oinsert(X2551,X2549,X2548)) = c_Set_Oinsert(X2551,X2549,c_Set_Oinsert(X2551,X2550,X2548)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_874,plain,
! [X2531,X2532,X2533] : hBOOL(hAPP(hAPP(c_member(X2533),X2532),c_Set_Oinsert(X2533,X2532,X2531))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_875,plain,
! [X2737,X2738] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2738),hAPP(c_Nat_OSuc,X2737)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2738),X2737))
| X2738 = X2737 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2738),X2737))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2738),hAPP(c_Nat_OSuc,X2737))) )
& ( X2738 != X2737
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2738),hAPP(c_Nat_OSuc,X2737))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_876,plain,
! [X2733,X2734] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2734),hAPP(c_Nat_OSuc,X2733)))
| X2734 = X2733
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2734),X2733)) )
& ( X2734 != X2733
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2734),hAPP(c_Nat_OSuc,X2733)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2734),X2733)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])])]) ).
fof(i_0_877,plain,
! [X2731,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),X2732),hAPP(c_Nat_OSuc,X2731)))
| X2731 = X2732 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])]) ).
fof(i_0_878,plain,
! [X2722,X2723] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2723),hAPP(c_Nat_OSuc,X2722)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2723),X2722))
| X2723 = X2722 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])]) ).
fof(i_0_879,plain,
! [X2796,X2797] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2797),X2796))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2797)),X2796)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_880,plain,
! [X2824,X2825,X2826,X2827] :
( ~ class_Rings_Ocomm__semiring__1(X2827)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2827),X2826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2827),X2825),X2824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2827),X2825),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2827),X2826),X2824)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_881,plain,
! [X2288,X2289,X2290] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2290),X2289))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2289),X2288))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2290),X2288)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_882,plain,
! [X2456,X2457,X2458] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2458,tc_HOL_Obool),X2457),X2456))
| ~ c_Finite__Set_Ofinite(X2458,X2456)
| c_Finite__Set_Ofinite(X2458,X2457) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_883,plain,
! [X2453,X2454,X2455] :
( ~ c_Finite__Set_Ofinite(X2455,X2454)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2455,tc_HOL_Obool),X2453),X2454))
| c_Finite__Set_Ofinite(X2455,X2453) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_884,plain,
! [X1843,X1844,X1845] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1845),X1844),X1843))
| X1844 = X1843
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1845,X1844),X1843))
| ~ class_Orderings_Olinorder(X1845) )
& ( X1844 != X1843
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1845),X1844),X1843))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1845,X1844),X1843))
| ~ class_Orderings_Olinorder(X1845) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])])]) ).
fof(i_0_885,plain,
! [X1837,X1838,X1839] :
( ~ class_Orderings_Olinorder(X1839)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1839,X1838),X1837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1839),X1837),X1838)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])]) ).
fof(i_0_886,plain,
! [X1804,X1805,X1806] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1806),X1805),X1804))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1806,X1804),X1805))
| ~ class_Orderings_Olinorder(X1806) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1806,X1804),X1805))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1806),X1805),X1804))
| ~ class_Orderings_Olinorder(X1806) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).
fof(i_0_887,plain,
! [X1807,X1808,X1809] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1809,X1808),X1807))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1809),X1807),X1808))
| ~ class_Orderings_Olinorder(X1809) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1809),X1807),X1808))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1809,X1808),X1807))
| ~ class_Orderings_Olinorder(X1809) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])])]) ).
fof(i_0_888,plain,
! [X2782,X2783,X2785,X2786,X2787] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2783),X2782))
| X2782 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2783),esk33_2(X2782,X2783))) )
& ( X2785 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2786),X2787))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2786),X2785)) ) ),
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_889,plain,
! [X2802,X2803] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2803),hAPP(c_Nat_OSuc,X2802)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2803),X2802)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2803),X2802))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2803),hAPP(c_Nat_OSuc,X2802))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_890,plain,
! [X3136,X3138,X3139,X3140] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3136)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3138),X3136))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3138),esk44_1(X3136))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk45_2(X3139,X3140)),X3139))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3139) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk45_2(X3139,X3140)),X3140))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3139) ) ),
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_891,plain,
! [X2831,X2832,X2833] :
( ~ c_Finite__Set_Ofinite(X2833,X2832)
| hBOOL(hAPP(hAPP(c_member(X2833),X2831),X2832))
| c_Finite__Set_Ocard(X2833,c_Set_Oinsert(X2833,X2831,X2832)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2833,X2832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).
fof(i_0_892,plain,
! [X2729,X2730] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2730),X2729))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2730),hAPP(c_Nat_OSuc,X2729))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_893,plain,
! [X2860,X2861] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2861),X2860),X2860) != c_Groups_Ozero__class_Ozero(X2861)
| X2860 = c_Groups_Ozero__class_Ozero(X2861)
| ~ hBOOL(hAPP(hAPP(c_member(X2861),X2860),c_Int_Oring__1__class_OInts(X2861)))
| ~ class_Int_Oring__char__0(X2861) )
& ( X2860 != c_Groups_Ozero__class_Ozero(X2861)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2861),X2860),X2860) = c_Groups_Ozero__class_Ozero(X2861)
| ~ hBOOL(hAPP(hAPP(c_member(X2861),X2860),c_Int_Oring__1__class_OInts(X2861)))
| ~ class_Int_Oring__char__0(X2861) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).
fof(i_0_894,plain,
! [X3037,X3038,X3039,X3040] : c_Nat_Onat_Onat__case(X3040,X3039,X3038,hAPP(c_Nat_OSuc,X3037)) = hAPP(X3038,X3037),
inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).
fof(i_0_895,plain,
! [X2756,X2757] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2757),hAPP(c_Nat_OSuc,X2756)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2757),X2756))
| X2757 = hAPP(c_Nat_OSuc,X2756) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])]) ).
fof(i_0_896,plain,
! [X2750,X2751] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2751),hAPP(c_Nat_OSuc,X2750)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2751),X2750))
| X2751 = hAPP(c_Nat_OSuc,X2750) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2751),X2750))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2751),hAPP(c_Nat_OSuc,X2750))) )
& ( X2751 != hAPP(c_Nat_OSuc,X2750)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2751),hAPP(c_Nat_OSuc,X2750))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_897,plain,
! [X2032,X2033] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2033,tc_HOL_Obool),X2032),c_Orderings_Otop__class_Otop(tc_fun(X2033,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_898,plain,
! [X2256,X2257,X2258] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2257),X2258))
| hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| X2258 = X2257
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2258),X2257)) )
& ( ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| X2258 = X2257
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2258),X2257)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2257),X2258))
| hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2258),X2257)) )
& ( ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2258),X2257)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2257),X2258))
| hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| X2258 = X2257
| ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258)) )
& ( ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| X2258 = X2257
| ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2257),X2258))
| hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258)) )
& ( ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258))
| ~ hBOOL(hAPP(hAPP(X2256,X2257),X2258)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_899,plain,
! [X2271,X2272,X2273] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2273),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2272),X2271)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2273),X2271)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_900,plain,
! [X1792,X1793,X1794] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1794,X1793),X1792))
| X1793 != X1792
| ~ class_Orderings_Oorder(X1794) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1794,X1792),X1793))
| X1793 != X1792
| ~ class_Orderings_Oorder(X1794) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1794,X1793),X1792))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1794,X1792),X1793))
| X1793 = X1792
| ~ class_Orderings_Oorder(X1794) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_901,plain,
! [X1781,X1782,X1783] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1783,X1781),X1782))
| X1781 = X1782
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1783,X1782),X1781))
| ~ class_Orderings_Oorder(X1783) )
& ( X1781 != X1782
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1783,X1781),X1782))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1783,X1782),X1781))
| ~ class_Orderings_Oorder(X1783) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_902,plain,
! [X1762,X1763,X1764] :
( ~ class_Orderings_Oorder(X1764)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1764,X1763),X1762))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1764,X1762),X1763))
| X1763 = X1762 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_903,plain,
! [X1755,X1756,X1757] :
( ~ class_Orderings_Oorder(X1757)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1757,X1756),X1755))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1757,X1755),X1756))
| X1755 = X1756 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_904,plain,
! [X2699,X2700] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2700,X2699)))
| c_Finite__Set_Ofinite(X2700,X2699) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
fof(i_0_905,plain,
! [X2747] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2747)),X2747)),
inference(variable_rename,[status(thm)],[i_0_560]) ).
fof(i_0_906,plain,
! [X2798,X2799] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2799),X2798))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2799),hAPP(c_Nat_OSuc,X2798))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_907,plain,
! [X2465,X2466] :
( ~ c_Finite__Set_Ofinite(X2466,c_Orderings_Otop__class_Otop(tc_fun(X2466,tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2466,X2465) != c_Finite__Set_Ocard(X2466,c_Orderings_Otop__class_Otop(tc_fun(X2466,tc_HOL_Obool)))
| X2465 = c_Orderings_Otop__class_Otop(tc_fun(X2466,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_908,plain,
! [X1819,X1820,X1821] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1821,X1820),X1819))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1821),X1820),X1819))
| X1820 = X1819
| ~ class_Orderings_Oorder(X1821) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1821),X1820),X1819))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1821,X1820),X1819))
| ~ class_Orderings_Oorder(X1821) )
& ( X1820 != X1819
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1821,X1820),X1819))
| ~ class_Orderings_Oorder(X1821) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_909,plain,
! [X1813,X1814,X1815] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1815,X1814),X1813))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1815),X1814),X1813))
| ~ class_Orderings_Oorder(X1815) )
& ( X1814 != X1813
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1815),X1814),X1813))
| ~ class_Orderings_Oorder(X1815) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1815,X1814),X1813))
| X1814 = X1813
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1815),X1814),X1813))
| ~ class_Orderings_Oorder(X1815) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_910,plain,
! [X1840,X1841,X1842] :
( ~ class_Orderings_Opreorder(X1842)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1842),X1841),X1840))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1842,X1841),X1840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_911,plain,
! [X2372,X2373] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2373),X2372))),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_912,plain,
! [X2370,X2371] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2371),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2370),X2371))),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_913,plain,
! [X3035,X3036] : c_Set_Oimage(X3036,X3036,c_COMBI(X3036),X3035) = X3035,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_914,plain,
! [X2307,X2308] : c_Fun_Oinj__on(X2308,X2308,c_COMBI(X2308),X2307),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_915,plain,
! [X3041,X3042,X3043] : c_Nat_Onat_Onat__case(X3043,X3042,X3041,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3042,
inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).
fof(i_0_916,plain,
! [X1852,X1853,X1854] :
( ~ class_Orderings_Oorder(X1854)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1854,X1853),X1852))
| X1852 = X1853
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1854),X1853),X1852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_917,plain,
! [X1849,X1850,X1851] :
( ~ class_Orderings_Oorder(X1851)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1851,X1850),X1849))
| X1850 = X1849
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1851),X1850),X1849)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_918,plain,
! [X1846,X1847,X1848] :
( ~ class_Orderings_Oorder(X1848)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1848,X1847),X1846))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1848),X1847),X1846))
| X1847 = X1846 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_919,plain,
! [X1831,X1832,X1833] :
( ~ class_Orderings_Oorder(X1833)
| X1832 = X1831
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1833,X1832),X1831))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1833),X1832),X1831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_920,plain,
! [X1828,X1829,X1830] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1830,X1829),X1828))
| X1829 = X1828
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1830),X1829),X1828))
| ~ class_Orderings_Olinorder(X1830) )
& ( X1829 != X1828
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1830,X1829),X1828))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1830),X1829),X1828))
| ~ class_Orderings_Olinorder(X1830) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])])]) ).
fof(i_0_921,plain,
! [X1834,X1835,X1836] :
( ~ class_Orderings_Oorder(X1836)
| X1835 = X1834
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1836,X1834),X1835))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1836),X1834),X1835)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_922,plain,
! [X2771] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2771),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X2771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2771),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_923,plain,
! [X2766] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2766),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_924,plain,
! [X2291,X2292] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2292),X2291))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2291),X2292))
| X2292 = X2291 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_925,plain,
! [X1672,X1673,X1674] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1674),X1673),hAPP(c_fequal,X1672)))
| X1673 = X1672 )
& ( X1673 != X1672
| hBOOL(hAPP(hAPP(c_member(X1674),X1673),hAPP(c_fequal,X1672))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_926,plain,
! [X2754,X2755] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2755),X2754))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2755),hAPP(c_Nat_OSuc,X2754))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_927,plain,
! [X2672] :
( ~ class_Rings_Olinordered__semidom(X2672)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2672),c_Groups_Oone__class_Oone(X2672)),c_Groups_Ozero__class_Ozero(X2672))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])]) ).
fof(i_0_928,plain,
! [X2368,X2369] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2369),X2368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2369),X2368)) )
& ( X2369 != X2368
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2369),X2368)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2369),X2368))
| X2369 = X2368
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2369),X2368)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_929,plain,
! [X2366,X2367] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2367),X2366))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2367),X2366))
| X2367 = X2366 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2367),X2366))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2367),X2366)) )
& ( X2367 != X2366
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2367),X2366)) ) ),
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,
! [X2364,X2365] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2365),X2364))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2365),X2364)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_931,plain,
! [X2360,X2361] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2361),X2360))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2361),X2360)) )
& ( X2361 != X2360
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2361),X2360)) ) ),
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,
! [X1879,X1880] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1880),X1879))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1880),X1879)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_933,plain,
! [X2516,X2517,X2518] :
( ~ hBOOL(hAPP(hAPP(c_member(X2518),X2517),X2516))
| c_Set_Oinsert(X2518,X2517,X2516) = X2516 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_934,plain,
! [X1896,X1897,X1898] :
( ( X1897 = X1896
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1898),X1897),X1896))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1898),X1896),X1897))
| ~ class_Orderings_Olinorder(X1898) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1898),X1897),X1896))
| X1897 != X1896
| ~ class_Orderings_Olinorder(X1898) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1898),X1896),X1897))
| X1897 != X1896
| ~ class_Orderings_Olinorder(X1898) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_935,plain,
! [X2132,X2133,X2134] :
( ~ class_Rings_Olinordered__idom(X2134)
| X2133 = X2132
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2134),X2133),X2132))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2134),X2132),X2133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_936,plain,
! [X1959,X1960,X1961] :
( ~ class_Orderings_Olinorder(X1961)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1961),X1960),X1959))
| X1960 = X1959
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1961),X1959),X1960)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])]) ).
fof(i_0_937,plain,
! [X1908,X1909,X1910] :
( ~ class_Orderings_Olinorder(X1910)
| X1909 = X1908
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1910),X1909),X1908))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1910),X1908),X1909)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])]) ).
fof(i_0_938,plain,
! [X1905,X1906,X1907] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1907),X1905),X1906))
| X1905 = X1906
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1907),X1906),X1905))
| ~ class_Orderings_Olinorder(X1907) )
& ( X1905 != X1906
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1907),X1905),X1906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1907),X1906),X1905))
| ~ class_Orderings_Olinorder(X1907) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])])]) ).
fof(i_0_939,plain,
! [X1902,X1903,X1904] :
( ~ class_Orderings_Olinorder(X1904)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1904),X1903),X1902))
| X1903 = X1902
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1904),X1902),X1903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_940,plain,
! [X2464] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X2464),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2464),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2464,c_Orderings_Otop__class_Otop(tc_fun(X2464,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2464,c_Orderings_Otop__class_Otop(tc_fun(X2464,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X2464),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2464),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_941,plain,
! [X2362,X2363] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2363),X2362))
| X2363 = X2362
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2363),X2362)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_942,plain,
! [X2545,X2546,X2547] : c_Set_Oinsert(X2547,X2546,c_Set_Oinsert(X2547,X2546,X2545)) = c_Set_Oinsert(X2547,X2546,X2545),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
fof(i_0_943,plain,
! [X2412,X2413] : hBOOL(hAPP(hAPP(c_member(X2413),X2412),c_Orderings_Otop__class_Otop(tc_fun(X2413,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_944,plain,
! [X1656,X1657] : hBOOL(hAPP(hAPP(c_member(X1657),X1656),c_Orderings_Otop__class_Otop(tc_fun(X1657,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_945,plain,
! [X2506,X2507,X2508] :
( ( ~ c_Finite__Set_Ofinite(X2508,c_Set_Oinsert(X2508,X2507,X2506))
| c_Finite__Set_Ofinite(X2508,X2506) )
& ( ~ c_Finite__Set_Ofinite(X2508,X2506)
| c_Finite__Set_Ofinite(X2508,c_Set_Oinsert(X2508,X2507,X2506)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).
fof(i_0_946,plain,
! [X1675,X1676,X1677] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1677),X1676),X1675))
| hBOOL(hAPP(X1675,X1676)) )
& ( ~ hBOOL(hAPP(X1675,X1676))
| hBOOL(hAPP(hAPP(c_member(X1677),X1676),X1675)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_947,plain,
! [X1825,X1826,X1827] :
( ~ class_Orderings_Olinorder(X1827)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1827,X1826),X1825))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1827),X1825),X1826)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_948,plain,
! [X1810,X1811,X1812] :
( ~ class_Orderings_Olinorder(X1812)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1812,X1811),X1810))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1812),X1810),X1811)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_949,plain,
! [X1822,X1823,X1824] :
( ~ class_Orderings_Olinorder(X1824)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1824),X1823),X1822))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1824,X1822),X1823)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_950,plain,
! [X2743,X2744] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2744)),X2743) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2744),X2743)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_951,plain,
! [X2670] :
( ~ class_Rings_Olinordered__semidom(X2670)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2670,c_Groups_Oone__class_Oone(X2670)),c_Groups_Ozero__class_Ozero(X2670))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_952,plain,
! [X2374,X2375,X2377,X2378,X2379] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2375),X2374))
| X2374 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2375),esk24_2(X2374,X2375)) )
& ( X2377 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2378),X2379)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2378),X2377)) ) ),
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_953,plain,
! [X2266,X2267] :
( ( X2267 = X2266
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2267),X2266))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2266),X2267)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2267),X2266))
| X2267 != X2266 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2266),X2267))
| X2267 != X2266 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_954,plain,
! [X2264,X2265] :
( X2265 = X2264
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2265),X2264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2264),X2265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])]) ).
