%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT166+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 : n010.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 05:06:12 PM UTC 2026
% Result : Theorem 4.17s 5.75s
% Output : CNFRefutation 10.47s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1078)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
! [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',conj_0) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X27] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> ( ! [X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X27))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X17))),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),X27),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,X40,X1,X5,X2,X14,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X14,X2,X5,X1,X40)
=> ( c_Finite__Set_Ofinite(X14,X12)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X14),X8),X12))
=> hAPP(X40,c_Set_Oinsert(X14,X8,X12)) = hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X40,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,X14,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X10,c_Set_Oimage(X14,X10,X2,X12))),c_Finite__Set_Ocard(X14,X12)))
=> ~ c_Fun_Oinj__on(X14,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,
! [X22,X23,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),X23),X22)),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),X22),X23)),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_PiE,axiom,
! [X8,X11,X12,X2,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X14)),X2),c_FuncSet_OPi(X10,X14,X12,X11)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X14),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_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,
~ ! [X31] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X31))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X31),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [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),v_a____),v_b____)),X30))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X30),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X10,X14] :
( class_Orderings_Oord(X14)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X14)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X14),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X14),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,
! [X50,X51] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X50)),X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X51,X50] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X51)),X51)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_ex__least__nat__less,axiom,
! [X18,X16] :
( ~ hBOOL(hAPP(X16,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X16,X18))
=> ? [X57] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X18))
& ! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X57))
=> ~ hBOOL(hAPP(X16,X4)) )
& hBOOL(hAPP(X16,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,
! [X22,X11,X23,X10] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X23),X11))
=> X23 = X22 )
=> hBOOL(hAPP(hAPP(c_member(X10),X23),c_Set_Oinsert(X10,X22,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,
! [X18,X52] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X18)),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X18,X52] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),hAPP(c_Nat_OSuc,X52))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_xt1_I9_J,axiom,
! [X32,X35,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X32))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35)) ) ),
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,
! [X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X35,X32,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X32)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ),
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,
! [X52,X18] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X52))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),hAPP(c_Nat_OSuc,X52)))
<=> X18 = X52 ) ),
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,
! [X21,X20,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20)) ) ),
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__cases,axiom,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ( X21 != X20
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( X21 != X20
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ) ),
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_linorder__neqE__linordered__idom,axiom,
! [X20,X21,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X21 != X20
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_not__leE,axiom,
! [X21,X20,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21)) ) ),
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,
! [X20,X21] :
( X21 != X20
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21)) ) ),
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,
! [X21,X10] :
( class_Orderings_Opreorder(X10)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_linorder__le__cases,axiom,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
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__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_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_PW,axiom,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,v_P____)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PW) ).
fof(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096,axiom,
? [X27] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
& ! [X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X27))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X17))),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),X27),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,
! [X18] : hBOOL(hAPP(hAPP(c_member(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____)),X18))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiProf) ).
fof(fact_n_I2_J,axiom,
! [X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X17))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I2_J) ).
fof(fact_pred__subset__eq2,axiom,
! [X37,X13,X14,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X14,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X10,c_COMBC(X14,tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X14,tc_prod(X10,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),X10,c_COMBB(tc_prod(X10,X14),tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool),X14,c_member(tc_prod(X10,X14)))),c_Product__Type_OPair(X10,X14)))),X13)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X10,c_COMBC(X14,tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X14,tc_prod(X10,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),X10,c_COMBB(tc_prod(X10,X14),tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool),X14,c_member(tc_prod(X10,X14)))),c_Product__Type_OPair(X10,X14)))),X37)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),X13),X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact__C2_C,axiom,
! [X24,X16,X25,X26,X22,X23] :
( X23 != X22
=> ( X26 != X25
=> ( X23 != X25
=> ( X22 != X26
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16),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))),X24),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),X23),X22)),hAPP(X16,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),X26),X25)),hAPP(X24,X4))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X22)),hAPP(v_F,X16)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X25)),hAPP(v_F,X24))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).
fof(fact__C1_C,axiom,
! [X24,X16,X25,X26,X22,X23] :
( X23 != X22
=> ( X26 != X25
=> ( X23 != X25
=> ( X22 != X26
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16),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))),X24),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),X23),X22)),hAPP(X16,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),X26),X25)),hAPP(X24,X4))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X22)),hAPP(v_F,X16)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X25)),hAPP(v_F,X24))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_pairwise__neutrality,axiom,
! [X24,X16,X25,X26,X22,X23] :
( X23 != X22
=> ( X26 != 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))),X16),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))),X24),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),X23),X22)),hAPP(X16,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),X26),X25)),hAPP(X24,X4))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X22)),hAPP(v_F,X16)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X25)),hAPP(v_F,X24))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
fof(fact_pred__equals__eq2,axiom,
! [X37,X13,X14,X10] :
( hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X10,c_COMBC(X14,tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X14,tc_prod(X10,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),X10,c_COMBB(tc_prod(X10,X14),tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool),X14,c_member(tc_prod(X10,X14)))),c_Product__Type_OPair(X10,X14)))),X13) = hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X14,tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_fun(X14,tc_HOL_Obool)),X10,c_COMBC(X14,tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X14,tc_prod(X10,X14)),tc_fun(X14,tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool)),X10,c_COMBB(tc_prod(X10,X14),tc_fun(tc_fun(tc_prod(X10,X14),tc_HOL_Obool),tc_HOL_Obool),X14,c_member(tc_prod(X10,X14)))),c_Product__Type_OPair(X10,X14)))),X37)
<=> X13 = X37 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_Pi__mono,axiom,
! [X44,X11,X14,X12,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),hAPP(X11,X3)),hAPP(X44,X3))) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,X14),tc_HOL_Obool),c_FuncSet_OPi(X10,X14,X12,X11)),c_FuncSet_OPi(X10,X14,X12,X44))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_Pi__I,axiom,
! [X11,X2,X14,X12,X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X3)),hAPP(X11,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X14)),X2),c_FuncSet_OPi(X10,X14,X12,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_IIA__def,axiom,
! [X40] :
( c_Arrow__Order__Mirabelle_OIIA(X40)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X38),c_Arrow__Order__Mirabelle_OProf))
=> ! [X41,X42] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X3,X4)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X38,X4))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X40,X3)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X40,X38))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact__C4_C,axiom,
! [X24,X16,X9,X22,X23] :
( X23 != X22
=> ( X22 != X9
=> ( X23 != 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))),X16),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))),X24),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),X23),X22)),hAPP(X16,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),X9)),hAPP(X24,X4))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X22)),hAPP(v_F,X16)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X9)),hAPP(v_F,X24))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C4_C) ).
fof(fact_dictatorI,axiom,
! [X39,X40] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X40),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X41,X42] :
( X41 != X42
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X3,X39)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X40,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X40,X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_in__lex__prod,axiom,
! [X28,X29,X25,X26,X22,X23,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X14),tc_prod(X10,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X14),tc_prod(X10,X14)),hAPP(hAPP(c_Product__Type_OPair(X10,X14),X23),X22)),hAPP(hAPP(c_Product__Type_OPair(X10,X14),X26),X25))),c_Wellfounded_Olex__prod(X10,X14,X29,X28)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X23),X26)),X29))
| ( X23 = X26
& hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X14)),hAPP(hAPP(c_Product__Type_OPair(X14,X14),X22),X25)),X28)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact__C3_C,axiom,
! [X24,X16,X22,X23] :
( X23 != X22
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16),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))),X24),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),X23),X22)),hAPP(X16,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),X23)),hAPP(X24,X4))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X22)),hAPP(v_F,X16)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X23)),hAPP(v_F,X24))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C3_C) ).
fof(fact_folding__image__simple_Oeq__fold__g,axiom,
! [X12,X40,X1,X5,X2,X14,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X14,X2,X5,X1,X40)
=> ( c_Finite__Set_Ofinite(X14,X12)
=> hAPP(X40,X12) = c_Finite__Set_Ofold__image(X10,X14,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,X14,X11,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),c_Set_Oimage(X14,X10,X2,X12)))
<=> ? [X69] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),X69),X12))
& X11 = c_Set_Oimage(X14,X10,X2,X69) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_same__fstI,axiom,
! [X10,X13,X7,X15,X14,X8,X16] :
( hBOOL(hAPP(X16,X8))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X14,X14)),hAPP(hAPP(c_Product__Type_OPair(X14,X14),X15),X7)),hAPP(X13,X8)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X14),tc_prod(X10,X14))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X14),tc_prod(X10,X14)),hAPP(hAPP(c_Product__Type_OPair(X10,X14),X8),X15)),hAPP(hAPP(c_Product__Type_OPair(X10,X14),X8),X7))),c_Recdef_Osame__fst(X10,X14,X16,X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X10,X14] :
( class_Orderings_Oord(X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X14),X2),X1))
<=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,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,X40,X1,X5,X2,X14,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X14,X2,X5,X1,X40)
=> ( c_Finite__Set_Ofinite(X14,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),X11),X12))
=> hAPP(hAPP(X2,hAPP(X40,X11)),hAPP(X40,X12)) = hAPP(X40,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,X40,X1,X5,X2,X14,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X14,X2,X5,X1,X40)
=> ( c_Finite__Set_Ofinite(X14,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X14),X8),X12))
=> hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X40,X12)) = hAPP(X40,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,X40,X1,X5,X2,X14,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X14,X2,X5,X1,X40)
=> ( c_Finite__Set_Ofinite(X14,X12)
=> hAPP(X40,c_Set_Oinsert(X14,X8,X12)) = hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X40,X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [X8,X40,X1,X5,X2,X14,X10] :
( c_Finite__Set_Ofolding__image__simple__idem(X10,X14,X2,X5,X1,X40)
=> 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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),c_Set_Oimage(X10,X14,X2,X12)),X11))
=> ( c_Fun_Oinj__on(X14,X10,X1,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oimage(X14,X10,X1,X11)),X12))
=> ( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X14,X11)
=> c_Finite__Set_Ocard(X10,X12) = c_Finite__Set_Ocard(X14,X11) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(fact_unanimity__def,axiom,
! [X40] :
( c_Arrow__Order__Mirabelle_Ounanimity(X40)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X41,X42] :
( ! [X4] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X3,X4)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(X40,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_card__bij,axiom,
! [X1,X11,X12,X2,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X14)),X2),c_FuncSet_OPi(X10,X14,X12,hAPP(c_COMBK(tc_fun(X14,tc_HOL_Obool),X10),X11))))
=> ( c_Fun_Oinj__on(X10,X14,X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X14,X10)),X1),c_FuncSet_OPi(X14,X10,X11,hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X14),X12))))
=> ( c_Fun_Oinj__on(X14,X10,X1,X11)
=> ( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X14,X11)
=> c_Finite__Set_Ocard(X10,X12) = c_Finite__Set_Ocard(X14,X11) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij) ).