fof(i_0_955,plain,
! [X2767,X2769,X2770] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2767))
| X2767 = hAPP(c_Nat_OSuc,esk31_1(X2767)) )
& ( X2769 != hAPP(c_Nat_OSuc,X2770)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2769)) ) ),
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_956,plain,
! [X1923,X1924,X1925] :
( ~ class_Orderings_Oorder(X1925)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1925),X1924),X1923))
| X1923 != X1924 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_957,plain,
! [X1920,X1921,X1922] :
( ~ class_Orderings_Oorder(X1922)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1922),X1921),X1920))
| X1921 != X1920 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_958,plain,
! [X1911,X1912,X1913] :
( ~ class_Orderings_Oorder(X1913)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1913),X1912),X1911))
| X1912 != X1911 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_959,plain,
! [X2119,X2120,X2121] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2119,tc_HOL_Obool),X2121),X2120))
| X2121 != X2120 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2119,tc_HOL_Obool),X2120),X2121))
| X2121 != X2120 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])])]) ).
fof(i_0_960,plain,
! [X2088,X2089,X2090] :
( X2090 != X2089
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2088,tc_HOL_Obool),X2090),X2089)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_961,plain,
! [X2091,X2092,X2093] :
( X2093 != X2092
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2091,tc_HOL_Obool),X2092),X2093)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_962,plain,
! [X1894,X1895] :
( ~ class_Orderings_Opreorder(X1895)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1895),X1894),X1894)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).
fof(i_0_963,plain,
! [X2073,X2074] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2074,tc_HOL_Obool),X2073),X2073)),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_964,plain,
! [X2608] :
( ( X2608 = 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)),X2608)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2608))
| X2608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_965,plain,
! [X2147,X2148,X2149,X2150] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2150),X2149),X2148) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2150),X2147),X2148)
| X2149 = X2147
| ~ class_Groups_Ocancel__semigroup__add(X2150) )
& ( X2149 != X2147
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2150),X2149),X2148) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2150),X2147),X2148)
| ~ class_Groups_Ocancel__semigroup__add(X2150) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_966,plain,
! [X2135,X2136,X2137,X2138] :
( ~ class_Groups_Ocancel__semigroup__add(X2138)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2138),X2137),X2136) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2138),X2135),X2136)
| X2137 = X2135 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_967,plain,
! [X2139,X2140,X2141,X2142] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X2142)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2142),X2141),X2140) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2142),X2141),X2139)
| X2140 = X2139 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_968,plain,
! [X2151,X2152,X2153,X2154] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),X2153),X2152) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),X2153),X2151)
| X2152 = X2151
| ~ class_Groups_Ocancel__semigroup__add(X2154) )
& ( X2152 != X2151
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),X2153),X2152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2154),X2153),X2151)
| ~ class_Groups_Ocancel__semigroup__add(X2154) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_969,plain,
! [X2143,X2144,X2145,X2146] :
( ~ class_Groups_Ocancel__semigroup__add(X2146)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2146),X2145),X2144) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2146),X2145),X2143)
| X2144 = X2143 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_970,plain,
! [X1795,X1796,X1797] :
( ~ class_Orderings_Olinorder(X1797)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1797,X1796),X1795))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1797,X1795),X1796)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_971,plain,
! [X1743,X1744,X1745] :
( ~ class_Orderings_Olinorder(X1745)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1745,X1744),X1743))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1745,X1743),X1744)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_573])]) ).
fof(i_0_972,plain,
! [X2741,X2742] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2742),hAPP(c_Nat_OSuc,X2741)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2742),X2741)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_973,plain,
! [X2745,X2746] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2746)),X2745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2746),hAPP(c_Nat_OSuc,X2745)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_974,plain,
! [X2609] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2609),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_574]) ).
fof(i_0_975,plain,
! [X2607] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2607),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_575]) ).
fof(i_0_976,plain,
! [X2605] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2605),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_576]) ).
fof(i_0_977,plain,
! [X2847] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2847)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2847)),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_978,plain,
! [X2610,X2611] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2611),X2610))
| X2610 != 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_979,plain,
! [X2284,X2285] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2285),X2284))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2284),X2285)) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_980,plain,
! [X2711] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2711))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_981,plain,
! [X2261,X2262] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2262),X2261))
| X2261 != X2262 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_982,plain,
! [X2259,X2260] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2260),X2259))
| X2260 != X2259 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_983,plain,
! [X2673] :
( ~ class_Rings_Olinordered__semidom(X2673)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2673),c_Groups_Ozero__class_Ozero(X2673)),c_Groups_Oone__class_Oone(X2673))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_984,plain,
! [X2855] :
( ~ class_Rings_Oring__1(X2855)
| hBOOL(hAPP(hAPP(c_member(X2855),c_Groups_Ozero__class_Ozero(X2855)),c_Int_Oring__1__class_OInts(X2855))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).
fof(i_0_985,plain,
! [X2859] :
( ~ class_Rings_Oring__1(X2859)
| hBOOL(hAPP(hAPP(c_member(X2859),c_Groups_Oone__class_Oone(X2859)),c_Int_Oring__1__class_OInts(X2859))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).
fof(i_0_986,plain,
! [X2268] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2268),X2268)),
inference(variable_rename,[status(thm)],[i_0_577]) ).
fof(i_0_987,plain,
! [X2263] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2263),X2263)),
inference(variable_rename,[status(thm)],[i_0_578]) ).
fof(i_0_988,plain,
! [X2280,X2281,X2282] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2282),X2281) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2280),X2281)
| X2282 = X2280 )
& ( X2282 != X2280
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2282),X2281) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2280),X2281) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_989,plain,
! [X2277,X2278,X2279] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2279),X2278) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2279),X2277)
| X2278 = X2277 )
& ( X2278 != X2277
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2279),X2278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2279),X2277) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_990,plain,
! [X2495,X2496,X2497] :
( ~ c_Finite__Set_Ofinite(X2497,X2496)
| c_Finite__Set_Ofinite(X2497,c_Set_Oinsert(X2497,X2495,X2496)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).
fof(i_0_991,plain,
! [X2710] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2710),hAPP(c_Nat_OSuc,X2710))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_992,plain,
! [X1654,X1655] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1655,tc_HOL_Obool)),X1654)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_993,plain,
! [X2619] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2619),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X2619 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2619 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2619),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_994,plain,
! [X2780,X2781] :
( ( X2781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2781 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2781),X2780) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2780 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2781 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2781),X2780) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2781),X2780) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2780 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2781),X2780) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2781 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2781),X2780) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2781 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2780 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2781),X2780) = 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_995,plain,
! [X2778,X2779] :
( ( X2779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2779 = 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),X2779),X2778) )
& ( X2778 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2779 = 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),X2779),X2778) )
& ( X2779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2778 = 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),X2779),X2778) )
& ( X2778 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2778 = 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),X2779),X2778) )
& ( X2779 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2778 != 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),X2779),X2778) )
& ( X2779 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2778 != 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),X2779),X2778) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_996,plain,
! [X1603,X1604] :
( hAPP(X1604,esk1_2(X1603,X1604)) != hAPP(X1603,esk1_2(X1603,X1604))
| X1604 = X1603 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_997,plain,
! [X2671] :
( ~ class_Rings_Olinordered__semidom(X2671)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2671,c_Groups_Ozero__class_Ozero(X2671)),c_Groups_Oone__class_Oone(X2671))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_998,plain,
! [X3181,X3182] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X3182),X3181))
| X3182 = X3181 ),
inference(variable_rename,[status(thm)],[i_0_579]) ).
fof(i_0_999,plain,
! [X3123,X3124] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3124,X3123)),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).
fof(i_0_1000,plain,
! [X2846] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X2846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X2846)),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_1001,plain,
! [X2828,X2829,X2830] :
( ~ class_Rings_Ocomm__semiring__1(X2830)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2830),X2829),X2828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2830),X2828),X2829) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_1002,plain,
! [X2612] :
( X2612 = 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)),X2612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_1003,plain,
! [X1871,X1872] :
( ~ class_Orderings_Otop(X1872)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1872,X1871),c_Orderings_Otop__class_Otop(X1872))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_1004,plain,
! [X2837,X2838] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2838),X2837),X2837) != c_Groups_Ozero__class_Ozero(X2838)
| X2837 = c_Groups_Ozero__class_Ozero(X2838)
| ~ class_Groups_Olinordered__ab__group__add(X2838) )
& ( X2837 != c_Groups_Ozero__class_Ozero(X2838)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2838),X2837),X2837) = c_Groups_Ozero__class_Ozero(X2838)
| ~ class_Groups_Olinordered__ab__group__add(X2838) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_1005,plain,
! [X2629,X2630] :
( ( c_Groups_Ozero__class_Ozero(X2630) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2630),X2629),X2629)
| X2629 = c_Groups_Ozero__class_Ozero(X2630)
| ~ class_Groups_Olinordered__ab__group__add(X2630) )
& ( X2629 != c_Groups_Ozero__class_Ozero(X2630)
| c_Groups_Ozero__class_Ozero(X2630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2630),X2629),X2629)
| ~ class_Groups_Olinordered__ab__group__add(X2630) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_1006,plain,
! [X2839,X2840,X2841] :
( ( X2840 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2841),X2840),X2839)
| X2839 = c_Groups_Ozero__class_Ozero(X2841)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2841) )
& ( X2839 != c_Groups_Ozero__class_Ozero(X2841)
| X2840 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2841),X2840),X2839)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2841) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_1007,plain,
! [X1789,X1790,X1791] :
( ~ class_Orderings_Opreorder(X1791)
| X1790 != X1789
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1791,X1790),X1789)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1008,plain,
! [X3159,X3160,X3161,X3162] : hAPP(hAPP(c_COMBK(X3162,X3161),X3160),X3159) = X3160,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_1009,plain,
! [X2269,X2270] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2270),X2269) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2269),X2270),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_1010,plain,
! [X1735,X1736] :
( ~ class_Orderings_Opreorder(X1736)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1736,X1735),X1735)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1011,plain,
! [X2620] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2620)),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_1012,plain,
! [X2606] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2606)),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_1013,plain,
! [X1719,X1720,X1721] :
( ~ class_Orderings_Otop(X1721)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1720,X1721)),X1719) = c_Orderings_Otop__class_Otop(X1721) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_1014,plain,
! [X2615,X2616] :
( ( X2616 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2616),X2615) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2615 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2616),X2615) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2616 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2615 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2616),X2615) = 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_1015,plain,
! [X2286,X2287] :
( X2287 != X2286
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2287),X2286)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1016,plain,
! [X3183,X3184] :
( X3184 != X3183
| hBOOL(hAPP(hAPP(c_fequal,X3184),X3183)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1017,plain,
! [X2613,X2614] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2614),X2613) != X2614
| X2613 = 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_1018,plain,
! [X2283] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2283),X2283)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1019,plain,
! [X2459] :
( ~ class_Finite__Set_Ofinite(X2459)
| c_Finite__Set_Ofinite(X2459,c_Orderings_Otop__class_Otop(tc_fun(X2459,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_1020,plain,
! [X2706,X2707] :
( ~ class_Rings_Ocomm__semiring__1(X2707)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2707),c_Groups_Ozero__class_Ozero(X2707)),X2706) = X2706 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_1021,plain,
! [X2627,X2628] :
( ~ class_Groups_Ocomm__monoid__add(X2628)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2628),c_Groups_Ozero__class_Ozero(X2628)),X2627) = X2627 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_1022,plain,
! [X2625,X2626] :
( ~ class_Groups_Omonoid__add(X2626)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2626),c_Groups_Ozero__class_Ozero(X2626)),X2625) = X2625 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_1023,plain,
! [X2842,X2843] :
( ~ class_Rings_Ocomm__semiring__1(X2843)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2843),X2842),c_Groups_Ozero__class_Ozero(X2843)) = X2842 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_1024,plain,
! [X2633,X2634] :
( ~ class_Groups_Ocomm__monoid__add(X2634)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2634),X2633),c_Groups_Ozero__class_Ozero(X2634)) = X2633 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_1025,plain,
! [X2631,X2632] :
( ~ class_Groups_Omonoid__add(X2632)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2632),X2631),c_Groups_Ozero__class_Ozero(X2632)) = X2631 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_1026,plain,
! [X2844] : hAPP(c_Nat_OSuc,X2844) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2844),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1027,plain,
! [X2845] : hAPP(c_Nat_OSuc,X2845) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2845),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1028,plain,
! [X2618] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2618) = X2618,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_1029,plain,
! [X2806] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2806) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2806)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(i_0_1030,plain,
! [X2617] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2617),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2617,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_1031,plain,
! [X3152,X3153] :
( ~ class_Finite__Set_Ofinite(X3153)
| ~ class_Finite__Set_Ofinite(X3152)
| class_Finite__Set_Ofinite(tc_sum(X3153,X3152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_1032,plain,
! [X3144,X3145] :
( ~ class_Finite__Set_Ofinite(X3145)
| ~ class_Finite__Set_Ofinite(X3144)
| class_Finite__Set_Ofinite(tc_fun(X3145,X3144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_1033,plain,
! [X3155,X3156] :
( ~ class_Finite__Set_Ofinite(X3156)
| ~ class_Finite__Set_Ofinite(X3155)
| class_Finite__Set_Ofinite(tc_prod(X3156,X3155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_1034,plain,
! [X2764,X2765] :
( hAPP(c_Nat_OSuc,X2765) != hAPP(c_Nat_OSuc,X2764)
| X2765 = X2764 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1035,plain,
! [X2762,X2763] :
( ( hAPP(c_Nat_OSuc,X2763) != hAPP(c_Nat_OSuc,X2762)
| X2763 = X2762 )
& ( X2763 != X2762
| hAPP(c_Nat_OSuc,X2763) = hAPP(c_Nat_OSuc,X2762) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1036,plain,
! [X3146,X3147] :
( ~ class_Orderings_Oorder(X3147)
| class_Orderings_Oorder(tc_fun(X3146,X3147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1037,plain,
! [X3150,X3151] :
( ~ class_Orderings_Oord(X3151)
| class_Orderings_Oord(tc_fun(X3150,X3151)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1038,plain,
! [X3142,X3143] :
( ~ class_Orderings_Opreorder(X3143)
| class_Orderings_Opreorder(tc_fun(X3142,X3143)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1039,plain,
! [X3148,X3149] :
( ~ class_Orderings_Otop(X3149)
| class_Orderings_Otop(tc_fun(X3148,X3149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_1040,plain,
! [X2676,X2677] :
( c_Finite__Set_Ofinite(X2677,X2676)
| c_Finite__Set_Ocard(X2677,X2676) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_580])]) ).
fof(i_0_1041,plain,
! [X2715] : hAPP(c_Nat_OSuc,X2715) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1042,plain,
! [X2714] : hAPP(c_Nat_OSuc,X2714) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1043,plain,
! [X2712] : hAPP(c_Nat_OSuc,X2712) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1044,plain,
! [X2717] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2717),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1045,plain,
! [X2716] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2716),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1046,plain,
! [X2713] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2713),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1047,plain,
! [X2451,X2452] :
( ~ class_Finite__Set_Ofinite(X2452)
| c_Finite__Set_Ofinite(X2452,X2451) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_1048,plain,
! [X2449,X2450] :
( ~ class_Finite__Set_Ofinite(X2450)
| c_Finite__Set_Ofinite(X2450,X2449) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(i_0_1049,plain,
! [X2761] : hAPP(c_Nat_OSuc,X2761) != X2761,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1050,plain,
! [X2760] : X2760 != hAPP(c_Nat_OSuc,X2760),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1051,plain,
! [X3157,X3158] : hAPP(c_COMBI(X3158),X3157) = X3157,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1052,plain,
! [X2624] :
( ~ class_Rings_Ozero__neq__one(X2624)
| c_Groups_Ozero__class_Ozero(X2624) != c_Groups_Oone__class_Oone(X2624) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_1053,plain,
! [X2623] :
( ~ class_Rings_Ozero__neq__one(X2623)
| c_Groups_Oone__class_Oone(X2623) != c_Groups_Ozero__class_Ozero(X2623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_1054,plain,
! [X3154] :
( ~ class_Finite__Set_Ofinite(X3154)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X3154)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_1055,plain,
! [X2848] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X2848) = X2848,
inference(variable_rename,[status(thm)],[fact_nat__size]) ).
fof(i_0_1056,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
cnf(i_0_1057,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
inference(split_conjunct,[status(thm)],[i_0_581]),
[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_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
inference(split_conjunct,[status(thm)],[i_0_582]),
[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_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_581]),
[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_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))) ),
inference(split_conjunct,[status(thm)],[i_0_582]),
[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_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_583]),
[final] ).
cnf(i_0_1062,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_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_584]),
[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_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_583]),
[final] ).
cnf(i_0_1064,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_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_e____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))),
inference(split_conjunct,[status(thm)],[fact__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_096]),
[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_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))),
inference(split_conjunct,[status(thm)],[fact__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ae_096]),
[final] ).
cnf(i_0_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),esk17_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
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),esk14_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_586]),
[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____)))),
inference(split_conjunct,[status(thm)],[fact_n_I3_J]),
[final] ).
cnf(i_0_1070,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_587]),
[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_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),esk17_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_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),esk14_0)) ),
inference(split_conjunct,[status(thm)],[i_0_586]),
[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_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_588]),
[final] ).
cnf(i_0_1074,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_589]),
[final] ).
cnf(i_0_1075,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_589]),
[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),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_590]),
[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),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_590]),
[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),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_591]),
[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),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_592]),
[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),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_592]),
[final] ).
cnf(i_0_1081,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_593]),
[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),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_590]),
[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),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_590]),
[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),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_591]),
[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),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_592]),
[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),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_592]),
[final] ).
cnf(i_0_1087,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,esk29_5(X3,X2,X1,X4,X5))),hAPP(X3,esk29_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1088,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,esk30_5(X3,X2,X1,X4,X5))),hAPP(X3,esk30_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[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),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,esk8_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,esk8_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_596]),
[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),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,esk8_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,esk8_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_596]),
[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),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_597]),
[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),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_597]),
[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),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,esk8_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,esk8_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_596]),
[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),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,esk8_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,esk8_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_596]),
[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),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_597]),
[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),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_597]),
[final] ).
cnf(i_0_1097,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),esk19_2(X1,X2)),esk20_2(X1,X2))),hAPP(X2,esk18_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_598]),
[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),esk19_2(X1,X2)),esk20_2(X1,X2))),hAPP(esk18_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_598]),
[final] ).
cnf(i_0_1099,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_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_598]),
[final] ).
cnf(i_0_1100,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk19_2(X1,X2) != esk20_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_598]),
[final] ).
cnf(i_0_1101,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_599]),
[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),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_600]),
[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),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_600]),
[final] ).
cnf(i_0_1104,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_601]),
[final] ).
cnf(i_0_1105,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_599]),
[final] ).
cnf(i_0_1106,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk29_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_594]),
[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),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_600]),
[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),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_600]),
[final] ).
cnf(i_0_1109,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk39_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_602]),
[final] ).
cnf(i_0_1110,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk30_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_595]),
[final] ).
cnf(i_0_1111,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_603]),
[final] ).
cnf(i_0_1112,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_1113,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_599]),
[final] ).
cnf(i_0_1114,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_599]),
[final] ).
cnf(i_0_1115,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,esk13_4(X3,X2,X4,X1))),hAPP(X3,esk13_4(X3,X2,X4,X1))))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1116,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_605]),
[final] ).
cnf(i_0_1117,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_606]),
[final] ).
cnf(i_0_1118,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_607]),
[final] ).
cnf(i_0_1119,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_608]),
[final] ).
cnf(i_0_1120,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_609]),
[final] ).
cnf(i_0_1121,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_610]),
[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),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,esk25_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1123,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_612]),
[final] ).
cnf(i_0_1124,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_612]),
[final] ).
cnf(i_0_1125,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1126,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1127,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_613]),
[final] ).
cnf(i_0_1128,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_614]),
[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),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_615]),
[final] ).
cnf(i_0_1130,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_616]),
[final] ).
cnf(i_0_1131,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk41_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_617]),
[final] ).
cnf(i_0_1132,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_618]),
[final] ).
cnf(i_0_1133,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_619]),
[final] ).
cnf(i_0_1134,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_620]),
[final] ).
cnf(i_0_1135,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_621]),
[final] ).
cnf(i_0_1136,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_612]),
[final] ).
cnf(i_0_1137,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_622]),
[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),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_612]),
[final] ).
cnf(i_0_1139,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_612]),
[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),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_1141,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_623]),
[final] ).
cnf(i_0_1142,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_612]),
[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),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hAPP(v_h____,X1) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1144,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_624]),
[final] ).
cnf(i_0_1145,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_615]),
[final] ).
cnf(i_0_1146,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,X1) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1147,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
inference(cn,[status(thm)],[i_0_625]),
[final] ).
cnf(i_0_1148,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_626]),
[final] ).
cnf(i_0_1149,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_615]),
[final] ).
cnf(i_0_1150,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_612]),
[final] ).
cnf(i_0_1151,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_624]),
[final] ).
cnf(i_0_1152,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_627]),
[final] ).
cnf(i_0_1153,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_618]),
[final] ).
cnf(i_0_1154,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_618]),
[final] ).
cnf(i_0_1155,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_618]),
[final] ).
cnf(i_0_1156,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_618]),
[final] ).
cnf(i_0_1157,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_612]),
[final] ).
cnf(i_0_1158,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_619]),
[final] ).
cnf(i_0_1159,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_619]),
[final] ).
cnf(i_0_1160,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_619]),
[final] ).
cnf(i_0_1161,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_619]),
[final] ).
cnf(i_0_1162,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,X1) = v_n____
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1163,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,X1) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1164,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_614]),
[final] ).
cnf(i_0_1165,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_615]),
[final] ).
cnf(i_0_1166,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk39_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_602]),
[final] ).
cnf(i_0_1167,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hAPP(v_h____,X1) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1168,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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_612]),
[final] ).
cnf(i_0_1169,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_628]),
[final] ).
cnf(i_0_1170,plain,
( X1 = hAPP(X2,esk36_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_629]),
[final] ).
cnf(i_0_1171,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_630]),
[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_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1173,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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_612]),
[final] ).
cnf(i_0_1174,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_631]),
[final] ).
cnf(i_0_1175,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_612]),
[final] ).
cnf(i_0_1176,plain,
( hAPP(v_h____,X1) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1177,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_612]),
[final] ).
cnf(i_0_1178,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_617]),
[final] ).
cnf(i_0_1179,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_632]),
[final] ).
cnf(i_0_1180,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_633]),
[final] ).
cnf(i_0_1181,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_623]),
[final] ).
cnf(i_0_1182,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_612]),
[final] ).
cnf(i_0_1183,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_634]),
[final] ).
cnf(i_0_1184,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_618]),
[final] ).
cnf(i_0_1185,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_618]),
[final] ).
cnf(i_0_1186,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_618]),
[final] ).
cnf(i_0_1187,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_635]),
[final] ).
cnf(i_0_1188,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_636]),
[final] ).
cnf(i_0_1189,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_637]),
[final] ).
cnf(i_0_1190,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_624]),
[final] ).
cnf(i_0_1191,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)))))
| esk36_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_629]),
[final] ).
cnf(i_0_1192,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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_612]),
[final] ).
cnf(i_0_1193,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_638]),
[final] ).
cnf(i_0_1194,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_618]),
[final] ).
cnf(i_0_1195,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_618]),
[final] ).
cnf(i_0_1196,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_618]),
[final] ).
cnf(i_0_1197,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_618]),
[final] ).
cnf(i_0_1198,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_618]),
[final] ).
cnf(i_0_1199,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_619]),
[final] ).
cnf(i_0_1200,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_639]),
[final] ).
cnf(i_0_1201,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_619]),
[final] ).
cnf(i_0_1202,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_619]),
[final] ).
cnf(i_0_1203,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_612]),
[final] ).
cnf(i_0_1204,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_615]),
[final] ).
cnf(i_0_1205,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_640]),
[final] ).
cnf(i_0_1206,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),esk11_1(X1)),esk12_1(X1))),hAPP(X1,esk9_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),esk11_1(X1)),esk12_1(X1))),hAPP(X1,esk10_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1207,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_641]),
[final] ).
cnf(i_0_1208,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,X1) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
inference(cn,[status(thm)],[i_0_642]),
[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_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_612]),
[final] ).
cnf(i_0_1210,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_619]),
[final] ).
cnf(i_0_1211,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_619]),
[final] ).
cnf(i_0_1212,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_619]),
[final] ).
cnf(i_0_1213,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_619]),
[final] ).
cnf(i_0_1214,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_619]),
[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_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_612]),
[final] ).
cnf(i_0_1216,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_1217,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_612]),
[final] ).
cnf(i_0_1218,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_612]),
[final] ).
cnf(i_0_1219,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_612]),
[final] ).
cnf(i_0_1220,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_612]),
[final] ).
cnf(i_0_1221,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_1222,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_612]),
[final] ).
cnf(i_0_1223,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_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_615]),
[final] ).
cnf(i_0_1224,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____)))
| hAPP(v_h____,X1) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ),
inference(cn,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1225,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_612]),
[final] ).
cnf(i_0_1226,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_615]),
[final] ).
cnf(i_0_1227,plain,
( X1 = hAPP(X2,esk35_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_629]),
[final] ).
cnf(i_0_1228,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____))) ),
inference(cn,[status(thm)],[i_0_646]),
[final] ).
cnf(i_0_1229,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_615]),
[final] ).
cnf(i_0_1230,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_628]),
[final] ).
cnf(i_0_1231,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_647]),
[final] ).
cnf(i_0_1232,plain,
( hAPP(v_h____,X1) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
inference(cn,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1233,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_618]),
[final] ).
cnf(i_0_1234,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_615]),
[final] ).
cnf(i_0_1235,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1)),esk12_1(X1))),hAPP(esk10_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),esk11_1(X1)),esk12_1(X1))),hAPP(esk9_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1236,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1)),esk12_1(X1))),hAPP(esk9_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),esk11_1(X1)),esk12_1(X1))),hAPP(esk10_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1237,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_647]),
[final] ).
cnf(i_0_1238,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)) ),
inference(cn,[status(thm)],[i_0_649]),
[final] ).
cnf(i_0_1239,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_615]),
[final] ).
cnf(i_0_1240,plain,
( X3 = esk35_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_629]),
[final] ).
cnf(i_0_1241,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_650]),
[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),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_635]),
[final] ).
cnf(i_0_1243,plain,
( hAPP(v_h____,X1) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)) ),
inference(cn,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1244,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_619]),
[final] ).
cnf(i_0_1245,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),esk37_3(X1,X3,X2))) != esk37_3(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1246,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk2_2(X2,X1)),esk2_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1247,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_654]),
[final] ).
cnf(i_0_1248,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_655]),
[final] ).
cnf(i_0_1249,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_656]),
[final] ).
cnf(i_0_1250,plain,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_657]),
[final] ).
cnf(i_0_1251,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_658]),
[final] ).
cnf(i_0_1252,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_659]),
[final] ).
cnf(i_0_1253,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_660]),
[final] ).
cnf(i_0_1254,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_661]),
[final] ).
cnf(i_0_1255,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_656]),
[final] ).
cnf(i_0_1256,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_655]),
[final] ).
cnf(i_0_1257,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_655]),
[final] ).
cnf(i_0_1258,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_656]),
[final] ).
cnf(i_0_1259,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_662]),
[final] ).
cnf(i_0_1260,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk22_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_663]),
[final] ).
cnf(i_0_1261,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk21_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_663]),
[final] ).
cnf(i_0_1262,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk11_1(X1)),esk12_1(X1))),hAPP(X1,esk9_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),esk11_1(X1)),esk12_1(X1))),hAPP(X1,esk10_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1263,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_664]),
[final] ).
cnf(i_0_1264,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_634]),
[final] ).
cnf(i_0_1265,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_618]),
[final] ).
cnf(i_0_1266,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_665]),
[final] ).
cnf(i_0_1267,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_666]),
[final] ).
cnf(i_0_1268,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_667]),
[final] ).
cnf(i_0_1269,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_619]),
[final] ).
cnf(i_0_1270,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_668]),
[final] ).
cnf(i_0_1271,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_669]),
[final] ).
cnf(i_0_1272,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_670]),
[final] ).
cnf(i_0_1273,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_671]),
[final] ).
cnf(i_0_1274,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_672]),
[final] ).
cnf(i_0_1275,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_673]),
[final] ).
cnf(i_0_1276,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_674]),
[final] ).
cnf(i_0_1277,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_675]),
[final] ).
cnf(i_0_1278,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_676]),
[final] ).
cnf(i_0_1279,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_660]),
[final] ).
cnf(i_0_1280,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_602]),
[final] ).
cnf(i_0_1281,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_677]),
[final] ).
cnf(i_0_1282,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_678]),
[final] ).
cnf(i_0_1283,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),esk27_1(X1)),esk28_1(X1))),hAPP(X1,esk26_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1284,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_652]),
[final] ).
cnf(i_0_1285,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_679]),
[final] ).
cnf(i_0_1286,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_680]),
[final] ).
cnf(i_0_1287,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_655]),
[final] ).
cnf(i_0_1288,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_656]),
[final] ).
cnf(i_0_1289,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_656]),
[final] ).
cnf(i_0_1290,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_655]),
[final] ).
cnf(i_0_1291,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_672]),
[final] ).
cnf(i_0_1292,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_681]),
[final] ).
cnf(i_0_1293,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))),esk23_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_667]),
[final] ).
cnf(i_0_1294,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_682]),
[final] ).
cnf(i_0_1295,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_683]),
[final] ).
cnf(i_0_1296,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_684]),
[final] ).
cnf(i_0_1297,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_1298,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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_686]),
[final] ).
cnf(i_0_1299,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_687]),
[final] ).
cnf(i_0_1300,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))),esk26_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1301,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))),esk10_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1302,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))),esk9_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1303,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_688]),
[final] ).
cnf(i_0_1304,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_634]),
[final] ).
cnf(i_0_1305,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_689]),
[final] ).
cnf(i_0_1306,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_1307,plain,
( hAPP(X1,esk21_4(X2,X1,X3,X4)) = hAPP(X1,esk22_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_663]),
[final] ).
cnf(i_0_1308,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_690]),
[final] ).
cnf(i_0_1309,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_691]),
[final] ).
cnf(i_0_1310,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_692]),
[final] ).
cnf(i_0_1311,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_693]),
[final] ).
cnf(i_0_1312,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_694]),
[final] ).
cnf(i_0_1313,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_695]),
[final] ).
cnf(i_0_1314,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_696]),
[final] ).
cnf(i_0_1315,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_697]),
[final] ).
cnf(i_0_1316,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_698]),
[final] ).
cnf(i_0_1317,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_699]),
[final] ).
cnf(i_0_1318,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_700]),
[final] ).
cnf(i_0_1319,plain,
( c_Fun_Oinj__on(X1,X2,esk41_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_617]),
[final] ).
cnf(i_0_1320,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk27_1(X1)),esk28_1(X1))),hAPP(esk26_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1321,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_701]),
[final] ).
cnf(i_0_1322,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_702]),
[final] ).
cnf(i_0_1323,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_703]),
[final] ).
cnf(i_0_1324,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_704]),
[final] ).
cnf(i_0_1325,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_705]),
[final] ).
cnf(i_0_1326,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_706]),
[final] ).
cnf(i_0_1327,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_707]),
[final] ).
cnf(i_0_1328,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_708]),
[final] ).
cnf(i_0_1329,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_709]),
[final] ).
cnf(i_0_1330,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_710]),
[final] ).
cnf(i_0_1331,plain,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_711]),
[final] ).
cnf(i_0_1332,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1333,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_712]),
[final] ).
cnf(i_0_1334,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_713]),
[final] ).
cnf(i_0_1335,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_701]),
[final] ).
cnf(i_0_1336,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_655]),
[final] ).
cnf(i_0_1337,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_656]),
[final] ).
cnf(i_0_1338,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_714]),
[final] ).
cnf(i_0_1339,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_701]),
[final] ).
cnf(i_0_1340,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk21_4(X1,X2,X3,X4) != esk22_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_663]),
[final] ).
cnf(i_0_1341,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_715]),
[final] ).
cnf(i_0_1342,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_716]),
[final] ).
cnf(i_0_1343,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_717]),
[final] ).
cnf(i_0_1344,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_718]),
[final] ).
cnf(i_0_1345,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_1346,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_719]),
[final] ).
cnf(i_0_1347,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_720]),
[final] ).
cnf(i_0_1348,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_721]),
[final] ).
cnf(i_0_1349,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_722]),
[final] ).
cnf(i_0_1350,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_723]),
[final] ).
cnf(i_0_1351,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_724]),
[final] ).
cnf(i_0_1352,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_709]),
[final] ).
cnf(i_0_1353,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_725]),
[final] ).
cnf(i_0_1354,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_726]),
[final] ).
cnf(i_0_1355,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_727]),
[final] ).
cnf(i_0_1356,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_728]),
[final] ).
cnf(i_0_1357,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_729]),
[final] ).
cnf(i_0_1358,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_730]),
[final] ).
cnf(i_0_1359,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_731]),
[final] ).
cnf(i_0_1360,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_732]),
[final] ).
cnf(i_0_1361,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_692]),
[final] ).
cnf(i_0_1362,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_733]),
[final] ).
cnf(i_0_1363,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_694]),
[final] ).
cnf(i_0_1364,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_734]),
[final] ).
cnf(i_0_1365,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_735]),
[final] ).
cnf(i_0_1366,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_736]),
[final] ).
cnf(i_0_1367,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_737]),
[final] ).
cnf(i_0_1368,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_738]),
[final] ).
cnf(i_0_1369,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_739]),
[final] ).
cnf(i_0_1370,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk15_0)),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_1371,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_1372,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk16_0)),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1373,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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_1374,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_742]),
[final] ).
cnf(i_0_1375,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_742]),
[final] ).
cnf(i_0_1376,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_743]),
[final] ).
cnf(i_0_1377,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_744]),
[final] ).
cnf(i_0_1378,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_745]),
[final] ).
cnf(i_0_1379,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_697]),
[final] ).
cnf(i_0_1380,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_746]),
[final] ).
cnf(i_0_1381,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_699]),
[final] ).
cnf(i_0_1382,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_747]),
[final] ).
cnf(i_0_1383,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_748]),
[final] ).
cnf(i_0_1384,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_719]),
[final] ).
cnf(i_0_1385,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_749]),
[final] ).
cnf(i_0_1386,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_749]),
[final] ).
cnf(i_0_1387,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_750]),
[final] ).
cnf(i_0_1388,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_751]),
[final] ).
cnf(i_0_1389,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_752]),
[final] ).
cnf(i_0_1390,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_705]),
[final] ).
cnf(i_0_1391,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_753]),
[final] ).
cnf(i_0_1392,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_754]),
[final] ).
cnf(i_0_1393,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_755]),
[final] ).
cnf(i_0_1394,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_663]),
[final] ).
cnf(i_0_1395,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_736]),
[final] ).
cnf(i_0_1396,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_756]),
[final] ).
cnf(i_0_1397,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_756]),
[final] ).
cnf(i_0_1398,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_757]),
[final] ).
cnf(i_0_1399,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_758]),
[final] ).
cnf(i_0_1400,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_759]),
[final] ).
cnf(i_0_1401,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_760]),
[final] ).
cnf(i_0_1402,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_714]),
[final] ).