fof(fact_pred__subset__eq,axiom,
! [X37,X13,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)),X13)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X37)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X13),X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_inj__on__iff__card__le,axiom,
! [X11,X14,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X14,X11)
=> ( ? [X74] :
( c_Fun_Oinj__on(X10,X14,X74,X12)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),c_Set_Oimage(X10,X14,X74,X12)),X11)) )
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X14,X11))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_in__above,axiom,
! [X7,X8,X6,X22,X23] :
( X23 != X22
=> ( 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),X23),X22)))
<=> ( X8 != X7
& ( 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),X23),X7)),X6)) )
& ( X8 != X22
=> ( ( X7 = X22
=> ( X8 = X23
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X23)),X6)) ) )
& ( 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),X7)),X6)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_in__below,axiom,
! [X7,X8,X6,X22,X23] :
( X23 != X22
=> ( 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,X23,X22)))
<=> ( X8 != X7
& ( X7 = X23
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X22)),X6)) )
& ( X7 != X23
=> ( ( X8 = X23
=> ( 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),X22),X7)),X6)) ) )
& ( X8 != X23
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,X14,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),c_Set_Oimage(X14,X10,X2,X12)))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(c_Hilbert__Choice_Oinv__into(X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),c_Set_Oimage(X10,X14,X2,X12)),c_Set_Oimage(X10,X14,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,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X14)),X2),c_FuncSet_OPi(X10,X14,X12,hAPP(c_COMBK(tc_fun(X14,tc_HOL_Obool),X10),X11))))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),c_Set_Oimage(X10,X14,X2,X12)),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__image) ).
fof(fact_inv__into__injective,axiom,
! [X7,X8,X2,X12,X14,X10] :
( hAPP(c_Hilbert__Choice_Oinv__into(X10,X14,X12,X2),X8) = hAPP(c_Hilbert__Choice_Oinv__into(X10,X14,X12,X2),X7)
=> ( hBOOL(hAPP(hAPP(c_member(X14),X8),c_Set_Oimage(X10,X14,X2,X12)))
=> ( hBOOL(hAPP(hAPP(c_member(X14),X7),c_Set_Oimage(X10,X14,X2,X12)))
=> X8 = X7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).
fof(fact_Ints__odd__less__0,axiom,
! [X23,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X23),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)),X23)),X23)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X23),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_range__ex1__eq,axiom,
! [X22,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X14),X22),c_Set_Oimage(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))))
<=> ? [X3] :
( X22 = hAPP(X2,X3)
& ! [X66] :
( X22 = hAPP(X2,X66)
=> X66 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_card__image__le,axiom,
! [X2,X14,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X14,c_Set_Oimage(X10,X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,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(X14,tc_HOL_Obool)),c_Set_Oimage(X10,X14,X2,X12)),c_Set_Oimage(X10,X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),c_Set_Oimage(X10,X14,X2,X12)),X11))
=> ( c_Finite__Set_Ofinite(X14,X11)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X14,X11))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_image__iff,axiom,
! [X12,X2,X14,X5,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X5),c_Set_Oimage(X14,X10,X2,X12)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X14),X3),X12))
& X5 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_card__inj,axiom,
! [X11,X12,X2,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X14)),X2),c_FuncSet_OPi(X10,X14,X12,hAPP(c_COMBK(tc_fun(X14,tc_HOL_Obool),X10),X11))))
=> ( c_Fun_Oinj__on(X10,X14,X2,X12)
=> ( c_Finite__Set_Ofinite(X14,X11)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X14,X11))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj) ).
fof(fact_Pi__anti__mono,axiom,
! [X11,X14,X12,X45,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X45),X12))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,X14),tc_HOL_Obool),c_FuncSet_OPi(X10,X14,X12,X11)),c_FuncSet_OPi(X10,X14,X45,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_finite__range__imageI,axiom,
! [X2,X36,X1,X14,X10] :
( c_Finite__Set_Ofinite(X10,c_Set_Oimage(X14,X10,X1,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))))
=> c_Finite__Set_Ofinite(X36,c_Set_Oimage(X14,X36,hAPP(c_COMBB(X10,X36,X14,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X14,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,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X14)),X2),c_FuncSet_OPi(X10,X14,X12,hAPP(c_COMBK(tc_fun(X14,tc_HOL_Obool),X10),X11))))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X8)),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_image__mono,axiom,
! [X2,X14,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(X14,tc_HOL_Obool),c_Set_Oimage(X10,X14,X2,X12)),c_Set_Oimage(X10,X14,X2,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_mlex__leq,axiom,
! [X13,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)),X13))
=> 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,X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_in__rel__def,axiom,
! [X7,X8,X13,X14,X10] :
( c_FunDef_Oin__rel(X10,X14,X13,X8,X7)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X14)),hAPP(hAPP(c_Product__Type_OPair(X10,X14),X8),X7)),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_f__inv__into__f,axiom,
! [X12,X2,X14,X7,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X7),c_Set_Oimage(X14,X10,X2,X12)))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X14,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,X14] :
( c_Set_Oimage(X14,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
<=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X14,X10,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool)),X2),X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(fact_inj__on__inv__into,axiom,
! [X12,X2,X14,X11,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),c_Set_Oimage(X14,X10,X2,X12)))
=> c_Fun_Oinj__on(X10,X14,c_Hilbert__Choice_Oinv__into(X14,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,
! [X13,X43,X16,X10,X36,X14] : hAPP(c_COMBS(X14,X36,X10,X16,X43),X13) = hAPP(hAPP(X16,X13),hAPP(X43,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_Pi__mem,axiom,
! [X8,X11,X12,X2,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X14)),X2),c_FuncSet_OPi(X10,X14,X12,X11)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X8)),hAPP(X11,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_inj__image__mem__iff,axiom,
! [X12,X23,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X23)),c_Set_Oimage(X10,X14,X2,X12)))
<=> hBOOL(hAPP(hAPP(c_member(X10),X23),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_image__surj__f__inv__f,axiom,
! [X12,X2,X10,X14] :
( c_Set_Oimage(X14,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> c_Set_Oimage(X14,X10,X2,c_Set_Oimage(X10,X14,c_Hilbert__Choice_Oinv__into(X14,X10,c_Orderings_Otop__class_Otop(tc_fun(X14,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,X45,X12,X2,X10,X14] :
( c_Set_Oimage(X14,X10,X2,X12) = X45
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X67),X45))
=> c_Set_Oimage(X14,X10,X2,c_Set_Oimage(X10,X14,c_Hilbert__Choice_Oinv__into(X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X12)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
=> ! [X38] :
( hBOOL(hAPP(hAPP(c_member(X10),X38),X12))
=> ( hAPP(X2,X3) = hAPP(X2,X38)
=> X3 = X38 ) ) ) ),
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,X36,X10,X14] : c_Set_Oimage(X14,X10,hAPP(c_COMBB(X36,X10,X14,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))) = c_Set_Oimage(X36,X10,X2,c_Set_Oimage(X14,X36,X1,c_Orderings_Otop__class_Otop(tc_fun(X14,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,
! [X39,X40] :
( c_Arrow__Order__Mirabelle_Odictator(X40,X39)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> hAPP(X40,X3) = hAPP(X3,X39) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_inj__fun,axiom,
! [X36,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X10,tc_fun(X36,X14),hAPP(c_COMBB(X14,tc_fun(X36,X14),X10,c_COMBK(X14,X36)),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,X36,X2,X10,X14] : c_Set_Oimage(X14,X10,X2,c_Set_Oimage(X36,X14,X1,X12)) = c_Set_Oimage(X36,X10,hAPP(c_COMBB(X14,X10,X36,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,
! [X37,X12,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X37),X12))
=> c_Set_Oimage(X14,X10,c_Hilbert__Choice_Oinv__into(X10,X14,X12,X2),c_Set_Oimage(X10,X14,X2,X37)) = X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
fof(fact_finite__surj,axiom,
! [X2,X11,X14,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X14,tc_HOL_Obool),X11),c_Set_Oimage(X10,X14,X2,X12)))
=> c_Finite__Set_Ofinite(X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Set_Oimage(X14,X10,c_Hilbert__Choice_Oinv__into(X10,X14,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),c_Set_Oimage(X10,X14,X2,X72)) = X72 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).