cnf(i_0_1403,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_761]),
[final] ).
cnf(i_0_1404,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_762]),
[final] ).
cnf(i_0_1405,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_763]),
[final] ).
cnf(i_0_1406,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_764]),
[final] ).
cnf(i_0_1407,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_723]),
[final] ).
cnf(i_0_1408,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_724]),
[final] ).
cnf(i_0_1409,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_765]),
[final] ).
cnf(i_0_1410,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_766]),
[final] ).
cnf(i_0_1411,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_767]),
[final] ).
cnf(i_0_1412,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_768]),
[final] ).
cnf(i_0_1413,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_769]),
[final] ).
cnf(i_0_1414,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_770]),
[final] ).
cnf(i_0_1415,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_771]),
[final] ).
cnf(i_0_1416,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_772]),
[final] ).
cnf(i_0_1417,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_749]),
[final] ).
cnf(i_0_1418,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_773]),
[final] ).
cnf(i_0_1419,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_774]),
[final] ).
cnf(i_0_1420,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_775]),
[final] ).
cnf(i_0_1421,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_776]),
[final] ).
cnf(i_0_1422,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_777]),
[final] ).
cnf(i_0_1423,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_778]),
[final] ).
cnf(i_0_1424,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_735]),
[final] ).
cnf(i_0_1425,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_779]),
[final] ).
cnf(i_0_1426,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_780]),
[final] ).
cnf(i_0_1427,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_781]),
[final] ).
cnf(i_0_1428,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_782]),
[final] ).
cnf(i_0_1429,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_783]),
[final] ).
cnf(i_0_1430,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_784]),
[final] ).
cnf(i_0_1431,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_785]),
[final] ).
cnf(i_0_1432,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_786]),
[final] ).
cnf(i_0_1433,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_787]),
[final] ).
cnf(i_0_1434,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_788]),
[final] ).
cnf(i_0_1435,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk16_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1436,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk15_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_1437,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_1438,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_1439,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_789]),
[final] ).
cnf(i_0_1440,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_790]),
[final] ).
cnf(i_0_1441,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_791]),
[final] ).
cnf(i_0_1442,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_742]),
[final] ).
cnf(i_0_1443,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_783]),
[final] ).
cnf(i_0_1444,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_784]),
[final] ).
cnf(i_0_1445,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1446,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_770]),
[final] ).
cnf(i_0_1447,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_770]),
[final] ).
cnf(i_0_1448,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_775]),
[final] ).
cnf(i_0_1449,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_793]),
[final] ).
cnf(i_0_1450,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_794]),
[final] ).
cnf(i_0_1451,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_795]),
[final] ).
cnf(i_0_1452,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_796]),
[final] ).
cnf(i_0_1453,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_797]),
[final] ).
cnf(i_0_1454,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_798]),
[final] ).
cnf(i_0_1455,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_799]),
[final] ).
cnf(i_0_1456,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_800]),
[final] ).
cnf(i_0_1457,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_604]),
[final] ).
cnf(i_0_1458,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_801]),
[final] ).
cnf(i_0_1459,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_802]),
[final] ).
cnf(i_0_1460,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_803]),
[final] ).
cnf(i_0_1461,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_804]),
[final] ).
cnf(i_0_1462,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_805]),
[final] ).
cnf(i_0_1463,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk34_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_806]),
[final] ).
cnf(i_0_1464,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_807]),
[final] ).
cnf(i_0_1465,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_808]),
[final] ).
cnf(i_0_1466,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_785]),
[final] ).
cnf(i_0_1467,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_1468,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_810]),
[final] ).
cnf(i_0_1469,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_787]),
[final] ).
cnf(i_0_1470,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_811]),
[final] ).
cnf(i_0_1471,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_812]),
[final] ).
cnf(i_0_1472,plain,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk40_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_813]),
[final] ).
cnf(i_0_1473,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_1474,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_784]),
[final] ).
cnf(i_0_1475,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_1476,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_815]),
[final] ).
cnf(i_0_1477,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_816]),
[final] ).
cnf(i_0_1478,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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_776]),
[final] ).
cnf(i_0_1479,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_776]),
[final] ).
cnf(i_0_1480,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_817]),
[final] ).
cnf(i_0_1481,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_818]),
[final] ).
cnf(i_0_1482,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_819]),
[final] ).
cnf(i_0_1483,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_820]),
[final] ).
cnf(i_0_1484,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_820]),
[final] ).
cnf(i_0_1485,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_821]),
[final] ).
cnf(i_0_1486,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_1487,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_823]),
[final] ).
cnf(i_0_1488,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_1489,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_825]),
[final] ).
cnf(i_0_1490,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_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_826]),
[final] ).
cnf(i_0_1491,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_827]),
[final] ).
cnf(i_0_1492,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_828]),
[final] ).
cnf(i_0_1493,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_829]),
[final] ).
cnf(i_0_1494,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1495,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_820]),
[final] ).
cnf(i_0_1496,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_831]),
[final] ).
cnf(i_0_1497,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_832]),
[final] ).
cnf(i_0_1498,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_833]),
[final] ).
cnf(i_0_1499,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_834]),
[final] ).
cnf(i_0_1500,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_835]),
[final] ).
cnf(i_0_1501,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_836]),
[final] ).
cnf(i_0_1502,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_837]),
[final] ).
cnf(i_0_1503,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_838]),
[final] ).
cnf(i_0_1504,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_839]),
[final] ).
cnf(i_0_1505,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_840]),
[final] ).
cnf(i_0_1506,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_841]),
[final] ).
cnf(i_0_1507,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_842]),
[final] ).
cnf(i_0_1508,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_843]),
[final] ).
cnf(i_0_1509,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_814]),
[final] ).
cnf(i_0_1510,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_844]),
[final] ).
cnf(i_0_1511,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_1512,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_846]),
[final] ).
cnf(i_0_1513,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_1514,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_848]),
[final] ).
cnf(i_0_1515,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_837]),
[final] ).
cnf(i_0_1516,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_837]),
[final] ).
cnf(i_0_1517,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_849]),
[final] ).
cnf(i_0_1518,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_850]),
[final] ).
cnf(i_0_1519,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_851]),
[final] ).
cnf(i_0_1520,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_1521,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_1522,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_854]),
[final] ).
cnf(i_0_1523,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_855]),
[final] ).
cnf(i_0_1524,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_856]),
[final] ).
cnf(i_0_1525,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_857]),
[final] ).
cnf(i_0_1526,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_858]),
[final] ).
cnf(i_0_1527,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_859]),
[final] ).
cnf(i_0_1528,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_860]),
[final] ).
cnf(i_0_1529,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_861]),
[final] ).
cnf(i_0_1530,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_1531,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_1532,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_1533,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_865]),
[final] ).
cnf(i_0_1534,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_866]),
[final] ).
cnf(i_0_1535,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_867]),
[final] ).
cnf(i_0_1536,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_868]),
[final] ).
cnf(i_0_1537,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk34_2(X2,X3)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_806]),
[final] ).
cnf(i_0_1538,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_832]),
[final] ).
cnf(i_0_1539,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_869]),
[final] ).
cnf(i_0_1540,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_870]),
[final] ).
cnf(i_0_1541,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_871]),
[final] ).
cnf(i_0_1542,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk43_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1543,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_785]),
[final] ).
cnf(i_0_1544,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_810]),
[final] ).
cnf(i_0_1545,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_873]),
[final] ).
cnf(i_0_1546,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_874]),
[final] ).
cnf(i_0_1547,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_875]),
[final] ).
cnf(i_0_1548,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_876]),
[final] ).
cnf(i_0_1549,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_877]),
[final] ).
cnf(i_0_1550,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_878]),
[final] ).
cnf(i_0_1551,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk17_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_585]),
[final] ).
cnf(i_0_1552,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk14_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_586]),
[final] ).
cnf(i_0_1553,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_1554,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_1555,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_853]),
[final] ).
cnf(i_0_1556,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_879]),
[final] ).
cnf(i_0_1557,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_880]),
[final] ).
cnf(i_0_1558,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_881]),
[final] ).
cnf(i_0_1559,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_826]),
[final] ).
cnf(i_0_1560,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_882]),
[final] ).
cnf(i_0_1561,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_883]),
[final] ).
cnf(i_0_1562,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_884]),
[final] ).
cnf(i_0_1563,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_885]),
[final] ).
cnf(i_0_1564,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_1565,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_887]),
[final] ).
cnf(i_0_1566,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_870]),
[final] ).
cnf(i_0_1567,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk33_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1568,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_889]),
[final] ).
cnf(i_0_1569,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk45_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1570,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1571,plain,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk40_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_813]),
[final] ).
cnf(i_0_1572,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_1573,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_871]),
[final] ).
cnf(i_0_1574,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_891]),
[final] ).
cnf(i_0_1575,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_875]),
[final] ).
cnf(i_0_1576,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_892]),
[final] ).
cnf(i_0_1577,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_893]),
[final] ).
cnf(i_0_1578,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_894]),
[final] ).
cnf(i_0_1579,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk34_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_806]),
[final] ).
cnf(i_0_1580,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_1581,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_896]),
[final] ).
cnf(i_0_1582,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_897]),
[final] ).
cnf(i_0_1583,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk42_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_872]),
[final] ).
cnf(i_0_1584,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_898]),
[final] ).
cnf(i_0_1585,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_899]),
[final] ).
cnf(i_0_1586,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_1587,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_901]),
[final] ).
cnf(i_0_1588,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_902]),
[final] ).
cnf(i_0_1589,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_903]),
[final] ).
cnf(i_0_1590,plain,
( X1 = hAPP(c_Nat_OSuc,esk32_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_826]),
[final] ).
cnf(i_0_1591,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_867]),
[final] ).
cnf(i_0_1592,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_904]),
[final] ).
cnf(i_0_1593,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_905]),
[final] ).
cnf(i_0_1594,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_889]),
[final] ).
cnf(i_0_1595,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_906]),
[final] ).
cnf(i_0_1596,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_893]),
[final] ).
cnf(i_0_1597,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_907]),
[final] ).
cnf(i_0_1598,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_888]),
[final] ).
cnf(i_0_1599,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk44_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_890]),
[final] ).
cnf(i_0_1600,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_1601,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_909]),
[final] ).
cnf(i_0_1602,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_910]),
[final] ).
cnf(i_0_1603,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_870]),
[final] ).
cnf(i_0_1604,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_911]),
[final] ).
cnf(i_0_1605,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_912]),
[final] ).
cnf(i_0_1606,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1607,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1608,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_915]),
[final] ).
cnf(i_0_1609,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_830]),
[final] ).
cnf(i_0_1610,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_916]),
[final] ).
cnf(i_0_1611,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_917]),
[final] ).
cnf(i_0_1612,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_918]),
[final] ).
cnf(i_0_1613,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_919]),
[final] ).
cnf(i_0_1614,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_908]),
[final] ).
cnf(i_0_1615,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_909]),
[final] ).
cnf(i_0_1616,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_884]),
[final] ).
cnf(i_0_1617,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_920]),
[final] ).
cnf(i_0_1618,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_921]),
[final] ).
cnf(i_0_1619,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_843]),
[final] ).
cnf(i_0_1620,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_922]),
[final] ).
cnf(i_0_1621,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_923]),
[final] ).
cnf(i_0_1622,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_924]),
[final] ).
cnf(i_0_1623,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1624,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_926]),
[final] ).
cnf(i_0_1625,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_896]),
[final] ).
cnf(i_0_1626,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_876]),
[final] ).
cnf(i_0_1627,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_850]),
[final] ).
cnf(i_0_1628,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_927]),
[final] ).
cnf(i_0_1629,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_1630,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_1631,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1632,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_1633,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_932]),
[final] ).
cnf(i_0_1634,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1635,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_934]),
[final] ).
cnf(i_0_1636,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_935]),
[final] ).
cnf(i_0_1637,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_1638,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_937]),
[final] ).
cnf(i_0_1639,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_938]),
[final] ).
cnf(i_0_1640,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_939]),
[final] ).
cnf(i_0_1641,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_861]),
[final] ).
cnf(i_0_1642,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_940]),
[final] ).
cnf(i_0_1643,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_1644,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_1645,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_941]),
[final] ).
cnf(i_0_1646,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_942]),
[final] ).
cnf(i_0_1647,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk45_2(X1,X2)),X1))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1648,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk43_2(X1,X2)),X1))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1649,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_1650,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_944]),
[final] ).
cnf(i_0_1651,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_945]),
[final] ).
cnf(i_0_1652,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_940]),
[final] ).
cnf(i_0_1653,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_920]),
[final] ).
cnf(i_0_1654,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1655,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_1656,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_948]),
[final] ).
cnf(i_0_1657,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_887]),
[final] ).
cnf(i_0_1658,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_949]),
[final] ).
cnf(i_0_1659,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_1660,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_950]),
[final] ).
cnf(i_0_1661,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_951]),
[final] ).
cnf(i_0_1662,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk24_2(X2,X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_952]),
[final] ).
cnf(i_0_1663,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_1664,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_954]),
[final] ).
cnf(i_0_1665,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_955]),
[final] ).
cnf(i_0_1666,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_909]),
[final] ).
cnf(i_0_1667,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_861]),
[final] ).
cnf(i_0_1668,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_956]),
[final] ).
cnf(i_0_1669,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_1670,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_958]),
[final] ).
cnf(i_0_1671,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_934]),
[final] ).
cnf(i_0_1672,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_934]),
[final] ).
cnf(i_0_1673,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_959]),
[final] ).
cnf(i_0_1674,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_959]),
[final] ).
cnf(i_0_1675,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_793]),
[final] ).
cnf(i_0_1676,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_793]),
[final] ).
cnf(i_0_1677,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_960]),
[final] ).
cnf(i_0_1678,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_783]),
[final] ).
cnf(i_0_1679,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_961]),
[final] ).
cnf(i_0_1680,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_962]),
[final] ).
cnf(i_0_1681,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1682,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_964]),
[final] ).
cnf(i_0_1683,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_1684,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_966]),
[final] ).
cnf(i_0_1685,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_967]),
[final] ).
cnf(i_0_1686,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_1687,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_969]),
[final] ).
cnf(i_0_1688,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_1689,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_971]),
[final] ).
cnf(i_0_1690,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_972]),
[final] ).
cnf(i_0_1691,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_973]),
[final] ).
cnf(i_0_1692,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_922]),
[final] ).
cnf(i_0_1693,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_1694,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_1695,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_976]),
[final] ).
cnf(i_0_1696,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_977]),
[final] ).
cnf(i_0_1697,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1698,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1699,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_978]),
[final] ).
cnf(i_0_1700,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_979]),
[final] ).
cnf(i_0_1701,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_980]),
[final] ).
cnf(i_0_1702,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_1703,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1704,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1705,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1706,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1707,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_952]),
[final] ).
cnf(i_0_1708,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_983]),
[final] ).
cnf(i_0_1709,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_984]),
[final] ).
cnf(i_0_1710,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_985]),
[final] ).
cnf(i_0_1711,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_1712,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_987]),
[final] ).
cnf(i_0_1713,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_988]),
[final] ).
cnf(i_0_1714,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_989]),
[final] ).
cnf(i_0_1715,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_826]),
[final] ).
cnf(i_0_1716,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_945]),
[final] ).
cnf(i_0_1717,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_990]),
[final] ).
cnf(i_0_1718,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_875]),
[final] ).
cnf(i_0_1719,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_896]),
[final] ).
cnf(i_0_1720,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk23_2(X2,X1)) != hAPP(esk23_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_667]),
[final] ).
cnf(i_0_1721,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_991]),
[final] ).
cnf(i_0_1722,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1723,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_993]),
[final] ).
cnf(i_0_1724,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_994]),
[final] ).
cnf(i_0_1725,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_995]),
[final] ).
cnf(i_0_1726,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_955]),
[final] ).
cnf(i_0_1727,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_996]),
[final] ).
cnf(i_0_1728,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_997]),
[final] ).
cnf(i_0_1729,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1730,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_994]),
[final] ).
cnf(i_0_1731,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_994]),
[final] ).
cnf(i_0_1732,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_995]),
[final] ).
cnf(i_0_1733,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_995]),
[final] ).
cnf(i_0_1734,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_999]),
[final] ).
cnf(i_0_1735,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_1000]),
[final] ).
cnf(i_0_1736,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_1001]),
[final] ).
cnf(i_0_1737,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_1002]),
[final] ).
cnf(i_0_1738,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_964]),
[final] ).
cnf(i_0_1739,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_994]),
[final] ).
cnf(i_0_1740,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_995]),
[final] ).
cnf(i_0_1741,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_1003]),
[final] ).
cnf(i_0_1742,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_1004]),
[final] ).
cnf(i_0_1743,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_1005]),
[final] ).
cnf(i_0_1744,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_1006]),
[final] ).
cnf(i_0_1745,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_994]),
[final] ).
cnf(i_0_1746,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_994]),
[final] ).
cnf(i_0_1747,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_995]),
[final] ).
cnf(i_0_1748,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_995]),
[final] ).
cnf(i_0_1749,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_900]),
[final] ).
cnf(i_0_1750,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_900]),
[final] ).
cnf(i_0_1751,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_1007]),
[final] ).
cnf(i_0_1752,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_908]),
[final] ).
cnf(i_0_1753,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_1008]),
[final] ).
cnf(i_0_1754,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_1009]),
[final] ).
cnf(i_0_1755,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1010]),
[final] ).
cnf(i_0_1756,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_1757,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_1012]),
[final] ).
cnf(i_0_1758,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_993]),
[final] ).
cnf(i_0_1759,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_1013]),
[final] ).
cnf(i_0_1760,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_1014]),
[final] ).
cnf(i_0_1761,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_1014]),
[final] ).
cnf(i_0_1762,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_1763,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_1764,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1015]),
[final] ).
cnf(i_0_1765,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1766,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_1017]),
[final] ).
cnf(i_0_1767,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1768,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_1019]),
[final] ).
cnf(i_0_1769,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_1020]),
[final] ).