fof(fact_image__inv__f__f,axiom,
! [X12,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Set_Oimage(X14,X10,c_Hilbert__Choice_Oinv__into(X10,X14,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),c_Set_Oimage(X10,X14,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,X14] :
( c_Set_Oimage(X14,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X14,X10,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool)),X2),X7)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
fof(fact_mlex__less,axiom,
! [X13,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,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_subset__card__intvl__is__intvl,axiom,
! [X55,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X12),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X55,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),c_Finite__Set_Ocard(tc_Nat_Onat,X12)))))
=> X12 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X55,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),c_Finite__Set_Ocard(tc_Nat_Onat,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
fof(fact_surj__imp__inj__inv,axiom,
! [X2,X10,X14] :
( c_Set_Oimage(X14,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
=> c_Fun_Oinj__on(X10,X14,c_Hilbert__Choice_Oinv__into(X14,X10,c_Orderings_Otop__class_Otop(tc_fun(X14,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,
! [X14,X8,X2,X10] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X8)),c_Set_Oimage(X14,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_inj__imp__surj__inv,axiom,
! [X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> c_Set_Oimage(X14,X10,c_Hilbert__Choice_Oinv__into(X10,X14,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X14,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,X14,X12,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X14),hAPP(X2,X8)),c_Set_Oimage(X10,X14,X2,X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
fof(fact_range__eqI,axiom,
! [X14,X10,X8,X2,X22] :
( X22 = hAPP(X2,X8)
=> hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oimage(X14,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_image__eqI,axiom,
! [X10,X12,X14,X8,X2,X22] :
( X22 = hAPP(X2,X8)
=> ( hBOOL(hAPP(hAPP(c_member(X14),X8),X12))
=> hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oimage(X14,X10,X2,X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X14,X2,X22,X12,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( X22 = hAPP(X2,X8)
=> hBOOL(hAPP(hAPP(c_member(X14),X22),c_Set_Oimage(X10,X14,X2,X12))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__image__eq__iff,axiom,
! [X11,X12,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( c_Set_Oimage(X10,X14,X2,X12) = c_Set_Oimage(X10,X14,X2,X11)
<=> X12 = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_add__less__cancel__right,axiom,
! [X22,X9,X23,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),X23),X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X9)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X23),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X35,X34,X32,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),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X22,X23,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),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X9),X22)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X23),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X35,X32,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),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_finite__imageD,axiom,
! [X12,X2,X14,X10] :
( c_Finite__Set_Ofinite(X10,c_Set_Oimage(X14,X10,X2,X12))
=> ( c_Fun_Oinj__on(X14,X10,X2,X12)
=> c_Finite__Set_Ofinite(X14,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_psubset__trans,axiom,
! [X44,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),X44))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_add__le__imp__le__right,axiom,
! [X35,X34,X32,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),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X22,X9,X23,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),X23),X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X23),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X35,X32,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),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X22,X23,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),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X9),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X23),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> hAPP(c_Hilbert__Choice_Oinv__into(X10,X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( hAPP(X2,X8) = X7
=> hAPP(c_Hilbert__Choice_Oinv__into(X10,X14,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,
! [X37,X13,X10] :
( hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X13) = hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X37)
<=> X13 = X37 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X18,X52,X55] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X52)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_inv__into__f__f,axiom,
! [X8,X12,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> hAPP(c_Hilbert__Choice_Oinv__into(X10,X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X12)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> ( hAPP(X2,X8) = X7
=> hAPP(c_Hilbert__Choice_Oinv__into(X10,X14,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,X14,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ocard(X14,c_Set_Oimage(X10,X14,X2,X12)) = c_Finite__Set_Ocard(X10,X12)
=> c_Fun_Oinj__on(X10,X14,X2,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X14,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Fun_Oinj__on(X10,X14,X2,X12)
<=> c_Finite__Set_Ocard(X14,c_Set_Oimage(X10,X14,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,
! [X23,X58,X44,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X44),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10,X23,X44)),c_Set_Oinsert(X10,X23,X58))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(help_c__COMBB__1,axiom,
! [X13,X43,X16,X36,X10,X14] : hAPP(hAPP(c_COMBB(X14,X10,X36,X16),X43),X13) = hAPP(X16,hAPP(X43,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__strict__mono,axiom,
! [X33,X34,X35,X32,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X34),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_image__add__atLeastLessThan,axiom,
! [X77,X39,X55] : 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)),X55),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X39,X77)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X39),X55),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X55)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X18,X52,X55] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X52)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X18)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_add__le__less__mono,axiom,
! [X33,X34,X35,X32,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X34),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X33,X34,X35,X32,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X34),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_subset__psubset__trans,axiom,
! [X44,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),X44))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X44,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),X44))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [X18,X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X52)),X18))
<=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_insert__image,axiom,
! [X2,X14,X12,X8,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X8),X12))
=> c_Set_Oinsert(X14,hAPP(X2,X8),c_Set_Oimage(X10,X14,X2,X12)) = c_Set_Oimage(X10,X14,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,
! [X33,X34,X35,X32,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X34),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X23,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),X23),X23)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X23),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,
! [X23,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X23),X23)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X23),c_Groups_Ozero__class_Ozero(X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_add__less__mono,axiom,
! [X49,X47,X50,X51] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X50))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),X49))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X49))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_image__insert,axiom,
! [X11,X23,X2,X10,X14] : c_Set_Oimage(X14,X10,X2,c_Set_Oinsert(X14,X23,X11)) = c_Set_Oinsert(X10,hAPP(X2,X23),c_Set_Oimage(X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X11))
=> c_Fun_Oinj__on(X10,X14,X2,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_card__image,axiom,
! [X12,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,X2,X12)
=> c_Finite__Set_Ocard(X14,c_Set_Oimage(X10,X14,X2,X12)) = c_Finite__Set_Ocard(X10,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_add__neg__neg,axiom,
! [X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),c_Groups_Ozero__class_Ozero(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35)),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_Ints__add,axiom,
! [X22,X23,X10] :
( class_Rings_Oring__1(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X23),c_Int_Oring__1__class_OInts(X10)))
=> ( hBOOL(hAPP(hAPP(c_member(X10),X22),c_Int_Oring__1__class_OInts(X10)))
=> hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X23),X22)),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,X35,X32,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X34,X35,X32,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X23,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),X23),X23)),c_Groups_Ozero__class_Ozero(X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X23),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,
! [X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),c_Groups_Ozero__class_Ozero(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35)),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),c_Groups_Ozero__class_Ozero(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35)),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__le__mono,axiom,
! [X49,X47,X50,X51] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),X50))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X47),X49))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X49))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_finite__Plus__iff,axiom,
! [X11,X12,X14,X10] :
( c_Finite__Set_Ofinite(tc_sum(X10,X14),c_Sum__Type_OPlus(X10,X14,X12,X11))
<=> ( c_Finite__Set_Ofinite(X10,X12)
& c_Finite__Set_Ofinite(X14,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X11,X12,X14,X10] :
( c_Finite__Set_Ofinite(tc_sum(X10,X14),c_Sum__Type_OPlus(X10,X14,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,X14,X10] :
( c_Finite__Set_Ofinite(tc_sum(X10,X14),c_Sum__Type_OPlus(X10,X14,X12,X11))
=> c_Finite__Set_Ofinite(X14,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_add__right__mono,axiom,
! [X34,X35,X32,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X35))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X34))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X34,X35,X32,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X35))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X35))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__lessD1,axiom,
! [X47,X50,X51] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X50)),X47))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X47)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),c_Groups_Ozero__class_Ozero(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35)),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_predicate2D,axiom,
! [X7,X8,X43,X16,X14,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X14,tc_HOL_Obool)),X16),X43))
=> ( hBOOL(hAPP(hAPP(X16,X8),X7))
=> hBOOL(hAPP(hAPP(X43,X8),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X43,X14,X10,X7,X8,X16] :
( hBOOL(hAPP(hAPP(X16,X8),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X14,tc_HOL_Obool)),X16),X43))
=> hBOOL(hAPP(hAPP(X43,X8),X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_add__less__mono1,axiom,
! [X47,X50,X51] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X50))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X47))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_inj__on__iff,axiom,
! [X7,X8,X12,X2,X14,X10] :
( c_Fun_Oinj__on(X10,X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,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,
! [X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X32))
=> ( 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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__le__mono1,axiom,
! [X47,X50,X51] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),X50))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X47)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),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,
! [X56,X55] : 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)),X55),X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X33,X34,X35,X32,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_subset__trans,axiom,
! [X44,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),X44))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X12),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_add__nonneg__pos,axiom,
! [X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X32))
=> ( 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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X32))
=> ( 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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_card__Plus__conv__if,axiom,
! [X11,X14,X12,X10] :
( ( ( c_Finite__Set_Ofinite(X10,X12)
& c_Finite__Set_Ofinite(X14,X11) )
=> c_Finite__Set_Ocard(tc_sum(X10,X14),c_Sum__Type_OPlus(X10,X14,X12,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X14,X11)) )
& ( ~ ( c_Finite__Set_Ofinite(X10,X12)
& c_Finite__Set_Ofinite(X14,X11) )
=> c_Finite__Set_Ocard(tc_sum(X10,X14),c_Sum__Type_OPlus(X10,X14,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,X14,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X14,X11)
=> c_Finite__Set_Ocard(tc_sum(X10,X14),c_Sum__Type_OPlus(X10,X14,X12,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X10,X12)),c_Finite__Set_Ocard(X14,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_pos__add__strict,axiom,
! [X34,X35,X32,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X32))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),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,
! [X23,X10] :
( class_Int_Oring__char__0(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X23),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)),X23)),X23) != 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,
! [X23,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),X23),X23)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_add__gr__0,axiom,
! [X18,X52] :
( 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),X52),X18)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X52))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)) ) ),
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,
! [X22,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,X22,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_add__strict__increasing2,axiom,