cnf(i_0_1770,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_1021]),
[final] ).
cnf(i_0_1771,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_1022]),
[final] ).
cnf(i_0_1772,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_1004]),
[final] ).
cnf(i_0_1773,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_1005]),
[final] ).
cnf(i_0_1774,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_1006]),
[final] ).
cnf(i_0_1775,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_1023]),
[final] ).
cnf(i_0_1776,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_1024]),
[final] ).
cnf(i_0_1777,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_1025]),
[final] ).
cnf(i_0_1778,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_1026]),
[final] ).
cnf(i_0_1779,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_1027]),
[final] ).
cnf(i_0_1780,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_1781,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_1014]),
[final] ).
cnf(i_0_1782,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_1783,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_1028]),
[final] ).
cnf(i_0_1784,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_1029]),
[final] ).
cnf(i_0_1785,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_1030]),
[final] ).
cnf(i_0_1786,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_1031]),
[final] ).
cnf(i_0_1787,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_1032]),
[final] ).
cnf(i_0_1788,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_1033]),
[final] ).
cnf(i_0_1789,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_1790,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1791,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1792,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1793,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1794,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1795,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_620]),
[final] ).
cnf(i_0_1796,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_1040]),
[final] ).
cnf(i_0_1797,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_1798,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_1799,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1800,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_1801,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_1802,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1803,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1804,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1805,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1806,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1807,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1808,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_1052]),
[final] ).
cnf(i_0_1809,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_1053]),
[final] ).
cnf(i_0_1810,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_1811,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_1812,plain,
( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1054]),
[final] ).
cnf(i_0_1813,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1055]),
[final] ).
cnf(i_0_1814,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_1815,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1816,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_1817,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_1818,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_1819,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_1820,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_1821,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_1822,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_1823,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_1824,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_1825,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_1826,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_1827,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_1828,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_1829,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_1830,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_1831,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_1832,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_1833,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1834,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1835,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1836,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1837,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1838,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1839,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1840,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_1841,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1842,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1843,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1844,plain,
v_c____ != v_d____,
inference(split_conjunct,[status(thm)],[fact__096c_A_126_061_Ad_096]),
[final] ).
cnf(i_0_1845,axiom,
X1 = X1 ).
cnf(i_0_1846,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1847,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1848,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1849,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1850,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1851,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1852,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1853,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1854,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1855,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1856,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1857,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_1858,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_1859,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1860,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1861,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_1862,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_1863,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_1864,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_1865,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_1866,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_1867,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1869,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1870,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1871,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| esk36_5(X1,X3,X4,X5,X6) = esk36_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| esk36_5(X3,X1,X4,X5,X6) = esk36_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| esk36_5(X3,X4,X1,X5,X6) = esk36_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| esk36_5(X3,X4,X5,X1,X6) = esk36_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| esk36_5(X3,X4,X5,X6,X1) = esk36_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| esk35_4(X1,X3,X4,X5) = esk35_4(X2,X3,X4,X5) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| esk35_4(X3,X1,X4,X5) = esk35_4(X3,X2,X4,X5) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| esk35_4(X3,X4,X1,X5) = esk35_4(X3,X4,X2,X5) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| esk35_4(X3,X4,X5,X1) = esk35_4(X3,X4,X5,X2) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| esk37_3(X1,X3,X4) = esk37_3(X2,X3,X4) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| esk37_3(X3,X1,X4) = esk37_3(X3,X2,X4) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| esk37_3(X3,X4,X1) = esk37_3(X3,X4,X2) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| esk22_4(X1,X3,X4,X5) = esk22_4(X2,X3,X4,X5) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| esk22_4(X3,X1,X4,X5) = esk22_4(X3,X2,X4,X5) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| esk22_4(X3,X4,X1,X5) = esk22_4(X3,X4,X2,X5) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| esk22_4(X3,X4,X5,X1) = esk22_4(X3,X4,X5,X2) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| esk21_4(X1,X3,X4,X5) = esk21_4(X2,X3,X4,X5) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| esk21_4(X3,X1,X4,X5) = esk21_4(X3,X2,X4,X5) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| esk21_4(X3,X4,X1,X5) = esk21_4(X3,X4,X2,X5) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| esk21_4(X3,X4,X5,X1) = esk21_4(X3,X4,X5,X2) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1925,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1926,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1938,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1939,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1940,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1941,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1942,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1943,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1944,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1945,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1946,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1947,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_1948,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_1949,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_1950,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_1951,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_1952,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_1953,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1954,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1955,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1956,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_1957,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_1958,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_1959,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_1960,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_1961,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_1962,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1963,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1964,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1965,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1966,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1845_001,axiom,
X1 = X1 ).
cnf(i_0_1846_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1847_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1848_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1849_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1850_006,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1851_007,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1852_008,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1853_009,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1854_010,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1855_011,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1856_012,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1857_013,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_1858_014,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_1859_015,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1860_016,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1861_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_1862_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_1863_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_1864_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_1865_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_1866_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_1867_023,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1868_024,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1869_025,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1870_026,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1871_027,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1872_028,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1873_029,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1874_030,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1875_031,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1876_032,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1877_033,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1878_034,axiom,
( X1 != X2
| esk36_5(X1,X3,X4,X5,X6) = esk36_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1879_035,axiom,
( X1 != X2
| esk36_5(X3,X1,X4,X5,X6) = esk36_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1880_036,axiom,
( X1 != X2
| esk36_5(X3,X4,X1,X5,X6) = esk36_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1881_037,axiom,
( X1 != X2
| esk36_5(X3,X4,X5,X1,X6) = esk36_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1882_038,axiom,
( X1 != X2
| esk36_5(X3,X4,X5,X6,X1) = esk36_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1883_039,axiom,
( X1 != X2
| esk35_4(X1,X3,X4,X5) = esk35_4(X2,X3,X4,X5) ) ).
cnf(i_0_1884_040,axiom,
( X1 != X2
| esk35_4(X3,X1,X4,X5) = esk35_4(X3,X2,X4,X5) ) ).
cnf(i_0_1885_041,axiom,
( X1 != X2
| esk35_4(X3,X4,X1,X5) = esk35_4(X3,X4,X2,X5) ) ).
cnf(i_0_1886_042,axiom,
( X1 != X2
| esk35_4(X3,X4,X5,X1) = esk35_4(X3,X4,X5,X2) ) ).
cnf(i_0_1887_043,axiom,
( X1 != X2
| esk37_3(X1,X3,X4) = esk37_3(X2,X3,X4) ) ).
cnf(i_0_1888_044,axiom,
( X1 != X2
| esk37_3(X3,X1,X4) = esk37_3(X3,X2,X4) ) ).
cnf(i_0_1889_045,axiom,
( X1 != X2
| esk37_3(X3,X4,X1) = esk37_3(X3,X4,X2) ) ).
cnf(i_0_1890_046,axiom,
( X1 != X2
| esk22_4(X1,X3,X4,X5) = esk22_4(X2,X3,X4,X5) ) ).
cnf(i_0_1891_047,axiom,
( X1 != X2
| esk22_4(X3,X1,X4,X5) = esk22_4(X3,X2,X4,X5) ) ).
cnf(i_0_1892_048,axiom,
( X1 != X2
| esk22_4(X3,X4,X1,X5) = esk22_4(X3,X4,X2,X5) ) ).
cnf(i_0_1893_049,axiom,
( X1 != X2
| esk22_4(X3,X4,X5,X1) = esk22_4(X3,X4,X5,X2) ) ).
cnf(i_0_1894_050,axiom,
( X1 != X2
| esk21_4(X1,X3,X4,X5) = esk21_4(X2,X3,X4,X5) ) ).
cnf(i_0_1895_051,axiom,
( X1 != X2
| esk21_4(X3,X1,X4,X5) = esk21_4(X3,X2,X4,X5) ) ).
cnf(i_0_1896_052,axiom,
( X1 != X2
| esk21_4(X3,X4,X1,X5) = esk21_4(X3,X4,X2,X5) ) ).
cnf(i_0_1897_053,axiom,
( X1 != X2
| esk21_4(X3,X4,X5,X1) = esk21_4(X3,X4,X5,X2) ) ).
cnf(i_0_1898_054,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1899_055,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1900_056,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1901_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_1902_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_1903_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_1904_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_1905_061,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1906_062,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1907_063,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1908_064,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1909_065,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1910_066,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1911_067,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1912_068,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1913_069,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1914_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_1915_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_1916_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_1917_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_1918_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_1919_075,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1920_076,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1921_077,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1922_078,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1923_079,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1924_080,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1925_081,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1926_082,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1927_083,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1928_084,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1929_085,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1930_086,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1931_087,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1932_088,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1933_089,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1934_090,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1935_091,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1936_092,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1937_093,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1938_094,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1939_095,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1940_096,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1941_097,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1942_098,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1943_099,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1944_100,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1945_101,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1946_102,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1947_103,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_1948_104,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_1949_105,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_1950_106,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_1951_107,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_1952_108,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_1953_109,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1954_110,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1955_111,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1956_112,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_1957_113,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_1958_114,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_1959_115,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_1960_116,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_1961_117,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_1962_118,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1963_119,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1964_120,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1965_121,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1966_122,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1967,plain,
X1 = X1,
inference(equality_inference,[],[1081]) ).
cnf(i_0_1968,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,[],[1113]) ).
cnf(i_0_1969,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,[],[1152]) ).
cnf(i_0_1970,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,[],[1153]) ).
cnf(i_0_1971,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,[],[1154]) ).
cnf(i_0_1972,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,[],[1158]) ).
cnf(i_0_1973,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,[],[1159]) ).
cnf(i_0_1974,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,[],[1184]) ).
cnf(i_0_1975,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,[],[1186]) ).
cnf(i_0_1976,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,[],[1195]) ).
cnf(i_0_1977,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,[],[1196]) ).
cnf(i_0_1978,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,[],[1198]) ).
cnf(i_0_1979,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,[],[1199]) ).
cnf(i_0_1980,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,[],[1202]) ).
cnf(i_0_1981,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,[],[1211]) ).
cnf(i_0_1982,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,[],[1212]) ).
cnf(i_0_1983,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,[],[1214]) ).
cnf(i_0_1984,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,[],[1233]) ).
cnf(i_0_1985,plain,
( X1 = esk35_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,[],[1240]) ).
cnf(i_0_1986,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,[],[1244]) ).
cnf(i_0_1987,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,[],[1259]) ).
cnf(i_0_1988,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,[],[1280]) ).
cnf(i_0_1989,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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,[],[1289]) ).
cnf(i_0_1990,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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,[],[1290]) ).
cnf(i_0_1991,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,[],[1299]) ).
cnf(i_0_1992,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,[],[1305]) ).
cnf(i_0_1993,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1308]) ).
cnf(i_0_1994,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,[],[1323]) ).
cnf(i_0_1995,plain,
X1 = X1,
inference(equality_inference,[],[1324]) ).
cnf(i_0_1996,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,[],[1327]) ).
cnf(i_0_1997,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,[],[1336]) ).
cnf(i_0_1998,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,[],[1337]) ).
cnf(i_0_1999,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,[],[1394]) ).
cnf(i_0_2000,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1462]) ).
cnf(i_0_2001,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[1474]) ).
cnf(i_0_2002,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(equality_inference,[],[1506]) ).
cnf(i_0_2003,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(equality_inference,[],[1544]) ).
cnf(i_0_2004,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,[],[1559]) ).
cnf(i_0_2005,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,[],[1596]) ).
cnf(i_0_2006,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,[],[1597]) ).
cnf(i_0_2007,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,[],[1598]) ).
cnf(i_0_2008,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(equality_inference,[],[1609]) ).
cnf(i_0_2009,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,[],[1653]) ).
cnf(i_0_2010,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1668]) ).
cnf(i_0_2011,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1670]) ).
cnf(i_0_2012,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1671]) ).
cnf(i_0_2013,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1672]) ).
cnf(i_0_2014,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1678]) ).
cnf(i_0_2015,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1679]) ).
cnf(i_0_2016,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[1684]) ).
cnf(i_0_2017,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[1685]) ).
cnf(i_0_2018,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[1687]) ).
cnf(i_0_2019,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1697]) ).
cnf(i_0_2020,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[1699]) ).
cnf(i_0_2021,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1705]) ).
cnf(i_0_2022,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1706]) ).
cnf(i_0_2023,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,[],[1707]) ).
cnf(i_0_2024,plain,
X1 = X1,
inference(equality_inference,[],[1713]) ).
cnf(i_0_2025,plain,
X1 = X1,
inference(equality_inference,[],[1714]) ).
cnf(i_0_2026,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,[],[1715]) ).
cnf(i_0_2027,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[1718]) ).
cnf(i_0_2028,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,[],[1726]) ).
cnf(i_0_2029,plain,
X1 = X1,
inference(equality_inference,[],[1727]) ).
cnf(i_0_2030,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1750]) ).
cnf(i_0_2031,plain,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1751]) ).
cnf(i_0_2032,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1752]) ).
cnf(i_0_2033,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(equality_inference,[],[1764]) ).
cnf(i_0_2034,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1765]) ).
cnf(i_0_2035,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,[],[1772]) ).
cnf(i_0_2036,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,[],[1773]) ).
cnf(i_0_2037,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,[],[1774]) ).
cnf(i_0_2038,plain,
X1 = X1,
inference(equality_inference,[],[1790]) ).
cnf(i_0_2039,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____))),v_Lab____)),v_Lba____)))),
inference(scs_inference,[],[i_0_1065,i_0_1058]) ).
cnf(i_0_2040,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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(scs_inference,[],[i_0_1062,i_0_1063]) ).
cnf(i_0_2041,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_1297,i_0_1142]) ).
cnf(i_0_2042,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_1297,i_0_1182]) ).
cnf(i_0_2043,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_1371,i_0_1192]) ).
cnf(i_0_2044,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_1371,i_0_1217]) ).
cnf(i_0_2045,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_1371,i_0_1219]) ).
cnf(i_0_2046,plain,
( hAPP(v_h____,X1) != v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X1)),v_c____),v_e____))) ),
inference(scs_inference,[],[i_0_1373,i_0_1224]) ).
cnf(i_0_2047,plain,
( hAPP(v_h____,X1) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X1)),v_e____))) ),
inference(scs_inference,[],[i_0_1373,i_0_1243]) ).
cnf(i_0_2048,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_1989,i_0_1231]) ).
cnf(i_0_2049,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_1231]) ).
cnf(i_0_2050,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
inference(scs_inference,[],[i_0_1989,i_0_1505,i_0_1231,i_0_1335]) ).
cnf(i_0_2051,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_1505]) ).
cnf(i_0_2052,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_1335]) ).
cnf(i_0_2053,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_1989,i_0_1505,i_0_1294,i_0_1231,i_0_1335,i_0_1654]) ).
cnf(i_0_2054,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_2055,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_1989,i_0_1505,i_0_1294,i_0_1231,i_0_1335,i_0_1654,i_0_1698]) ).
cnf(i_0_2056,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1698]) ).
cnf(i_0_2057,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_2001,i_0_1989,i_0_1505,i_0_1294,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144]) ).
cnf(i_0_2058,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_1144]) ).
cnf(i_0_2059,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_2001,i_0_1989,i_0_1505,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148]) ).
cnf(i_0_2060,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_1148]) ).
cnf(i_0_2061,plain,
c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk39_5(X4,X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_1505,i_0_1681,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166]) ).
cnf(i_0_2062,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1681]) ).
cnf(i_0_2063,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,esk39_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_1166]) ).
cnf(i_0_2064,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_2001,i_0_1989,i_0_1505,i_0_2051,i_0_1681,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193]) ).
cnf(i_0_2065,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_1193]) ).
cnf(i_0_2066,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_2001,i_0_1989,i_0_1505,i_0_2051,i_0_1681,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216]) ).
cnf(i_0_2067,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_1216]) ).
cnf(i_0_2068,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_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237]) ).
cnf(i_0_2069,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2019]) ).
cnf(i_0_2070,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_1237]) ).
cnf(i_0_2071,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_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241]) ).
cnf(i_0_2072,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_1241]) ).
cnf(i_0_2073,plain,
c_Nitpick_Orefl_H(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_1650,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246]) ).
cnf(i_0_2074,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1650]) ).
cnf(i_0_2075,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk2_2(X2,X1)),esk2_2(X2,X1))),X2))
| c_Nitpick_Orefl_H(X1,X2) ),
inference(rename_variables,[],[i_0_1246]) ).
cnf(i_0_2076,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_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_2062,i_0_1650,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247]) ).
cnf(i_0_2077,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1681]) ).
cnf(i_0_2078,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_1247]) ).
cnf(i_0_2079,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_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_2062,i_0_1650,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264]) ).
cnf(i_0_2080,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_1264]) ).
cnf(i_0_2081,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_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274]) ).
cnf(i_0_2082,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2083,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_1274]) ).
cnf(i_0_2084,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,esk16_0),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277]) ).
cnf(i_0_2085,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_1277]) ).
cnf(i_0_2086,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,esk16_0),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278]) ).
cnf(i_0_2087,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_1278]) ).
cnf(i_0_2088,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_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285]) ).
cnf(i_0_2089,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1799]) ).
cnf(i_0_2090,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_1285]) ).
cnf(i_0_2091,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_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1721,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286]) ).
cnf(i_0_2092,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1721]) ).
cnf(i_0_2093,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_1286]) ).
cnf(i_0_2094,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_2001,i_0_1989,i_0_2019,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291]) ).
cnf(i_0_2095,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1721]) ).
cnf(i_0_2096,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_1291]) ).
cnf(i_0_2097,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_2001,i_0_1989,i_0_2019,i_0_1606,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292]) ).
cnf(i_0_2098,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1606]) ).
cnf(i_0_2099,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_1292]) ).
cnf(i_0_2100,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296]) ).
cnf(i_0_2101,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_1296]) ).
cnf(i_0_2102,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324]) ).
cnf(i_0_2103,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_1324]) ).
cnf(i_0_2104,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330]) ).
cnf(i_0_2105,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_1330]) ).
cnf(i_0_2106,plain,
~ c_Nitpick_Orefl_H(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2)),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332]) ).
cnf(i_0_2107,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1989]) ).
cnf(i_0_2108,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X3))
| ~ c_Nitpick_Orefl_H(X1,X3) ),
inference(rename_variables,[],[i_0_1332]) ).
cnf(i_0_2109,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346]) ).
cnf(i_0_2110,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_1346]) ).
cnf(i_0_2111,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1271,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347]) ).
cnf(i_0_2112,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_1347]) ).
cnf(i_0_2113,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1271,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382]) ).
cnf(i_0_2114,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_1465]) ).
cnf(i_0_2115,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_1382]) ).
cnf(i_0_2116,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1271,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384]) ).
cnf(i_0_2117,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2118,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_1384]) ).
cnf(i_0_2119,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_1271,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398]) ).
cnf(i_0_2120,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_1604]) ).
cnf(i_0_2121,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_1398]) ).
cnf(i_0_2122,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_1271,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399]) ).
cnf(i_0_2123,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_1604]) ).
cnf(i_0_2124,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_1399]) ).
cnf(i_0_2125,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_1271,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423]) ).
cnf(i_0_2126,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_1423]) ).
cnf(i_0_2127,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,hAPP(c_fequal,X2)))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_1271,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468]) ).
cnf(i_0_2128,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_1468]) ).
cnf(i_0_2129,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_1271,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476]) ).
cnf(i_0_2130,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_1476]) ).
cnf(i_0_2131,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_1271,i_0_1413,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487]) ).
cnf(i_0_2132,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_1413]) ).
cnf(i_0_2133,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_1487]) ).
cnf(i_0_2134,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489]) ).
cnf(i_0_2135,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_1413]) ).
cnf(i_0_2136,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_1489]) ).
cnf(i_0_2137,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507]) ).
cnf(i_0_2138,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1721]) ).
cnf(i_0_2139,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_1507]) ).
cnf(i_0_2140,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508]) ).
cnf(i_0_2141,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_1604]) ).
cnf(i_0_2142,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_1508]) ).
cnf(i_0_2143,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510]) ).
cnf(i_0_2144,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_1510]) ).
cnf(i_0_2145,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512]) ).
cnf(i_0_2146,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_2147,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_1512]) ).
cnf(i_0_2148,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514]) ).
cnf(i_0_2149,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_2150,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_1514]) ).
cnf(i_0_2151,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518]) ).
cnf(i_0_2152,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_1518]) ).
cnf(i_0_2153,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522]) ).