! [X34,X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X32))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X34,X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X32))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X32))
=> ( 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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
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_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__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_insert__iff,axiom,
! [X12,X22,X23,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X23),c_Set_Oinsert(X10,X22,X12)))
<=> ( X23 = X22
| hBOOL(hAPP(hAPP(c_member(X10),X23),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X12,X22,X23,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X23),c_Set_Oinsert(X10,X22,X12)))
=> ( X23 != X22
=> hBOOL(hAPP(hAPP(c_member(X10),X23),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X23,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),X23),X23)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_Pi__UNIV,axiom,
! [X12,X14,X10] : c_FuncSet_OPi(X10,X14,X12,hAPP(c_COMBK(tc_fun(X14,tc_HOL_Obool),X10),c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X14),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
fof(fact_add__increasing,axiom,
! [X34,X35,X32,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10)),X32))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X32,X35,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,X35),X32))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_finite__Plus,axiom,
! [X11,X14,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> ( c_Finite__Set_Ofinite(X14,X11)
=> c_Finite__Set_Ofinite(tc_sum(X10,X14),c_Sum__Type_OPlus(X10,X14,X12,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(help_c__COMBC__1,axiom,
! [X13,X43,X16,X10,X36,X14] : hAPP(hAPP(hAPP(c_COMBC(X14,X36,X10),X16),X43),X13) = hAPP(hAPP(X16,X13),X43),
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,X14] :
( class_Orderings_Oord(X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X14),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,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,X14] :
( class_Orderings_Oord(X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X14),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X14,hAPP(X2,X8)),hAPP(X1,X8))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_finite__imageI,axiom,
! [X65,X14,X40,X10] :
( c_Finite__Set_Ofinite(X10,X40)
=> c_Finite__Set_Ofinite(X14,c_Set_Oimage(X10,X14,X65,X40)) ),
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,X35,X32,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35)),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),X35) ),
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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,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,X14,X10] :
( c_Fun_Oinj__on(X10,X14,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_atLeastLessThan__eq__iff,axiom,
! [X78,X9,X22,X23,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X23),X22))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X9),X78))
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X10,X23,X22) = c_SetInterval_Oord__class_OatLeastLessThan(X10,X9,X78)
<=> ( X23 = X9
& X22 = X78 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [X78,X9,X22,X23,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X10,X23,X22) = c_SetInterval_Oord__class_OatLeastLessThan(X10,X9,X78)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X23),X22))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X9),X78))
=> X23 = X9 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__inj_I2_J,axiom,
! [X78,X9,X22,X23,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X10,X23,X22) = c_SetInterval_Oord__class_OatLeastLessThan(X10,X9,X78)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X23),X22))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X9),X78))
=> X22 = X78 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_less__add__Suc1,axiom,
! [X48,X51] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X48)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X48,X51] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X51)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_insertI2,axiom,
! [X22,X11,X23,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X23),X11))
=> hBOOL(hAPP(hAPP(c_member(X10),X23),c_Set_Oinsert(X10,X22,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_less__trans__Suc,axiom,
! [X47,X50,X51] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X50))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X50),X47))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X51)),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,
! [X18,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X52)),hAPP(c_Nat_OSuc,X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18)) ),
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,
! [X14,X10] :
( c_Finite__Set_Ofinite(tc_fun(X10,X14),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X14),tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X14,c_Orderings_Otop__class_Otop(tc_fun(X14,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,
! [X19,X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X19))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X19,X21,X20,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_image__Suc__atLeastLessThan,axiom,
! [X77,X39] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X39,X77)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X39),hAPP(c_Nat_OSuc,X77)),
file('/export/starexec/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,
! [X14,X10] : c_Sum__Type_OPlus(X10,X14,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X10,X14),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_trans__less__add1,axiom,
! [X48,X50,X51] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X50))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X48))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X19,X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add2,axiom,
! [X48,X50,X51] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X50))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X50))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X20,X19,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X19))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X18,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),hAPP(c_Nat_OSuc,X18)))
<=> ( X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X63] :
( X52 = hAPP(c_Nat_OSuc,X63)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X63),X18)) ) ) ),
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,X35,X32,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35)),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),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,X35,X32,X10] :
( class_Groups_Oab__semigroup__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35)),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),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,
! [X33,X34,X32,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)),X33) ),
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,
! [X52,X18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X18)),hAPP(c_Nat_OSuc,X52)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_order__le__less__trans,axiom,
! [X19,X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X19))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X19,X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X19))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I8_J,axiom,
! [X19,X21,X20,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X19,X21,X20,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X19),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X14,X10] :
( c_Finite__Set_Ofinite(tc_sum(X10,X14),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X10,X14),tc_HOL_Obool)))
<=> ( c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
& c_Finite__Set_Ofinite(X14,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X14,X10] :
( c_Finite__Set_Ofinite(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
=> ( c_Finite__Set_Ofinite(X14,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(tc_prod(X10,X14),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10,X14),tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_less__add__eq__less,axiom,
! [X46,X48,X49,X47] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),X49))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X49) = 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,
! [X23,X11,X10] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X11),c_Set_Oinsert(X10,X23,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,X50,X51] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),X50))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X48))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X19,X20,X21] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add2,axiom,
! [X48,X50,X51] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),X50))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X50))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X20,X19,X21] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X19))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X14,X10] :
( c_Finite__Set_Ofinite(tc_fun(X10,X14),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X14),tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(X14,c_Orderings_Otop__class_Otop(tc_fun(X14,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,
! [X52,X18] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X52))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X18)),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X18,X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X52)),X18))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18)) ),
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,X43,X16,X10] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X16),X43))
=> ( hBOOL(hAPP(X16,X8))
=> hBOOL(hAPP(X43,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X43,X10,X8,X16] :
( hBOOL(hAPP(X16,X8))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool),X16),X43))
=> hBOOL(hAPP(X43,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_order__trans,axiom,
! [X19,X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X19))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X19,X21,X20,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X19),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X19),X21)) ) ) ),
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,
! [X32,X10] :
( class_Rings_Olinordered__semidom(X10)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),c_Groups_Oone__class_Oone(X10)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_le__less__Suc__eq,axiom,
! [X18,X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),hAPP(c_Nat_OSuc,X52)))
<=> X18 = X52 ) ),
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,
! [X56] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X56)
<=> ? [X17] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X56))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X17)) ) ),
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,X23,X10] : hBOOL(hAPP(hAPP(c_member(X10),X23),c_Set_Oinsert(X10,X23,X11))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_less__Suc__eq,axiom,
! [X18,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),hAPP(c_Nat_OSuc,X18)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18))
| X52 = X18 ) ),
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,
! [X33,X34,X32,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_le__trans,axiom,
! [X47,X50,X51] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),X50))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X50),X47))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),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,
! [X18,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18))
<=> ? [X57] : X18 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X57)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__Suc__eq__le,axiom,
! [X18,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),hAPP(c_Nat_OSuc,X18)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X56] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X56)
<=> ? [X17] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X56))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X17)) ) ),
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,
! [X23,X10] :
( class_Int_Oring__char__0(X10)
=> ( hBOOL(hAPP(hAPP(c_member(X10),X23),c_Int_Oring__1__class_OInts(X10)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X23),X23) = c_Groups_Ozero__class_Ozero(X10)
<=> X23 = 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,
! [X18,X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),hAPP(c_Nat_OSuc,X18)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18))
| X52 = hAPP(c_Nat_OSuc,X18) ) ),
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,
! [X16,X18,X52] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18))
=> hBOOL(hAPP(hAPP(X16,X18),X52)) )
=> ( ( X52 = X18
=> hBOOL(hAPP(hAPP(X16,X18),X52)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X52))
=> hBOOL(hAPP(hAPP(X16,X18),X52)) )
=> hBOOL(hAPP(hAPP(X16,X18),X52)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_nat__add__left__commute,axiom,
! [X19,X20,X21] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X19)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X19)),
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,
! [X20,X21,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21))
=> X21 = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X21,X20,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
=> X21 = X20 ) ) ),
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,
! [X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20)) ) ),
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,
! [X68,X10] : c_Set_Oimage(X10,X10,c_COMBI(X10),X68) = X68,
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,
! [X32,X35,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X32))
=> ( X32 != X35
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X35,X32,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X35))
=> ( X32 != X35
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X20,X21,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
| X21 = X20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X35,X32,X10] :
( class_Orderings_Oorder(X10)
=> ( X32 != X35
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X32),X35))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_xt1_I12_J,axiom,
! [X35,X32,X10] :
( class_Orderings_Oorder(X10)
=> ( X32 != X35
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X35),X32))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_less__Suc0,axiom,
! [X18] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_inj__Suc,axiom,
! [X56] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X56),
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,
! [X18,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18))
& X52 != X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X18,X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18))
| X52 = X18 ) ),
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,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_insert__absorb,axiom,
! [X12,X23,X10] :
( hBOOL(hAPP(hAPP(c_member(X10),X23),X12))
=> c_Set_Oinsert(X10,X23,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,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