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),X1),X2))),
inference(rename_variables,[],[i_0_1604]) ).
cnf(i_0_2155,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_1522]) ).
cnf(i_0_2156,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536]) ).
cnf(i_0_2157,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2158,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_1536]) ).
cnf(i_0_2159,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538]) ).
cnf(i_0_2160,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_1538]) ).
cnf(i_0_2161,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)),esk33_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567]) ).
cnf(i_0_2162,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),esk33_2(X2,X1))) ),
inference(rename_variables,[],[i_0_1567]) ).
cnf(i_0_2163,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568]) ).
cnf(i_0_2164,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_1568]) ).
cnf(i_0_2165,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576]) ).
cnf(i_0_2166,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_1576]) ).
cnf(i_0_2167,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595]) ).
cnf(i_0_2168,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_1595]) ).
cnf(i_0_2169,plain,
X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598]) ).
cnf(i_0_2170,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_1598]) ).
cnf(i_0_2171,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625]) ).
cnf(i_0_2172,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_2173,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_1625]) ).
cnf(i_0_2174,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1))))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627]) ).
cnf(i_0_2175,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_1627]) ).
cnf(i_0_2176,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633]) ).
cnf(i_0_2177,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_1633]) ).
cnf(i_0_2178,plain,
c_Set_Oinsert(X1,X2,hAPP(c_fequal,X2)) = hAPP(c_fequal,X2),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634]) ).
cnf(i_0_2179,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Set_Oinsert(X1,X2,X3) = X3 ),
inference(rename_variables,[],[i_0_1634]) ).
cnf(i_0_2180,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk24_2(X1,X1)),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662]) ).
cnf(i_0_2181,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),esk24_2(X2,X1)) ),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2182,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,esk31_1(hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665]) ).
cnf(i_0_2183,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_1665]) ).
cnf(i_0_2184,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699]) ).
cnf(i_0_2185,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_1699]) ).
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),hAPP(c_Nat_OSuc,X1)),X2))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700]) ).
cnf(i_0_2187,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_1700]) ).
cnf(i_0_2188,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705]) ).
cnf(i_0_2189,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_1705]) ).
cnf(i_0_2190,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706]) ).
cnf(i_0_2191,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2192,plain,
X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707]) ).
cnf(i_0_2193,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_1707]) ).
cnf(i_0_2194,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715]) ).
cnf(i_0_2195,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_1412]) ).
cnf(i_0_2196,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_1715]) ).
cnf(i_0_2197,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718]) ).
cnf(i_0_2198,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_1412]) ).
cnf(i_0_2199,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_1718]) ).
cnf(i_0_2200,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727]) ).
cnf(i_0_2201,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_1778]) ).
cnf(i_0_2202,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(rename_variables,[],[i_0_1727]) ).
cnf(i_0_2203,plain,
~ class_Orderings_Otop(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741]) ).
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_1593]) ).
cnf(i_0_2205,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_1741]) ).
cnf(i_0_2206,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764]) ).
cnf(i_0_2207,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1764]) ).
cnf(i_0_2208,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk33_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790]) ).
cnf(i_0_2209,plain,
( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2210,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_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987]) ).
cnf(i_0_2211,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1681]) ).
cnf(i_0_2212,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_1987]) ).
cnf(i_0_2213,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846]) ).
cnf(i_0_2214,plain,
hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X1,X2))) != X1,
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848]) ).
cnf(i_0_2215,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1823,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804]) ).
cnf(i_0_2216,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1804]) ).
cnf(i_0_2217,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_COMBI(X1),X2)),hAPP(c_fequal,X2))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1799,i_0_1823,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207]) ).
cnf(i_0_2218,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(rename_variables,[],[i_0_1271]) ).
cnf(i_0_2219,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(hAPP(c_member(X1),X6),X4))
| hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5)) ),
inference(rename_variables,[],[i_0_1207]) ).
cnf(i_0_2220,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_2001,i_0_1989,i_0_2107,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1805,i_0_1799,i_0_1823,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248]) ).
cnf(i_0_2221,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1989]) ).
cnf(i_0_2222,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1248]) ).
cnf(i_0_2223,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1805,i_0_1799,i_0_1823,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249]) ).
cnf(i_0_2224,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1989]) ).
cnf(i_0_2225,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1249]) ).
cnf(i_0_2226,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_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253]) ).
cnf(i_0_2227,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1607]) ).
cnf(i_0_2228,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_1253]) ).
cnf(i_0_2229,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),c_Set_Oinsert(X1,X3,X2))))),
inference(scs_inference,[],[i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454]) ).
cnf(i_0_2230,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(rename_variables,[],[i_0_1271]) ).
cnf(i_0_2231,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_1454]) ).
cnf(i_0_2232,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,c_Set_Oinsert(X3,X4,X5)),X4)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524]) ).
cnf(i_0_2233,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_1505]) ).
cnf(i_0_2234,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_1524]) ).
cnf(i_0_2235,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),X2),X2)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1435,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115]) ).
cnf(i_0_2236,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2237,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk13_4(X3,X2,X4,X1))),hAPP(X3,esk13_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_1115]) ).
cnf(i_0_2238,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk16_0)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188]) ).
cnf(i_0_2239,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_1188]) ).
cnf(i_0_2240,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221]) ).
cnf(i_0_2241,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2019]) ).
cnf(i_0_2242,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2243,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_1221]) ).
cnf(i_0_2244,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_1813,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252]) ).
cnf(i_0_2245,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2019]) ).
cnf(i_0_2246,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1989]) ).
cnf(i_0_2247,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_1252]) ).
cnf(i_0_2248,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_1813,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259]) ).
cnf(i_0_2249,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_1505]) ).
cnf(i_0_2250,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_1259]) ).
cnf(i_0_2251,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_1813,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268]) ).
cnf(i_0_2252,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_1268]) ).
cnf(i_0_2253,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(esk16_0,hAPP(c_Nat_OSuc,X1),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_1813,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273]) ).
cnf(i_0_2254,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_1273]) ).
cnf(i_0_2255,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_1813,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275]) ).
cnf(i_0_2256,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_1505]) ).
cnf(i_0_2257,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1607]) ).
cnf(i_0_2258,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_1275]) ).
cnf(i_0_2259,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_1813,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1734,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276]) ).
cnf(i_0_2260,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1681]) ).
cnf(i_0_2261,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_1276]) ).
cnf(i_0_2262,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_1813,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1734,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280]) ).
cnf(i_0_2263,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2264,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_1280]) ).
cnf(i_0_2265,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_1805,i_0_1799,i_0_1823,i_0_1835,i_0_1734,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305]) ).
cnf(i_0_2266,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2267,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_1305]) ).
cnf(i_0_2268,plain,
X1 = esk39_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_1805,i_0_1621,i_0_1799,i_0_1823,i_0_1835,i_0_1734,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308]) ).
cnf(i_0_2269,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1621]) ).
cnf(i_0_2270,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_1308]) ).
cnf(i_0_2271,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_1805,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1734,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316]) ).
cnf(i_0_2272,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_1316]) ).
cnf(i_0_2273,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1734,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323]) ).
cnf(i_0_2274,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2275,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1607]) ).
cnf(i_0_2276,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_1323]) ).
cnf(i_0_2277,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1734,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326]) ).
cnf(i_0_2278,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2019]) ).
cnf(i_0_2279,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1607]) ).
cnf(i_0_2280,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_1326]) ).
cnf(i_0_2281,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X3)),X3)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1734,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344]) ).
cnf(i_0_2282,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(rename_variables,[],[i_0_2001]) ).
cnf(i_0_2283,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_1344]) ).
cnf(i_0_2284,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1734,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360]) ).
cnf(i_0_2285,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_1360]) ).
cnf(i_0_2286,plain,
c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1734,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444]) ).
cnf(i_0_2287,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_1582]) ).
cnf(i_0_2288,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| X2 = X3 ),
inference(rename_variables,[],[i_0_1444]) ).
cnf(i_0_2289,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1734,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450]) ).
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_1505]) ).
cnf(i_0_2291,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_1582]) ).
cnf(i_0_2292,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_1450]) ).
cnf(i_0_2293,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1836,i_0_1734,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457]) ).
cnf(i_0_2294,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_1457]) ).
cnf(i_0_2295,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1836,i_0_1734,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459]) ).
cnf(i_0_2296,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_1505]) ).
cnf(i_0_2297,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_1459]) ).
cnf(i_0_2298,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1836,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462]) ).
cnf(i_0_2299,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_1405]) ).
cnf(i_0_2300,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_1462]) ).
cnf(i_0_2301,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1835,i_0_1836,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504]) ).
cnf(i_0_2302,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_1504]) ).
cnf(i_0_2303,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528]) ).
cnf(i_0_2304,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_1528]) ).
cnf(i_0_2305,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529]) ).
cnf(i_0_2306,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_1529]) ).
cnf(i_0_2307,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)))),esk14_0)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533]) ).
cnf(i_0_2308,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_1533]) ).
cnf(i_0_2309,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535]) ).
cnf(i_0_2310,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_1535]) ).
cnf(i_0_2311,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541]) ).
cnf(i_0_2312,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(rename_variables,[],[i_0_1546]) ).
cnf(i_0_2313,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_1541]) ).
cnf(i_0_2314,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550]) ).
cnf(i_0_2315,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_1412]) ).
cnf(i_0_2316,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_1550]) ).
cnf(i_0_2317,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558]) ).
cnf(i_0_2318,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_2319,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_1558]) ).
cnf(i_0_2320,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559]) ).
cnf(i_0_2321,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2322,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_1559]) ).
cnf(i_0_2323,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561]) ).
cnf(i_0_2324,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_1582]) ).
cnf(i_0_2325,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_1561]) ).
cnf(i_0_2326,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)))),esk14_0)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565]) ).
cnf(i_0_2327,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_1565]) ).
cnf(i_0_2328,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)))),esk17_0)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566]) ).
cnf(i_0_2329,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_1566]) ).
cnf(i_0_2330,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583]) ).
cnf(i_0_2331,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1650]) ).
cnf(i_0_2332,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2333,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk42_1(X2)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(rename_variables,[],[i_0_1583]) ).
cnf(i_0_2334,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,esk32_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590]) ).
cnf(i_0_2335,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2336,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 = hAPP(c_Nat_OSuc,esk32_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1590]) ).
cnf(i_0_2337,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk14_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601]) ).
cnf(i_0_2338,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_1601]) ).
cnf(i_0_2339,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk17_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603]) ).
cnf(i_0_2340,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_1603]) ).
cnf(i_0_2341,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645]) ).
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),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1412]) ).
cnf(i_0_2343,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_1645]) ).
cnf(i_0_2344,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659]) ).
cnf(i_0_2345,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_1659]) ).
cnf(i_0_2346,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664]) ).
cnf(i_0_2347,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_1412]) ).
cnf(i_0_2348,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_1664]) ).
cnf(i_0_2349,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))) != esk14_0,
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668]) ).
cnf(i_0_2350,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1668]) ).
cnf(i_0_2351,plain,
esk14_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670]) ).
cnf(i_0_2352,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1670]) ).
cnf(i_0_2353,plain,
esk17_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671]) ).
cnf(i_0_2354,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1671]) ).
cnf(i_0_2355,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))) != esk17_0,
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672]) ).
cnf(i_0_2356,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1672]) ).
cnf(i_0_2357,plain,
X1 = esk33_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685]) ).
cnf(i_0_2358,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_1685]) ).
cnf(i_0_2359,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689]) ).
cnf(i_0_2360,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_1689]) ).
cnf(i_0_2361,plain,
esk24_2(hAPP(X1,esk13_4(X1,X1,X2,tc_Nat_Onat)),hAPP(X1,esk13_4(X1,X1,X2,tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744]) ).
cnf(i_0_2362,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_1744]) ).
cnf(i_0_2363,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750]) ).
cnf(i_0_2364,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1750]) ).
cnf(i_0_2365,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751]) ).
cnf(i_0_2366,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(rename_variables,[],[i_0_1751]) ).
cnf(i_0_2367,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != X2,
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752]) ).
cnf(i_0_2368,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1752]) ).
cnf(i_0_2369,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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,esk16_0),hAPP(c_Nat_OSuc,X2)),X2))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984]) ).
cnf(i_0_2370,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_1984]) ).
cnf(i_0_2371,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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(esk16_0,hAPP(c_Nat_OSuc,X2),X2))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986]) ).
cnf(i_0_2372,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_1986]) ).
cnf(i_0_2373,plain,
hAPP(c_Nat_OSuc,X1) != c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847]) ).
cnf(i_0_2374,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2375,plain,
class_Finite__Set_Ofinite(esk39_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941]) ).
cnf(i_0_2376,plain,
class_Groups_Ocomm__monoid__add(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942]) ).
cnf(i_0_2377,plain,
class_Groups_Omonoid__add(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943]) ).
cnf(i_0_2378,plain,
class_Rings_Ozero__neq__one(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944]) ).
cnf(i_0_2379,plain,
class_Groups_Ozero(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945]) ).
cnf(i_0_2380,plain,
class_Groups_Oone(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946]) ).
cnf(i_0_2381,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953]) ).
cnf(i_0_2382,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2383,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954]) ).
cnf(i_0_2384,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2385,plain,
class_Orderings_Oord(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955]) ).
cnf(i_0_2386,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962]) ).
cnf(i_0_2387,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2388,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963]) ).
cnf(i_0_2389,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2390,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964]) ).
cnf(i_0_2391,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2392,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965]) ).
cnf(i_0_2393,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2394,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),X2),X2,X2),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914]) ).
cnf(i_0_2395,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2396,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),X2),X2,X2),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915]) ).
cnf(i_0_2397,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2398,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),X2)),X2,X2),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916]) ).
cnf(i_0_2399,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2400,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2),X2),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917]) ).
cnf(i_0_2401,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),X2),X2,c_Nat_Osize__class_Osize(tc_Nat_Onat,X2)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918]) ).
cnf(i_0_2402,plain,
~ c_Nitpick_Orefl_H(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919]) ).
cnf(i_0_2403,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2404,plain,
~ c_Nitpick_Orefl_H(tc_Arrow__Order__Mirabelle_Oalt,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920]) ).
cnf(i_0_2405,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2406,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921]) ).
cnf(i_0_2407,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1826,i_0_1827,i_0_1829,i_0_1831,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922]) ).
cnf(i_0_2408,plain,
class_Groups_Oordered__ab__semigroup__add(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1829,i_0_1831,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923]) ).
cnf(i_0_2409,plain,
class_Groups_Oordered__comm__monoid__add(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1829,i_0_1831,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925]) ).
cnf(i_0_2410,plain,
class_Rings_Ocomm__semiring__1(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1829,i_0_1831,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927]) ).
cnf(i_0_2411,plain,
class_Rings_Olinordered__semidom(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1829,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929]) ).
cnf(i_0_2412,plain,
class_Orderings_Opreorder(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1829,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931]) ).
cnf(i_0_2413,plain,
class_Orderings_Oorder(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1829,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932]) ).
cnf(i_0_2414,plain,
class_Groups_Oab__semigroup__add(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933]) ).
cnf(i_0_2415,plain,
class_Orderings_Olinorder(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934]) ).
cnf(i_0_2416,plain,
class_Groups_Ocancel__semigroup__add(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935]) ).
cnf(i_0_2417,plain,
class_Groups_Ocancel__ab__semigroup__add(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936]) ).