| X21 = X20
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ),
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,X23,X10] :
( c_Finite__Set_Ofinite(X10,c_Set_Oinsert(X10,X23,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,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ),
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,
! [X18,X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18))
<=> ? [X57] : X18 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_nat__neq__iff,axiom,
! [X18,X52] :
( X52 != X18
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_gr0__conv__Suc,axiom,
! [X18] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18))
<=> ? [X17] : X18 = hAPP(c_Nat_OSuc,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X20,X21,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> X20 != X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X20,X21,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> X21 != X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X20,X21,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> X21 != X20 ) ),
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,
! [X18] :
( X18 != 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)),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_add__right__imp__eq,axiom,
! [X34,X32,X35,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X35),X32) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X32)
=> X35 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X9,X23,X22,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X9),X23)
<=> X22 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X34,X35,X32,X10] :
( class_Groups_Ocancel__ab__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)
=> X35 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X34,X35,X32,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34)
=> X35 = X34 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X9,X22,X23,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X23),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X23),X9)
<=> X22 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_linorder__linear,axiom,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21)) ) ),
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,
! [X53,X54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X54),X53))
=> X54 != X53 ),
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,
! [X18,X55,X52] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X55) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18),X55)
<=> X52 = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X18,X52,X55] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X52) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X18)
<=> X52 = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_finite_OinsertI,axiom,
! [X23,X12,X10] :
( c_Finite__Set_Ofinite(X10,X12)
=> c_Finite__Set_Ofinite(X10,c_Set_Oinsert(X10,X23,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,
! [X18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X18 = 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,
! [X18,X52] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X18) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X52 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X18 = 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,
! [X18,X52] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X18)
<=> ( ( X52 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X18 = 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,X32,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X34),X32) ),
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,
! [X21,X10] :
( class_Orderings_Otop(X10)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),c_Orderings_Otop__class_Otop(X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_double__eq__0__iff,axiom,
! [X23,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X23),X23) = c_Groups_Ozero__class_Ozero(X10)
<=> X23 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X23,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X23),X23)
<=> X23 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__iff,axiom,
! [X23,X22,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( X22 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X22),X23)
<=> X23 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_order__eq__refl,axiom,
! [X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( X21 = X20
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(help_c__COMBK__1,axiom,
! [X82,X81,X14,X10] : hAPP(hAPP(c_COMBK(X10,X14),X81),X82) = X81,
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,
! [X21,X10] :
( class_Orderings_Opreorder(X10)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X21)) ),
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,X14,X10] :
( class_Orderings_Otop(X10)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X14,X10)),X8) = c_Orderings_Otop__class_Otop(X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_add__is__0,axiom,
! [X18,X52] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X18) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X52 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X18 = 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,
! [X32,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X32) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0__left,axiom,
! [X32,X10] :
( class_Groups_Omonoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X32) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X32,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X32) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X32,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),c_Groups_Ozero__class_Ozero(X10)) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__right,axiom,
! [X32,X10] :
( class_Groups_Omonoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),c_Groups_Ozero__class_Ozero(X10)) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X32,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),c_Groups_Ozero__class_Ozero(X10)) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
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,
! [X18] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X18)),
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,
! [X80,X79] :
( ( class_Finite__Set_Ofinite(X79)
& class_Finite__Set_Ofinite(X80) )
=> class_Finite__Set_Ofinite(tc_sum(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [X80,X79] :
( ( class_Finite__Set_Ofinite(X79)
& class_Finite__Set_Ofinite(X80) )
=> class_Finite__Set_Ofinite(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X80,X79] :
( ( class_Finite__Set_Ofinite(X79)
& class_Finite__Set_Ofinite(X80) )
=> class_Finite__Set_Ofinite(tc_prod(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(fact_Suc__inject,axiom,
! [X20,X21] :
( hAPP(c_Nat_OSuc,X21) = hAPP(c_Nat_OSuc,X20)
=> X21 = X20 ),
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_Otop,axiom,
! [X79,X80] :
( class_Orderings_Otop(X80)
=> class_Orderings_Otop(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X79,X80] :
( class_Orderings_Oorder(X80)
=> class_Orderings_Oorder(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X79,X80] :
( class_Orderings_Oord(X80)
=> class_Orderings_Oord(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X79,X80] :
( class_Orderings_Opreorder(X80)
=> class_Orderings_Opreorder(tc_fun(X79,X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(fact_Suc__not__Zero,axiom,
! [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,
! [X81,X10] : hAPP(c_COMBI(X10),X81) = X81,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
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(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(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [X80] :
( class_Finite__Set_Ofinite(X80)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X80)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(fact_nat__size,axiom,
! [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__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__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
fof(fact__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096) ).
fof(fact__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096) ).
fof(fact_surjh,axiom,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjh) ).
fof(fact_n_I1_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I1_J) ).
fof(fact_injh,axiom,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injh) ).
fof(fact_card__UNIV__unit,axiom,
c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
fof(fact_finite__indi,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(fact_nat_Osize_I3_J,axiom,
c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_nat_Osize_I1_J,axiom,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_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__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__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_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(fact__096c_A_126_061_Ad_096,axiom,
v_c____ != v_d____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_126_061_Ad_096) ).
fof(fact__096a_A_126_061_Ab_096,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
fof(i_0_519,negated_conjecture,
~ ! [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)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_520,plain,
~ ! [X27] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> ( ! [X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X27))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X17))),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),X27),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,X40,X1,X5,X2,X14,X10] :
( c_Finite__Set_Ofolding__image__simple(X10,X14,X2,X5,X1,X40)
=> ( c_Finite__Set_Ofinite(X14,X12)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X14),X8),X12))
=> hAPP(X40,c_Set_Oinsert(X14,X8,X12)) = hAPP(hAPP(X2,hAPP(X1,X8)),hAPP(X40,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,X14,X10] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X10,c_Set_Oimage(X14,X10,X2,X12))),c_Finite__Set_Ocard(X14,X12)))
=> ~ c_Fun_Oinj__on(X14,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,negated_conjecture,
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,esk45_0) != v_n____
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk45_0) != v_n____
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,esk45_0)),v_e____)))
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,esk45_0) != v_n____
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0) != v_n____
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,esk45_0) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,esk45_0) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[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,
! [X22,X23,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),X23),X22)),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),X22),X23)),X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_529,plain,
! [X8,X11,X12,X2,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,X14)),X2),c_FuncSet_OPi(X10,X14,X12,X11)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X14),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,
~ ! [X31] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X31))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X31),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_532,plain,
~ ! [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),v_a____),v_b____)),X30))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X30),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_533,plain,
! [X1,X2,X10,X14] :
( class_Orderings_Oord(X14)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X14)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X14),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X14),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,
! [X50,X51] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X50)),X51)),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_536,plain,
! [X51,X50] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X51)),X51)),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_537,plain,
! [X18,X16] :
( ~ hBOOL(hAPP(X16,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X16,X18))
=> ? [X57] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X57),X18))
& ! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X57))
=> ~ hBOOL(hAPP(X16,X4)) )
& hBOOL(hAPP(X16,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,
! [X22,X11,X23,X10] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X23),X11))
=> X23 = X22 )
=> hBOOL(hAPP(hAPP(c_member(X10),X23),c_Set_Oinsert(X10,X22,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,
! [X18,X52] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),X18))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X18)),X52)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_541,plain,
! [X18,X52] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X18))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),hAPP(c_Nat_OSuc,X52))) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_542,plain,
! [X32,X35,X10] :
( class_Orderings_Oorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X32))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35)) ) ),
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,
! [X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_545,plain,
! [X35,X32,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X35))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X35),X32)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_546,plain,
! [X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_547,plain,
! [X20,X21,X10] :
( class_Orderings_Opreorder(X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ),
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,
! [X52,X18] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),X52))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18),hAPP(c_Nat_OSuc,X52)))
<=> X18 = X52 ) ),
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,
! [X21,X20,X10] :
( class_Orderings_Olinorder(X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20)) ) ),
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,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> ( X21 != X20
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_564,plain,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( X21 != X20
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_565,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_566,plain,
! [X20,X21,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X21 != X20
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X20),X21)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_567,plain,
! [X21,X20,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_568,plain,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21)) ) ),
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,
! [X20,X21] :
( X21 != X20
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21)) ) ),
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,
! [X21,X10] :
( class_Orderings_Opreorder(X10)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X21),X21)) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_573,plain,
! [X20,X21,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X21),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X10,X20),X21)) ) ),
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_not__less0]) ).
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_less__nat__zero__code]) ).