cnf(i_0_2418,plain,
tc_HOL_Obool != tc_Nat_Onat,
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937]) ).
cnf(i_0_2419,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938]) ).
cnf(i_0_2420,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939]) ).
cnf(i_0_2421,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2422,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940]) ).
cnf(i_0_2423,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2424,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk16_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_2274,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975]) ).
cnf(i_0_2425,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2426,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_1975]) ).
cnf(i_0_2427,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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(esk16_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_1805,i_0_2335,i_0_1806,i_0_2274,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980]) ).
cnf(i_0_2428,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2429,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_1980]) ).
cnf(i_0_2430,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_1805,i_0_2335,i_0_1806,i_0_2274,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180]) ).
cnf(i_0_2431,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_1505]) ).
cnf(i_0_2432,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1607]) ).
cnf(i_0_2433,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_1180]) ).
cnf(i_0_2434,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(X1,X2,X3))),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X4,c_Set_Oinsert(X1,X2,X3))))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_1806,i_0_2274,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189]) ).
cnf(i_0_2435,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1607]) ).
cnf(i_0_2436,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_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X5)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ c_Finite__Set_Ofinite(X2,X5) ),
inference(rename_variables,[],[i_0_1189]) ).
cnf(i_0_2437,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk16_0),hAPP(c_Nat_OSuc,X2)),X2))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233]) ).
cnf(i_0_2438,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_1233]) ).
cnf(i_0_2439,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(esk16_0,hAPP(c_Nat_OSuc,X2),X2))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244]) ).
cnf(i_0_2440,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_1244]) ).
cnf(i_0_2441,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,esk41_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319]) ).
cnf(i_0_2442,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2443,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,esk41_4(X4,X3,X2,X1),X2)
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1319]) ).
cnf(i_0_2444,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327]) ).
cnf(i_0_2445,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1650]) ).
cnf(i_0_2446,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2447,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(rename_variables,[],[i_0_1753]) ).
cnf(i_0_2448,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_1327]) ).
cnf(i_0_2449,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348]) ).
cnf(i_0_2450,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_1582]) ).
cnf(i_0_2451,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X1,X3)))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(rename_variables,[],[i_0_1348]) ).
cnf(i_0_2452,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383]) ).
cnf(i_0_2453,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2454,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_1383]) ).
cnf(i_0_2455,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425]) ).
cnf(i_0_2456,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2457,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_1425]) ).
cnf(i_0_2458,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439]) ).
cnf(i_0_2459,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2460,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_1439]) ).
cnf(i_0_2461,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440]) ).
cnf(i_0_2462,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2463,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_1440]) ).
cnf(i_0_2464,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)))),esk17_0)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480]) ).
cnf(i_0_2465,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2466,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_1480]) ).
cnf(i_0_2467,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481]) ).
cnf(i_0_2468,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2469,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_1481]) ).
cnf(i_0_2470,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498]) ).
cnf(i_0_2471,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2472,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_1498]) ).
cnf(i_0_2473,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499]) ).
cnf(i_0_2474,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1721]) ).
cnf(i_0_2475,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_1499]) ).
cnf(i_0_2476,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500]) ).
cnf(i_0_2477,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2478,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_1500]) ).
cnf(i_0_2479,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),v_n____)),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501]) ).
cnf(i_0_2480,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_1501]) ).
cnf(i_0_2481,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525]) ).
cnf(i_0_2482,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_2483,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_1525]) ).
cnf(i_0_2484,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526]) ).
cnf(i_0_2485,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_1526]) ).
cnf(i_0_2486,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537]) ).
cnf(i_0_2487,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2488,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2489,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_1701]) ).
cnf(i_0_2490,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk34_2(X3,X1)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(rename_variables,[],[i_0_1537]) ).
cnf(i_0_2491,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk34_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540]) ).
cnf(i_0_2492,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_1757]) ).
cnf(i_0_2493,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_1540]) ).
cnf(i_0_2494,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589]) ).
cnf(i_0_2495,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_1589]) ).
cnf(i_0_2496,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk34_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615]) ).
cnf(i_0_2497,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_1757]) ).
cnf(i_0_2498,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_1615]) ).
cnf(i_0_2499,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618]) ).
cnf(i_0_2500,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_1695]) ).
cnf(i_0_2501,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_1618]) ).
cnf(i_0_2502,plain,
esk34_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641]) ).
cnf(i_0_2503,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_1695]) ).
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),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1641]) ).
cnf(i_0_2505,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653]) ).
cnf(i_0_2506,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_1413]) ).
cnf(i_0_2507,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_1653]) ).
cnf(i_0_2508,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk16_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186]) ).
cnf(i_0_2509,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2510,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2511,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_1186]) ).
cnf(i_0_2512,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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(esk16_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202]) ).
cnf(i_0_2513,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2514,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2515,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_1202]) ).
cnf(i_0_2516,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483]) ).
cnf(i_0_2517,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_1605]) ).
cnf(i_0_2518,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_1483]) ).
cnf(i_0_2519,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk16_0),hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,X1)),X1))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_1990,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185]) ).
cnf(i_0_2520,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1990]) ).
cnf(i_0_2521,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_1185]) ).
cnf(i_0_2522,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk16_0),hAPP(c_Nat_OSuc,X1)),X1,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_1990,i_0_2520,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201]) ).
cnf(i_0_2523,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1990]) ).
cnf(i_0_2524,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2525,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2526,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_1201]) ).
cnf(i_0_2527,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk16_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_1354,i_0_1606,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2524,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979]) ).
cnf(i_0_2528,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1990]) ).
cnf(i_0_2529,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2530,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2531,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1799]) ).
cnf(i_0_2532,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_1979]) ).
cnf(i_0_2533,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1372,i_0_1435,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2524,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495]) ).
cnf(i_0_2534,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_1604]) ).
cnf(i_0_2535,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_1785]) ).
cnf(i_0_2536,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_1495]) ).
cnf(i_0_2537,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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,esk15_0),v_a____),v_b____))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2524,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971]) ).
cnf(i_0_2538,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_1971]) ).
cnf(i_0_2539,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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(esk15_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2524,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973]) ).
cnf(i_0_2540,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2541,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_1973]) ).
cnf(i_0_2542,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk16_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184]) ).
cnf(i_0_2543,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1989]) ).
cnf(i_0_2544,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2545,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1805]) ).
cnf(i_0_2546,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1799]) ).
cnf(i_0_2547,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1813]) ).
cnf(i_0_2548,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_1184]) ).
cnf(i_0_2549,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),esk37_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi))) != esk37_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245]) ).
cnf(i_0_2550,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),esk37_3(X3,X2,X1))) != esk37_3(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1245]) ).
cnf(i_0_2551,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497]) ).
cnf(i_0_2552,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_1497]) ).
cnf(i_0_2553,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556]) ).
cnf(i_0_2554,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_1556]) ).
cnf(i_0_2555,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619]) ).
cnf(i_0_2556,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_1619]) ).
cnf(i_0_2557,plain,
esk34_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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726]) ).
cnf(i_0_2558,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_1726]) ).
cnf(i_0_2559,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849]) ).
cnf(i_0_2560,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539]) ).
cnf(i_0_2561,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_1539]) ).
cnf(i_0_2562,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356]) ).
cnf(i_0_2563,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_1505]) ).
cnf(i_0_2564,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_1356]) ).
cnf(i_0_2565,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,esk14_0))),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549]) ).
cnf(i_0_2566,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_1549]) ).
cnf(i_0_2567,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341]) ).
cnf(i_0_2568,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_1412]) ).
cnf(i_0_2569,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_1341]) ).
cnf(i_0_2570,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_2506,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341,i_0_1342]) ).
cnf(i_0_2571,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_1413]) ).
cnf(i_0_2572,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_1342]) ).
cnf(i_0_2573,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_2506,i_0_2571,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341,i_0_1342,i_0_1426]) ).
cnf(i_0_2574,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_1413]) ).
cnf(i_0_2575,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_1426]) ).
cnf(i_0_2576,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_2506,i_0_2571,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341,i_0_1342,i_0_1426,i_0_1402]) ).
cnf(i_0_2577,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_1402]) ).
cnf(i_0_2578,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_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_2506,i_0_2571,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341,i_0_1342,i_0_1426,i_0_1402,i_0_1574]) ).
cnf(i_0_2579,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_1574]) ).
cnf(i_0_2580,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),esk19_2(X1,v_F)),esk20_2(X1,v_F))),hAPP(v_F,esk18_2(X1,v_F)))) ),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_2506,i_0_2571,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1112,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341,i_0_1342,i_0_1426,i_0_1402,i_0_1574,i_0_1097]) ).
cnf(i_0_2581,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),esk19_2(X2,X1)),esk20_2(X2,X1))),hAPP(X1,esk18_2(X2,X1))))
| c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
inference(rename_variables,[],[i_0_1097]) ).
cnf(i_0_2582,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),esk19_2(X1,v_F)),esk20_2(X1,v_F))),hAPP(esk18_2(X1,v_F),X1))) ),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_2506,i_0_2571,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1112,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341,i_0_1342,i_0_1426,i_0_1402,i_0_1574,i_0_1097,i_0_1098]) ).
cnf(i_0_2583,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),esk19_2(X2,X1)),esk20_2(X2,X1))),hAPP(esk18_2(X2,X1),X2)))
| c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
inference(rename_variables,[],[i_0_1098]) ).
cnf(i_0_2584,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))),esk18_2(X1,v_F)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_2506,i_0_2571,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1112,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341,i_0_1342,i_0_1426,i_0_1402,i_0_1574,i_0_1097,i_0_1098,i_0_1099]) ).
cnf(i_0_2585,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))),esk18_2(X2,X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
inference(rename_variables,[],[i_0_1099]) ).
cnf(i_0_2586,plain,
( c_Arrow__Order__Mirabelle_Odictator(v_F,X1)
| esk19_2(X1,v_F) != esk20_2(X1,v_F) ),
inference(scs_inference,[],[i_0_2008,i_0_2001,i_0_1989,i_0_2107,i_0_2221,i_0_2224,i_0_2246,i_0_2543,i_0_1990,i_0_2520,i_0_2523,i_0_2019,i_0_2069,i_0_2241,i_0_2245,i_0_1813,i_0_2263,i_0_2266,i_0_2374,i_0_2382,i_0_2384,i_0_2387,i_0_2389,i_0_2391,i_0_2393,i_0_2395,i_0_2397,i_0_2399,i_0_2403,i_0_2405,i_0_2421,i_0_2423,i_0_2510,i_0_2514,i_0_1354,i_0_1606,i_0_1785,i_0_1753,i_0_1778,i_0_1546,i_0_1505,i_0_2051,i_0_2233,i_0_2249,i_0_2256,i_0_2290,i_0_2296,i_0_2431,i_0_1767,i_0_2117,i_0_2157,i_0_2236,i_0_2242,i_0_2442,i_0_2453,i_0_2456,i_0_2459,i_0_2462,i_0_1701,i_0_2489,i_0_1721,i_0_2092,i_0_2095,i_0_2138,i_0_1695,i_0_2500,i_0_1681,i_0_2062,i_0_2077,i_0_2211,i_0_1712,i_0_2082,i_0_2321,i_0_2332,i_0_2465,i_0_2468,i_0_2471,i_0_2477,i_0_1582,i_0_2287,i_0_2291,i_0_2324,i_0_1650,i_0_2074,i_0_2331,i_0_1757,i_0_2492,i_0_1593,i_0_2146,i_0_2149,i_0_2172,i_0_2204,i_0_2318,i_0_2482,i_0_1294,i_0_1604,i_0_2120,i_0_2123,i_0_2141,i_0_2154,i_0_1605,i_0_1553,i_0_1552,i_0_1551,i_0_1271,i_0_2218,i_0_1412,i_0_2195,i_0_2198,i_0_2315,i_0_2342,i_0_2347,i_0_1413,i_0_2132,i_0_2135,i_0_2506,i_0_2571,i_0_1465,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1306,i_0_1112,i_0_1607,i_0_2227,i_0_2257,i_0_2275,i_0_2279,i_0_2432,i_0_1805,i_0_2335,i_0_2428,i_0_2513,i_0_2525,i_0_2529,i_0_2540,i_0_2524,i_0_2530,i_0_1806,i_0_2274,i_0_2425,i_0_2446,i_0_2509,i_0_1621,i_0_1799,i_0_2089,i_0_2531,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1825,i_0_1826,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1835,i_0_1836,i_0_1837,i_0_1838,i_0_1840,i_0_1843,i_0_1734,i_0_1405,i_0_1782,i_0_1231,i_0_1335,i_0_1654,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1246,i_0_1247,i_0_1264,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1292,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1468,i_0_1476,i_0_1487,i_0_1489,i_0_1507,i_0_1508,i_0_1510,i_0_1512,i_0_1514,i_0_1518,i_0_1522,i_0_1536,i_0_1538,i_0_1567,i_0_1568,i_0_1576,i_0_1595,i_0_1598,i_0_1625,i_0_1627,i_0_1633,i_0_1634,i_0_1662,i_0_1665,i_0_1699,i_0_1700,i_0_1705,i_0_1706,i_0_1707,i_0_1715,i_0_1718,i_0_1727,i_0_1741,i_0_1764,i_0_1790,i_0_1987,i_0_1846,i_0_1848,i_0_1804,i_0_1207,i_0_1248,i_0_1249,i_0_1253,i_0_1454,i_0_1524,i_0_1115,i_0_1188,i_0_1221,i_0_1252,i_0_1259,i_0_1268,i_0_1273,i_0_1275,i_0_1276,i_0_1280,i_0_1305,i_0_1308,i_0_1316,i_0_1323,i_0_1326,i_0_1344,i_0_1360,i_0_1444,i_0_1450,i_0_1457,i_0_1459,i_0_1462,i_0_1504,i_0_1528,i_0_1529,i_0_1533,i_0_1535,i_0_1541,i_0_1550,i_0_1558,i_0_1559,i_0_1561,i_0_1565,i_0_1566,i_0_1583,i_0_1590,i_0_1601,i_0_1603,i_0_1645,i_0_1659,i_0_1664,i_0_1668,i_0_1670,i_0_1671,i_0_1672,i_0_1685,i_0_1689,i_0_1744,i_0_1750,i_0_1751,i_0_1752,i_0_1984,i_0_1986,i_0_1847,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1945,i_0_1946,i_0_1953,i_0_1954,i_0_1955,i_0_1962,i_0_1963,i_0_1964,i_0_1965,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1925,i_0_1927,i_0_1929,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939,i_0_1940,i_0_1975,i_0_1980,i_0_1180,i_0_1189,i_0_1233,i_0_1244,i_0_1319,i_0_1327,i_0_1348,i_0_1383,i_0_1425,i_0_1439,i_0_1440,i_0_1480,i_0_1481,i_0_1498,i_0_1499,i_0_1500,i_0_1501,i_0_1525,i_0_1526,i_0_1537,i_0_1540,i_0_1589,i_0_1615,i_0_1618,i_0_1641,i_0_1653,i_0_1186,i_0_1202,i_0_1483,i_0_1185,i_0_1201,i_0_1979,i_0_1495,i_0_1971,i_0_1973,i_0_1184,i_0_1245,i_0_1497,i_0_1556,i_0_1619,i_0_1726,i_0_1849,i_0_1539,i_0_1356,i_0_1549,i_0_1341,i_0_1342,i_0_1426,i_0_1402,i_0_1574,i_0_1097,i_0_1098,i_0_1099,i_0_1100]) ).
cnf(i_0_2587,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))))
| esk19_2(X2,X1) != esk20_2(X2,X1)
| c_Arrow__Order__Mirabelle_Odictator(X1,X2) ),
inference(rename_variables,[],[i_0_1100]) ).
cnf(i_0_2588,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_2217,i_0_1088]) ).
cnf(i_0_2589,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_COMBI(X1),X2)),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2217]) ).
cnf(i_0_2590,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk30_5(X3,X2,X1,X4,X5))),hAPP(X3,esk30_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_1088]) ).
cnf(i_0_2591,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_2217,i_0_2323,i_0_1088,i_0_1200]) ).
cnf(i_0_2592,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
inference(rename_variables,[],[i_0_2323]) ).
cnf(i_0_2593,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_1200]) ).
cnf(i_0_2594,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_2217,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401]) ).
cnf(i_0_2595,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_2484]) ).
cnf(i_0_2596,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_1401]) ).
cnf(i_0_2597,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_2217,i_0_2071,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714]) ).
cnf(i_0_2598,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_2071]) ).
cnf(i_0_2599,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_1714]) ).
cnf(i_0_2600,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,esk16_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_2522,i_0_2217,i_0_2071,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231]) ).
cnf(i_0_2601,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_1231]) ).
cnf(i_0_2602,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_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698]) ).
cnf(i_0_2603,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1698]) ).
cnf(i_0_2604,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_Set_Oinsert(X1,X2,X3)),X3)),c_Wellfounded_Ofinite__psubset(X1))),
inference(scs_inference,[],[i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2281,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144]) ).
cnf(i_0_2605,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_1144]) ).
cnf(i_0_2606,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X1,X1,c_COMBI(X1),X2)),c_Set_Oinsert(X1,X3,X2))),
inference(scs_inference,[],[i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2281,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148]) ).
cnf(i_0_2607,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_1148]) ).
cnf(i_0_2608,plain,
c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk39_5(c_Set_Oinsert(X1,X5,X4),X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
inference(scs_inference,[],[i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2281,i_0_2066,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166]) ).
cnf(i_0_2609,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,esk39_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_1166]) ).
cnf(i_0_2610,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_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2281,i_0_2064,i_0_2066,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193]) ).
cnf(i_0_2611,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_1193]) ).
cnf(i_0_2612,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_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2281,i_0_2064,i_0_2066,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216]) ).
cnf(i_0_2613,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_1216]) ).
cnf(i_0_2614,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_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2281,i_0_2064,i_0_2066,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237]) ).
cnf(i_0_2615,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
inference(rename_variables,[],[i_0_2050]) ).