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_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_583,plain,
! [X1768] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk10_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,X1768),esk10_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____)),X1768))),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),esk10_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_584,plain,
! [X1717] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk7_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1717),esk7_0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1717))),v_Lab____)),v_Lba____)))) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096])])])]) ).
fof(i_0_585,plain,
! [X1654] : hBOOL(hAPP(hAPP(c_member(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____)),X1654))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
inference(variable_rename,[status(thm)],[fact_PiProf]) ).
fof(i_0_586,plain,
! [X1651] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1651),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X1651))),v_Lab____)),v_Lba____)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n_I2_J])]) ).
fof(i_0_587,plain,
! [X1801,X1802,X1803,X1804] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1804,tc_fun(X1803,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1804,tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_fun(X1803,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1803,tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_fun(X1803,tc_HOL_Obool)),X1804,c_COMBC(X1803,tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1803,tc_prod(X1804,X1803)),tc_fun(X1803,tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),X1804,c_COMBB(tc_prod(X1804,X1803),tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool),X1803,c_member(tc_prod(X1804,X1803)))),c_Product__Type_OPair(X1804,X1803)))),X1802)),hAPP(hAPP(c_COMBC(X1804,tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_fun(X1803,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1803,tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_fun(X1803,tc_HOL_Obool)),X1804,c_COMBC(X1803,tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1803,tc_prod(X1804,X1803)),tc_fun(X1803,tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),X1804,c_COMBB(tc_prod(X1804,X1803),tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool),X1803,c_member(tc_prod(X1804,X1803)))),c_Product__Type_OPair(X1804,X1803)))),X1801)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),X1802),X1801)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),X1802),X1801))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1804,tc_fun(X1803,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1804,tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_fun(X1803,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1803,tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_fun(X1803,tc_HOL_Obool)),X1804,c_COMBC(X1803,tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1803,tc_prod(X1804,X1803)),tc_fun(X1803,tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),X1804,c_COMBB(tc_prod(X1804,X1803),tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool),X1803,c_member(tc_prod(X1804,X1803)))),c_Product__Type_OPair(X1804,X1803)))),X1802)),hAPP(hAPP(c_COMBC(X1804,tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_fun(X1803,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1803,tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_fun(X1803,tc_HOL_Obool)),X1804,c_COMBC(X1803,tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1803,tc_prod(X1804,X1803)),tc_fun(X1803,tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool)),X1804,c_COMBB(tc_prod(X1804,X1803),tc_fun(tc_fun(tc_prod(X1804,X1803),tc_HOL_Obool),tc_HOL_Obool),X1803,c_member(tc_prod(X1804,X1803)))),c_Product__Type_OPair(X1804,X1803)))),X1801))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_588,plain,
! [X1709,X1710,X1711,X1712,X1713,X1714] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1714),X1713)),hAPP(v_F,X1710)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1712),X1711)),hAPP(v_F,X1709)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1714),X1713)),hAPP(X1710,esk6_6(X1709,X1710,X1711,X1712,X1713,X1714))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1712),X1711)),hAPP(X1709,esk6_6(X1709,X1710,X1711,X1712,X1713,X1714))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1709),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))),X1710),c_Arrow__Order__Mirabelle_OProf))
| X1713 = X1712
| X1714 = X1711
| X1712 = X1711
| X1714 = X1713 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1712),X1711)),hAPP(v_F,X1709)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1714),X1713)),hAPP(v_F,X1710)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1714),X1713)),hAPP(X1710,esk6_6(X1709,X1710,X1711,X1712,X1713,X1714))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1712),X1711)),hAPP(X1709,esk6_6(X1709,X1710,X1711,X1712,X1713,X1714))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1709),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))),X1710),c_Arrow__Order__Mirabelle_OProf))
| X1713 = X1712
| X1714 = X1711
| X1712 = X1711
| X1714 = X1713 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1714),X1713)),hAPP(v_F,X1710)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1712),X1711)),hAPP(v_F,X1709)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1714),X1713)),hAPP(X1710,esk6_6(X1709,X1710,X1711,X1712,X1713,X1714))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1712),X1711)),hAPP(X1709,esk6_6(X1709,X1710,X1711,X1712,X1713,X1714))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1709),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))),X1710),c_Arrow__Order__Mirabelle_OProf))
| X1713 = X1712
| X1714 = X1711
| X1712 = X1711
| X1714 = X1713 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1712),X1711)),hAPP(v_F,X1709)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1714),X1713)),hAPP(v_F,X1710)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1714),X1713)),hAPP(X1710,esk6_6(X1709,X1710,X1711,X1712,X1713,X1714))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1712),X1711)),hAPP(X1709,esk6_6(X1709,X1710,X1711,X1712,X1713,X1714))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1709),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))),X1710),c_Arrow__Order__Mirabelle_OProf))
| X1713 = X1712
| X1714 = X1711
| X1712 = X1711
| X1714 = X1713 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).
fof(i_0_589,plain,
! [X1702,X1703,X1704,X1705,X1706,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),X1707),X1706)),hAPP(X1703,esk5_6(X1702,X1703,X1704,X1705,X1706,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),X1705),X1704)),hAPP(X1702,esk5_6(X1702,X1703,X1704,X1705,X1706,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),X1707),X1706)),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),X1705),X1704)),hAPP(v_F,X1702)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1702),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))),X1703),c_Arrow__Order__Mirabelle_OProf))
| X1706 = X1705
| X1707 = X1704
| X1705 = X1704
| X1707 = X1706 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1707),X1706)),hAPP(X1703,esk5_6(X1702,X1703,X1704,X1705,X1706,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),X1705),X1704)),hAPP(X1702,esk5_6(X1702,X1703,X1704,X1705,X1706,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),X1707),X1706)),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),X1705),X1704)),hAPP(v_F,X1702)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1702),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))),X1703),c_Arrow__Order__Mirabelle_OProf))
| X1706 = X1705
| X1707 = X1704
| X1705 = X1704
| X1707 = X1706 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).
fof(i_0_590,plain,
! [X1689,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,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),X1692),X1691)),hAPP(v_F,X1689)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X1690,esk3_6(X1689,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),X1692),X1691)),hAPP(X1689,esk3_6(X1689,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))),X1689),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))),X1690),c_Arrow__Order__Mirabelle_OProf))
| X1692 = X1691
| 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),X1692),X1691)),hAPP(v_F,X1689)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,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(X1690,esk3_6(X1689,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),X1692),X1691)),hAPP(X1689,esk3_6(X1689,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))),X1689),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))),X1690),c_Arrow__Order__Mirabelle_OProf))
| X1692 = X1691
| 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,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),X1692),X1691)),hAPP(v_F,X1689)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X1690,esk3_6(X1689,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),X1692),X1691)),hAPP(X1689,esk3_6(X1689,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))),X1689),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))),X1690),c_Arrow__Order__Mirabelle_OProf))
| X1692 = X1691
| 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),X1692),X1691)),hAPP(v_F,X1689)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,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(X1690,esk3_6(X1689,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),X1692),X1691)),hAPP(X1689,esk3_6(X1689,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))),X1689),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))),X1690),c_Arrow__Order__Mirabelle_OProf))
| X1692 = X1691
| X1694 = X1693 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pairwise__neutrality])])])]) ).
fof(i_0_591,plain,
! [X1961,X1962,X1963,X1964] :
( ( hAPP(hAPP(c_COMBC(X1964,tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_fun(X1963,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1963,tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_fun(X1963,tc_HOL_Obool)),X1964,c_COMBC(X1963,tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1963,tc_prod(X1964,X1963)),tc_fun(X1963,tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),X1964,c_COMBB(tc_prod(X1964,X1963),tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool),X1963,c_member(tc_prod(X1964,X1963)))),c_Product__Type_OPair(X1964,X1963)))),X1962) != hAPP(hAPP(c_COMBC(X1964,tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_fun(X1963,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1963,tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_fun(X1963,tc_HOL_Obool)),X1964,c_COMBC(X1963,tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1963,tc_prod(X1964,X1963)),tc_fun(X1963,tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),X1964,c_COMBB(tc_prod(X1964,X1963),tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool),X1963,c_member(tc_prod(X1964,X1963)))),c_Product__Type_OPair(X1964,X1963)))),X1961)
| X1962 = X1961 )
& ( X1962 != X1961
| hAPP(hAPP(c_COMBC(X1964,tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_fun(X1963,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1963,tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_fun(X1963,tc_HOL_Obool)),X1964,c_COMBC(X1963,tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1963,tc_prod(X1964,X1963)),tc_fun(X1963,tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),X1964,c_COMBB(tc_prod(X1964,X1963),tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool),X1963,c_member(tc_prod(X1964,X1963)))),c_Product__Type_OPair(X1964,X1963)))),X1962) = hAPP(hAPP(c_COMBC(X1964,tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_fun(X1963,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1963,tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_fun(X1963,tc_HOL_Obool)),X1964,c_COMBC(X1963,tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1963,tc_prod(X1964,X1963)),tc_fun(X1963,tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool)),X1964,c_COMBB(tc_prod(X1964,X1963),tc_fun(tc_fun(tc_prod(X1964,X1963),tc_HOL_Obool),tc_HOL_Obool),X1963,c_member(tc_prod(X1964,X1963)))),c_Product__Type_OPair(X1964,X1963)))),X1961) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_592,plain,
! [X2427,X2428,X2429,X2430,X2431] :
( ( hBOOL(hAPP(hAPP(c_member(X2431),esk28_5(X2427,X2428,X2429,X2430,X2431)),X2430))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2431,X2429),tc_HOL_Obool),c_FuncSet_OPi(X2431,X2429,X2430,X2428)),c_FuncSet_OPi(X2431,X2429,X2430,X2427))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2429,tc_HOL_Obool),hAPP(X2428,esk28_5(X2427,X2428,X2429,X2430,X2431))),hAPP(X2427,esk28_5(X2427,X2428,X2429,X2430,X2431))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2431,X2429),tc_HOL_Obool),c_FuncSet_OPi(X2431,X2429,X2430,X2428)),c_FuncSet_OPi(X2431,X2429,X2430,X2427))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_593,plain,
! [X2481,X2482,X2483,X2484,X2485] :
( ( hBOOL(hAPP(hAPP(c_member(X2485),esk29_5(X2481,X2482,X2483,X2484,X2485)),X2484))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2485,X2483)),X2482),c_FuncSet_OPi(X2485,X2483,X2484,X2481))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2483),hAPP(X2482,esk29_5(X2481,X2482,X2483,X2484,X2485))),hAPP(X2481,esk29_5(X2481,X2482,X2483,X2484,X2485))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2485,X2483)),X2482),c_FuncSet_OPi(X2485,X2483,X2484,X2481))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_594,plain,
! [X2397,X2398,X2399,X2400,X2401,X2403,X2408,X2409] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2397,X2398)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2397,X2399)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2398,esk19_5(X2397,X2398,X2399,X2400,X2401))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2399,esk19_5(X2397,X2398,X2399,X2400,X2401))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2399),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))),X2398),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2397) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2397,X2399)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2397,X2398)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2398,esk19_5(X2397,X2398,X2399,X2400,X2401))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2399,esk19_5(X2397,X2398,X2399,X2400,X2401))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2399),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))),X2398),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2397) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2397,X2398)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2397,X2399)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2398,esk19_5(X2397,X2398,X2399,X2400,X2401))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2399,esk19_5(X2397,X2398,X2399,X2400,X2401))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2399),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))),X2398),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2397) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2397,X2399)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2397,X2398)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2398,esk19_5(X2397,X2398,X2399,X2400,X2401))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2400),X2401)),hAPP(X2399,esk19_5(X2397,X2398,X2399,X2400,X2401))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2399),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))),X2398),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2397) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk20_1(X2403)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(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))),esk21_1(X2403)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2403) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2403)),esk23_1(X2403))),hAPP(esk20_1(X2403),X2408)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2403)),esk23_1(X2403))),hAPP(esk21_1(X2403),X2408)))
| c_Arrow__Order__Mirabelle_OIIA(X2403) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2403)),esk23_1(X2403))),hAPP(esk21_1(X2403),X2409)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2403)),esk23_1(X2403))),hAPP(esk20_1(X2403),X2409)))
| c_Arrow__Order__Mirabelle_OIIA(X2403) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2403)),esk23_1(X2403))),hAPP(X2403,esk20_1(X2403))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2403)),esk23_1(X2403))),hAPP(X2403,esk21_1(X2403))))
| c_Arrow__Order__Mirabelle_OIIA(X2403) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2403)),esk23_1(X2403))),hAPP(X2403,esk20_1(X2403))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X2403)),esk23_1(X2403))),hAPP(X2403,esk21_1(X2403))))
| c_Arrow__Order__Mirabelle_OIIA(X2403) ) ),
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_595,plain,
! [X1696,X1697,X1698,X1699,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),X1700),X1699)),hAPP(v_F,X1697)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1699),X1698)),hAPP(v_F,X1696)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(X1697,esk4_5(X1696,X1697,X1698,X1699,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),X1699),X1698)),hAPP(X1696,esk4_5(X1696,X1697,X1698,X1699,X1700))))
| ~ hBOOL(hAPP(hAPP(c_member(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 = X1698
| X1699 = X1698
| X1700 = X1699 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(v_F,X1697)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(X1697,esk4_5(X1696,X1697,X1698,X1699,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),X1699),X1698)),hAPP(X1696,esk4_5(X1696,X1697,X1698,X1699,X1700))))
| ~ hBOOL(hAPP(hAPP(c_member(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 = X1698
| X1699 = X1698
| X1700 = X1699 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(v_F,X1697)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1699),X1698)),hAPP(v_F,X1696)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(X1697,esk4_5(X1696,X1697,X1698,X1699,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),X1699),X1698)),hAPP(X1696,esk4_5(X1696,X1697,X1698,X1699,X1700))))
| ~ hBOOL(hAPP(hAPP(c_member(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 = X1698
| X1699 = X1698
| X1700 = X1699 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(v_F,X1697)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1700),X1699)),hAPP(X1697,esk4_5(X1696,X1697,X1698,X1699,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),X1699),X1698)),hAPP(X1696,esk4_5(X1696,X1697,X1698,X1699,X1700))))
| ~ hBOOL(hAPP(hAPP(c_member(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 = X1698
| X1699 = X1698
| X1700 = X1699 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C4_C])])])]) ).
fof(i_0_596,plain,
! [X1993,X1994] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk13_2(X1993,X1994)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X1994,X1993)
| ~ 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))),X1994),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)))) )
& ( esk14_2(X1993,X1994) != esk15_2(X1993,X1994)
| c_Arrow__Order__Mirabelle_Odictator(X1994,X1993)
| ~ 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))),X1994),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),esk14_2(X1993,X1994)),esk15_2(X1993,X1994))),hAPP(esk13_2(X1993,X1994),X1993)))
| c_Arrow__Order__Mirabelle_Odictator(X1994,X1993)
| ~ 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))),X1994),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),esk14_2(X1993,X1994)),esk15_2(X1993,X1994))),hAPP(X1994,esk13_2(X1993,X1994))))
| c_Arrow__Order__Mirabelle_Odictator(X1994,X1993)
| ~ 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))),X1994),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_597,plain,
! [X1718,X1719,X1720,X1721,X1722,X1723,X1724,X1725] :
( ( X1723 = X1721
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1725,X1725)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1725),X1723),X1721)),X1719))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1725,X1724),tc_prod(X1725,X1724))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1725,X1724),tc_prod(X1725,X1724)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1724),X1723),X1722)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1724),X1721),X1720))),c_Wellfounded_Olex__prod(X1725,X1724,X1719,X1718))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1724,X1724)),hAPP(hAPP(c_Product__Type_OPair(X1724,X1724),X1722),X1720)),X1718))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1725,X1725)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1725),X1723),X1721)),X1719))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1725,X1724),tc_prod(X1725,X1724))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1725,X1724),tc_prod(X1725,X1724)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1724),X1723),X1722)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1724),X1721),X1720))),c_Wellfounded_Olex__prod(X1725,X1724,X1719,X1718))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1725,X1725)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1725),X1723),X1721)),X1719))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1725,X1724),tc_prod(X1725,X1724))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1725,X1724),tc_prod(X1725,X1724)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1724),X1723),X1722)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1724),X1721),X1720))),c_Wellfounded_Olex__prod(X1725,X1724,X1719,X1718))) )
& ( X1723 != X1721
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1724,X1724)),hAPP(hAPP(c_Product__Type_OPair(X1724,X1724),X1722),X1720)),X1718))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1725,X1724),tc_prod(X1725,X1724))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1725,X1724),tc_prod(X1725,X1724)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1724),X1723),X1722)),hAPP(hAPP(c_Product__Type_OPair(X1725,X1724),X1721),X1720))),c_Wellfounded_Olex__prod(X1725,X1724,X1719,X1718))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_598,plain,
! [X1684,X1685,X1686,X1687] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(v_F,X1685)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),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),X1687),X1686)),hAPP(X1685,esk2_4(X1684,X1685,X1686,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),X1687)),hAPP(X1684,esk2_4(X1684,X1685,X1686,X1687))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1684),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1685),c_Arrow__Order__Mirabelle_OProf))
| X1687 = X1686 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),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),X1687),X1686)),hAPP(v_F,X1685)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(X1685,esk2_4(X1684,X1685,X1686,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),X1687)),hAPP(X1684,esk2_4(X1684,X1685,X1686,X1687))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1684),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1685),c_Arrow__Order__Mirabelle_OProf))
| X1687 = X1686 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(v_F,X1685)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1686),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),X1687),X1686)),hAPP(X1685,esk2_4(X1684,X1685,X1686,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),X1687)),hAPP(X1684,esk2_4(X1684,X1685,X1686,X1687))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1684),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1685),c_Arrow__Order__Mirabelle_OProf))
| X1687 = X1686 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),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),X1687),X1686)),hAPP(v_F,X1685)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1687),X1686)),hAPP(X1685,esk2_4(X1684,X1685,X1686,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),X1687)),hAPP(X1684,esk2_4(X1684,X1685,X1686,X1687))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1684),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1685),c_Arrow__Order__Mirabelle_OProf))
| X1687 = X1686 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C3_C])])])]) ).
fof(i_0_599,plain,
! [X2874,X2875,X2876,X2877,X2878,X2879,X2880] :
( ~ c_Finite__Set_Ofolding__image__simple(X2880,X2879,X2878,X2877,X2876,X2875)
| ~ c_Finite__Set_Ofinite(X2879,X2874)
| hAPP(X2875,X2874) = c_Finite__Set_Ofold__image(X2880,X2879,X2878,X2876,X2877,X2874) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).