cnf(i_0_2616,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_1237]) ).
cnf(i_0_2617,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_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2484,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241]) ).
cnf(i_0_2618,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_1241]) ).
cnf(i_0_2619,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),esk37_3(c_Nat_OSuc,X2,X1))) != esk37_3(c_Nat_OSuc,X2,X1),
inference(scs_inference,[],[i_0_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2484,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245]) ).
cnf(i_0_2620,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),esk37_3(X3,X2,X1))) != esk37_3(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1245]) ).
cnf(i_0_2621,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_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2484,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247]) ).
cnf(i_0_2622,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_1247]) ).
cnf(i_0_2623,plain,
hAPP(X1,X2) = hAPP(X1,esk38_4(hAPP(c_fequal,X2),X1,X3,hAPP(X1,X2))),
inference(scs_inference,[],[i_0_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2484,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264]) ).
cnf(i_0_2624,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_1264]) ).
cnf(i_0_2625,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_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2303,i_0_2484,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274]) ).
cnf(i_0_2626,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_2303]) ).
cnf(i_0_2627,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_1274]) ).
cnf(i_0_2628,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_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2303,i_0_2484,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278]) ).
cnf(i_0_2629,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_1278]) ).
cnf(i_0_2630,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_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285]) ).
cnf(i_0_2631,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
inference(rename_variables,[],[i_0_2197]) ).
cnf(i_0_2632,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_1285]) ).
cnf(i_0_2633,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_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2137,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286]) ).
cnf(i_0_2634,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_2137]) ).
cnf(i_0_2635,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_1286]) ).
cnf(i_0_2636,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_2050,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291]) ).
cnf(i_0_2637,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_2137]) ).
cnf(i_0_2638,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_1291]) ).
cnf(i_0_2639,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296]) ).
cnf(i_0_2640,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_1296]) ).
cnf(i_0_2641,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324]) ).
cnf(i_0_2642,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_2079]) ).
cnf(i_0_2643,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_1324]) ).
cnf(i_0_2644,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330]) ).
cnf(i_0_2645,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_1330]) ).
cnf(i_0_2646,plain,
~ c_Nitpick_Orefl_H(tc_Arrow__Order__Mirabelle_Oalt,c_Arrow__Order__Mirabelle_Obelow(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,esk16_0),hAPP(c_Nat_OSuc,X1)),X1,hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332]) ).
cnf(i_0_2647,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X3))
| ~ c_Nitpick_Orefl_H(X1,X3) ),
inference(rename_variables,[],[i_0_1332]) ).
cnf(i_0_2648,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346]) ).
cnf(i_0_2649,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_1346]) ).
cnf(i_0_2650,plain,
c_Set_Oinsert(X1,hAPP(X2,X3),c_Set_Oimage(X4,X1,X2,c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X3,X6)))) = c_Set_Oimage(X4,X1,X2,c_Set_Oinsert(X4,X5,c_Set_Oinsert(X4,X3,X6))),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347]) ).
cnf(i_0_2651,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Set_Oinsert(X4,hAPP(X5,X2),c_Set_Oimage(X1,X4,X5,X3)) = c_Set_Oimage(X1,X4,X5,X3) ),
inference(rename_variables,[],[i_0_1347]) ).
cnf(i_0_2652,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384]) ).
cnf(i_0_2653,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_2122]) ).
cnf(i_0_2654,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_1384]) ).
cnf(i_0_2655,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423]) ).
cnf(i_0_2656,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_1423]) ).
cnf(i_0_2657,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468]) ).
cnf(i_0_2658,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_1468]) ).
cnf(i_0_2659,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,esk34_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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2303,i_0_2484,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476]) ).
cnf(i_0_2660,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_1476]) ).
cnf(i_0_2661,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2303,i_0_2484,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507]) ).
cnf(i_0_2662,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_2153]) ).
cnf(i_0_2663,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_1507]) ).
cnf(i_0_2664,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2303,i_0_2346,i_0_2484,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510]) ).
cnf(i_0_2665,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_1510]) ).
cnf(i_0_2666,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2303,i_0_2346,i_0_2484,i_0_2570,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512]) ).
cnf(i_0_2667,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_2570]) ).
cnf(i_0_2668,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_1512]) ).
cnf(i_0_2669,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2303,i_0_2346,i_0_2484,i_0_2570,i_0_2159,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514]) ).
cnf(i_0_2670,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_2159]) ).
cnf(i_0_2671,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_1514]) ).
cnf(i_0_2672,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),esk33_2(hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)),X1))),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2303,i_0_2346,i_0_2484,i_0_2570,i_0_2159,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567]) ).
cnf(i_0_2673,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),esk33_2(X2,X1))) ),
inference(rename_variables,[],[i_0_1567]) ).
cnf(i_0_2674,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2570,i_0_2159,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625]) ).
cnf(i_0_2675,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_2573]) ).
cnf(i_0_2676,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_1625]) ).
cnf(i_0_2677,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2570,i_0_2159,i_0_2122,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634]) ).
cnf(i_0_2678,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Set_Oinsert(X1,X2,X3) = X3 ),
inference(rename_variables,[],[i_0_1634]) ).
cnf(i_0_2679,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),esk24_2(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),X1)),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662]) ).
cnf(i_0_2680,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),esk24_2(X2,X1)) ),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2681,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665]) ).
cnf(i_0_2682,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_2153]) ).
cnf(i_0_2683,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_1665]) ).
cnf(i_0_2684,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707]) ).
cnf(i_0_2685,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_1707]) ).
cnf(i_0_2686,plain,
c_Set_Oimage(X1,X2,X3,c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),c_Set_Oimage(X2,X2,c_COMBI(X2),c_Set_Oimage(X1,X2,X3,X4)))) = c_Set_Oimage(X2,X2,c_COMBI(X2),c_Set_Oimage(X1,X2,X3,X4)),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987]) ).
cnf(i_0_2687,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(rename_variables,[],[i_0_2059]) ).
cnf(i_0_2688,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_1987]) ).
cnf(i_0_2689,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277]) ).
cnf(i_0_2690,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_1277]) ).
cnf(i_0_2691,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382]) ).
cnf(i_0_2692,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_1382]) ).
cnf(i_0_2693,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398]) ).
cnf(i_0_2694,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_1398]) ).
cnf(i_0_2695,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2156,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399]) ).
cnf(i_0_2696,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_2156]) ).
cnf(i_0_2697,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_1399]) ).
cnf(i_0_2698,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2156,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402]) ).
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),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_1402]) ).
cnf(i_0_2700,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2626,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2156,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489]) ).
cnf(i_0_2701,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_2303]) ).
cnf(i_0_2702,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_1489]) ).
cnf(i_0_2703,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2156,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598]) ).
cnf(i_0_2704,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_1598]) ).
cnf(i_0_2705,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2153,i_0_2662,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2156,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700]) ).
cnf(i_0_2706,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_1700]) ).
cnf(i_0_2707,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2153,i_0_2662,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2156,i_0_2088,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718]) ).
cnf(i_0_2708,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_2131]) ).
cnf(i_0_2709,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_1718]) ).
cnf(i_0_2710,plain,
c_Finite__Set_Ofinite(esk39_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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2153,i_0_2662,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804]) ).
cnf(i_0_2711,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1804]) ).
cnf(i_0_2712,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2153,i_0_2662,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518]) ).
cnf(i_0_2713,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_1518]) ).
cnf(i_0_2714,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2153,i_0_2662,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522]) ).
cnf(i_0_2715,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_2122]) ).
cnf(i_0_2716,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_1522]) ).
cnf(i_0_2717,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576]) ).
cnf(i_0_2718,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_1576]) ).
cnf(i_0_2719,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699]) ).
cnf(i_0_2720,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_1699]) ).
cnf(i_0_2721,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705]) ).
cnf(i_0_2722,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_1705]) ).
cnf(i_0_2723,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706]) ).
cnf(i_0_2724,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2725,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715]) ).
cnf(i_0_2726,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_2131]) ).
cnf(i_0_2727,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_1715]) ).
cnf(i_0_2728,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764]) ).
cnf(i_0_2729,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1764]) ).
cnf(i_0_2730,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790]) ).
cnf(i_0_2731,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_2071]) ).
cnf(i_0_2732,plain,
( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1790]) ).
cnf(i_0_2733,plain,
hBOOL(hAPP(c_FuncSet_OPi(X1,X1,X2,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),c_Set_Oinsert(X1,X3,X2))),c_COMBI(X1))),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654]) ).
cnf(i_0_2734,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_2735,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536]) ).
cnf(i_0_2736,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_2163]) ).
cnf(i_0_2737,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_1536]) ).
cnf(i_0_2738,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595]) ).
cnf(i_0_2739,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_2131]) ).
cnf(i_0_2740,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_1595]) ).
cnf(i_0_2741,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2113,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633]) ).
cnf(i_0_2742,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_1633]) ).
cnf(i_0_2743,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568]) ).
cnf(i_0_2744,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_1568]) ).
cnf(i_0_2745,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497]) ).
cnf(i_0_2746,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_2555]) ).
cnf(i_0_2747,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_1497]) ).
cnf(i_0_2748,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508]) ).
cnf(i_0_2749,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_2186]) ).
cnf(i_0_2750,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_1508]) ).
cnf(i_0_2751,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk34_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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627]) ).
cnf(i_0_2752,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_1627]) ).
cnf(i_0_2753,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538]) ).
cnf(i_0_2754,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_2473]) ).
cnf(i_0_2755,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_1538]) ).
cnf(i_0_2756,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619]) ).
cnf(i_0_2757,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_1619]) ).
cnf(i_0_2758,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846]) ).
cnf(i_0_2759,plain,
X1 != hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X1,X2))),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848]) ).
cnf(i_0_2760,plain,
X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),
inference(rename_variables,[],[i_0_2192]) ).
cnf(i_0_2761,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X2,
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849]) ).
cnf(i_0_2762,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != X2,
inference(rename_variables,[],[i_0_2367]) ).
cnf(i_0_2763,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104]) ).
cnf(i_0_2764,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
inference(rename_variables,[],[i_0_2197]) ).
cnf(i_0_2765,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_1104]) ).
cnf(i_0_2766,plain,
~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X4,c_Set_Oinsert(X2,X5,c_Set_Oimage(tc_Nat_Onat,X2,X6,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X7,X8)))))),X4),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119]) ).
cnf(i_0_2767,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_1119]) ).
cnf(i_0_2768,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)),esk35_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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227]) ).
cnf(i_0_2769,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_1294]) ).
cnf(i_0_2770,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,esk35_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_1227]) ).
cnf(i_0_2771,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421]) ).
cnf(i_0_2772,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_1421]) ).
cnf(i_0_2773,plain,
esk24_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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740]) ).
cnf(i_0_2774,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk24_2(X1,X1)),
inference(rename_variables,[],[i_0_2180]) ).
cnf(i_0_2775,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1799]) ).
cnf(i_0_2776,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_1740]) ).
cnf(i_0_2777,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745]) ).
cnf(i_0_2778,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_1783]) ).
cnf(i_0_2779,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_1745]) ).
cnf(i_0_2780,plain,
X1 = esk35_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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985]) ).
cnf(i_0_2781,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_2097]) ).
cnf(i_0_2782,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_1294]) ).
cnf(i_0_2783,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 = esk35_4(hAPP(X3,X4),X3,X2,X1) ),
inference(rename_variables,[],[i_0_1985]) ).
cnf(i_0_2784,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947]) ).
cnf(i_0_2785,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948]) ).
cnf(i_0_2786,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949]) ).
cnf(i_0_2787,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950]) ).
cnf(i_0_2788,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951]) ).
cnf(i_0_2789,plain,
~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X2,c_Set_Oinsert(X2,X4,c_Set_Oimage(tc_Nat_Onat,X2,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6,X7)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961]) ).
cnf(i_0_2790,plain,
c_Arrow__Order__Mirabelle_Ounanimity(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_F),esk24_2(v_F,v_F))),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2774,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1841,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961,i_0_1966]) ).
cnf(i_0_2791,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk24_2(X1,X1)),
inference(rename_variables,[],[i_0_2180]) ).
cnf(i_0_2792,plain,
c_Arrow__Order__Mirabelle_OIIA(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_F),esk24_2(v_F,v_F))),
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2774,i_0_2791,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1841,i_0_1842,i_0_1799,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961,i_0_1966,i_0_1928]) ).
cnf(i_0_2793,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk24_2(X1,X1)),
inference(rename_variables,[],[i_0_2180]) ).
cnf(i_0_2794,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2774,i_0_2791,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1841,i_0_1842,i_0_1799,i_0_1826,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961,i_0_1966,i_0_1928,i_0_1310]) ).
cnf(i_0_2795,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_1310]) ).
cnf(i_0_2796,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,esk34_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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2774,i_0_2791,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_1701,i_0_1841,i_0_1842,i_0_1799,i_0_1826,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961,i_0_1966,i_0_1928,i_0_1310,i_0_1527]) ).
cnf(i_0_2797,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_1701]) ).
cnf(i_0_2798,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_1527]) ).
cnf(i_0_2799,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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2774,i_0_2791,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2675,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_2782,i_0_1701,i_0_1841,i_0_1842,i_0_1799,i_0_1826,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961,i_0_1966,i_0_1928,i_0_1310,i_0_1527,i_0_1599]) ).
cnf(i_0_2800,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_1294]) ).
cnf(i_0_2801,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_2573]) ).
cnf(i_0_2802,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk44_1(X2)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(rename_variables,[],[i_0_1599]) ).
cnf(i_0_2803,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(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3),X4)) = X4,
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2731,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2774,i_0_2791,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2675,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_2782,i_0_1701,i_0_2416,i_0_1841,i_0_1842,i_0_1799,i_0_1826,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961,i_0_1966,i_0_1928,i_0_1310,i_0_1527,i_0_1599,i_0_1687]) ).
cnf(i_0_2804,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_2071]) ).
cnf(i_0_2805,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)
| X3 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_1687]) ).
cnf(i_0_2806,plain,
esk33_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_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2486,i_0_2071,i_0_2598,i_0_2731,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2774,i_0_2791,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2208,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2675,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_1294,i_0_2769,i_0_2782,i_0_1701,i_0_2416,i_0_1802,i_0_1841,i_0_1842,i_0_1799,i_0_1826,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961,i_0_1966,i_0_1928,i_0_1310,i_0_1527,i_0_1599,i_0_1687,i_0_1725]) ).
cnf(i_0_2807,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk33_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rename_variables,[],[i_0_2208]) ).
cnf(i_0_2808,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1802]) ).
cnf(i_0_2809,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_1725]) ).
cnf(i_0_2810,plain,
$false,
inference(scs_inference,[],[i_0_2050,i_0_2615,i_0_2229,i_0_2226,i_0_2522,i_0_2217,i_0_1783,i_0_2778,i_0_1438,i_0_2076,i_0_2486,i_0_2071,i_0_2598,i_0_2731,i_0_2079,i_0_2100,i_0_2281,i_0_2180,i_0_2774,i_0_2791,i_0_2064,i_0_2066,i_0_2059,i_0_2192,i_0_2197,i_0_2631,i_0_2208,i_0_2131,i_0_2708,i_0_2726,i_0_2097,i_0_2153,i_0_2662,i_0_2682,i_0_2367,i_0_2303,i_0_2626,i_0_2701,i_0_2346,i_0_2484,i_0_2595,i_0_2573,i_0_2675,i_0_2140,i_0_2570,i_0_2159,i_0_2122,i_0_2653,i_0_2163,i_0_2259,i_0_2186,i_0_2470,i_0_2473,i_0_2113,i_0_2174,i_0_2551,i_0_2137,i_0_2634,i_0_2637,i_0_2143,i_0_2156,i_0_2555,i_0_2088,i_0_2375,i_0_2323,i_0_2592,i_0_1294,i_0_2769,i_0_2782,i_0_1701,i_0_2416,i_0_1802,i_0_1841,i_0_1842,i_0_1799,i_0_1826,i_0_1088,i_0_1200,i_0_1401,i_0_1714,i_0_1231,i_0_1698,i_0_1144,i_0_1148,i_0_1166,i_0_1193,i_0_1216,i_0_1237,i_0_1241,i_0_1245,i_0_1247,i_0_1264,i_0_1274,i_0_1278,i_0_1285,i_0_1286,i_0_1291,i_0_1296,i_0_1324,i_0_1330,i_0_1332,i_0_1346,i_0_1347,i_0_1384,i_0_1423,i_0_1468,i_0_1476,i_0_1507,i_0_1510,i_0_1512,i_0_1514,i_0_1567,i_0_1625,i_0_1634,i_0_1662,i_0_1665,i_0_1707,i_0_1987,i_0_1277,i_0_1382,i_0_1398,i_0_1399,i_0_1402,i_0_1489,i_0_1598,i_0_1700,i_0_1718,i_0_1804,i_0_1518,i_0_1522,i_0_1576,i_0_1699,i_0_1705,i_0_1706,i_0_1715,i_0_1764,i_0_1790,i_0_1654,i_0_1536,i_0_1595,i_0_1633,i_0_1568,i_0_1497,i_0_1508,i_0_1627,i_0_1538,i_0_1619,i_0_1846,i_0_1848,i_0_1849,i_0_1104,i_0_1119,i_0_1227,i_0_1421,i_0_1740,i_0_1745,i_0_1985,i_0_1947,i_0_1948,i_0_1949,i_0_1950,i_0_1951,i_0_1961,i_0_1966,i_0_1928,i_0_1310,i_0_1527,i_0_1599,i_0_1687,i_0_1725,i_0_1313]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT168+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
% 0.15/0.33 % Computer : n028.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:00:15 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 5.24/5.75 % Version : CSE_E---1.7
% 5.24/5.75 % Problem : theBenchmark.p
% 5.24/5.75 % SZS status Theorem for theBenchmark.p
% 5.24/5.75 % SZS output start CNFRefutation
% See solution above
% 16.43/16.30 % Total time : 5.396s
%------------------------------------------------------------------------------