fof(i_0_600,plain,
! [X3060,X3061,X3062,X3063,X3064,X3066,X3067,X3068,X3069,X3070,X3071] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3062,tc_HOL_Obool),esk38_5(X3060,X3061,X3062,X3063,X3064)),X3060))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),X3063),c_Set_Oimage(X3062,X3064,X3061,X3060))) )
& ( X3063 = c_Set_Oimage(X3062,X3064,X3061,esk38_5(X3060,X3061,X3062,X3063,X3064))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3064,tc_HOL_Obool),X3063),c_Set_Oimage(X3062,X3064,X3061,X3060))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3068,tc_HOL_Obool),X3071),X3066))
| X3069 != c_Set_Oimage(X3068,X3070,X3067,X3071)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3070,tc_HOL_Obool),X3069),c_Set_Oimage(X3068,X3070,X3067,X3066))) ) ),
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_601,plain,
! [X1640,X1641,X1642,X1643,X1644,X1645,X1646] :
( ~ hBOOL(hAPP(X1646,X1645))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1644,X1644)),hAPP(hAPP(c_Product__Type_OPair(X1644,X1644),X1643),X1642)),hAPP(X1641,X1645)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1640,X1644),tc_prod(X1640,X1644))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1640,X1644),tc_prod(X1640,X1644)),hAPP(hAPP(c_Product__Type_OPair(X1640,X1644),X1645),X1643)),hAPP(hAPP(c_Product__Type_OPair(X1640,X1644),X1645),X1642))),c_Recdef_Osame__fst(X1640,X1644,X1646,X1641))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_602,plain,
! [X2129,X2130,X2131,X2132,X2133] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2131,X2132),X2130),X2129))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2132,hAPP(X2130,X2133)),hAPP(X2129,X2133)))
| ~ class_Orderings_Oord(X2132) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2132,hAPP(X2130,esk16_4(X2129,X2130,X2131,X2132))),hAPP(X2129,esk16_4(X2129,X2130,X2131,X2132))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2131,X2132),X2130),X2129))
| ~ class_Orderings_Oord(X2132) ) ),
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_603,plain,
! [X2582,X2583,X2584,X2585,X2586,X2587,X2588,X2589] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2589,X2588,X2587,X2586,X2585,X2584)
| ~ c_Finite__Set_Ofinite(X2588,X2583)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2588,tc_HOL_Obool),X2582),X2583))
| hAPP(hAPP(X2587,hAPP(X2584,X2582)),hAPP(X2584,X2583)) = hAPP(X2584,X2583) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_604,plain,
! [X2574,X2575,X2576,X2577,X2578,X2579,X2580,X2581] :
( ~ c_Finite__Set_Ofolding__image__simple(X2581,X2580,X2579,X2578,X2577,X2576)
| ~ c_Finite__Set_Ofinite(X2580,X2575)
| hBOOL(hAPP(hAPP(c_member(X2580),X2574),X2575))
| hAPP(X2576,c_Set_Oinsert(X2580,X2574,X2575)) = hAPP(hAPP(X2579,hAPP(X2577,X2574)),hAPP(X2576,X2575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_521])]) ).
fof(i_0_605,plain,
! [X2694,X2695,X2696,X2697,X2698,X2699,X2700,X2701] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2701,X2700,X2699,X2698,X2697,X2696)
| ~ c_Finite__Set_Ofinite(X2700,X2695)
| ~ hBOOL(hAPP(hAPP(c_member(X2700),X2694),X2695))
| hAPP(hAPP(X2699,hAPP(X2697,X2694)),hAPP(X2696,X2695)) = hAPP(X2696,X2695) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_606,plain,
! [X2702,X2703,X2704,X2705,X2706,X2707,X2708,X2709] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2709,X2708,X2707,X2706,X2705,X2704)
| ~ c_Finite__Set_Ofinite(X2708,X2703)
| hAPP(X2704,c_Set_Oinsert(X2708,X2702,X2703)) = hAPP(hAPP(X2707,hAPP(X2705,X2702)),hAPP(X2704,X2703)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).
fof(i_0_607,plain,
! [X2620,X2621,X2622,X2623,X2624,X2625,X2626] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2626,X2625,X2624,X2623,X2622,X2621)
| hAPP(hAPP(X2624,X2620),X2620) = X2620 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).
fof(i_0_608,plain,
! [X3113,X3114,X3115,X3116,X3117,X3118] :
( ~ c_Fun_Oinj__on(X3118,X3117,X3116,X3115)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3117,tc_HOL_Obool),c_Set_Oimage(X3118,X3117,X3116,X3115)),X3114))
| ~ c_Fun_Oinj__on(X3117,X3118,X3113,X3114)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3118,tc_HOL_Obool),c_Set_Oimage(X3117,X3118,X3113,X3114)),X3115))
| ~ c_Finite__Set_Ofinite(X3118,X3115)
| ~ c_Finite__Set_Ofinite(X3117,X3114)
| c_Finite__Set_Ocard(X3118,X3115) = c_Finite__Set_Ocard(X3117,X3114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).
fof(i_0_609,plain,
! [X2410,X2411,X2412,X2413,X2415,X2419] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2410)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2411),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),X2412),X2413)),hAPP(X2411,esk24_4(X2410,X2411,X2412,X2413))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2412),X2413)),hAPP(X2410,X2411))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk25_1(X2415)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X2415) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2415)),esk27_1(X2415))),hAPP(esk25_1(X2415),X2419)))
| c_Arrow__Order__Mirabelle_Ounanimity(X2415) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2415)),esk27_1(X2415))),hAPP(X2415,esk25_1(X2415))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2415) ) ),
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_610,plain,
! [X1630] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| hAPP(v_h____,X1630) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| hAPP(v_h____,X1630) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_e____)))
| hAPP(v_h____,X1630) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_e____)))
| hAPP(v_h____,X1630) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| hAPP(v_h____,X1630) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| hAPP(v_h____,X1630) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_e____)))
| hAPP(v_h____,X1630) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_e____)))
| hAPP(v_h____,X1630) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),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____,X1630)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),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____,X1630)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),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____,X1630)),v_e____))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),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____,X1630)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( hAPP(v_h____,X1630) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( hAPP(v_h____,X1630) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),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____,X1630)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1630)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( hAPP(v_h____,X1630) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1630)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( hAPP(v_h____,X1630) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1630)),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____,X1630)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),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____,X1630)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1630) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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____,X1630)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1630) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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____,X1630)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1630)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_611,plain,
! [X2433,X2434,X2435,X2436,X2437,X2438] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2438,X2437)),X2436),c_FuncSet_OPi(X2438,X2437,X2435,hAPP(c_COMBK(tc_fun(X2437,tc_HOL_Obool),X2438),X2434))))
| ~ c_Fun_Oinj__on(X2438,X2437,X2436,X2435)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2437,X2438)),X2433),c_FuncSet_OPi(X2437,X2438,X2434,hAPP(c_COMBK(tc_fun(X2438,tc_HOL_Obool),X2437),X2435))))
| ~ c_Fun_Oinj__on(X2437,X2438,X2433,X2434)
| ~ c_Finite__Set_Ofinite(X2438,X2435)
| ~ c_Finite__Set_Ofinite(X2437,X2434)
| c_Finite__Set_Ocard(X2438,X2435) = c_Finite__Set_Ocard(X2437,X2434) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij])]) ).
fof(i_0_612,plain,
! [X1805,X1806,X1807] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1807,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1807,tc_fun(X1807,tc_HOL_Obool),tc_HOL_Obool),c_member(X1807)),X1806)),hAPP(hAPP(c_COMBC(X1807,tc_fun(X1807,tc_HOL_Obool),tc_HOL_Obool),c_member(X1807)),X1805)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1807,tc_HOL_Obool),X1806),X1805)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1807,tc_HOL_Obool),X1806),X1805))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1807,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X1807,tc_fun(X1807,tc_HOL_Obool),tc_HOL_Obool),c_member(X1807)),X1806)),hAPP(hAPP(c_COMBC(X1807,tc_fun(X1807,tc_HOL_Obool),tc_HOL_Obool),c_member(X1807)),X1805))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_613,plain,
! [X1621] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( hAPP(v_h____,X1621) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( hAPP(v_h____,X1621) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( hAPP(v_h____,X1621) != v_n____
| hAPP(v_h____,X1621) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| hAPP(v_h____,X1621) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( hAPP(v_h____,X1621) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1621)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( hAPP(v_h____,X1621) != v_n____
| hAPP(v_h____,X1621) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| hAPP(v_h____,X1621) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( hAPP(v_h____,X1621) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),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____,X1621)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621)),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____,X1621)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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____,X1621))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])])]) ).
fof(i_0_614,plain,
! [X2935,X2936,X2937,X2938] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2938,c_Set_Oimage(X2937,X2938,X2936,X2935))),c_Finite__Set_Ocard(X2937,X2935)))
| ~ c_Fun_Oinj__on(X2937,X2938,X2936,X2935) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])]) ).
fof(i_0_615,plain,
! [X3125,X3126,X3127,X3128,X3129] :
( ( ~ c_Fun_Oinj__on(X3128,X3126,X3129,X3127)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3126,tc_HOL_Obool),c_Set_Oimage(X3128,X3126,X3129,X3127)),X3125))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3128,X3127)),c_Finite__Set_Ocard(X3126,X3125)))
| ~ c_Finite__Set_Ofinite(X3126,X3125)
| ~ c_Finite__Set_Ofinite(X3128,X3127) )
& ( c_Fun_Oinj__on(X3128,X3126,esk40_4(X3125,X3126,X3127,X3128),X3127)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3128,X3127)),c_Finite__Set_Ocard(X3126,X3125)))
| ~ c_Finite__Set_Ofinite(X3126,X3125)
| ~ c_Finite__Set_Ofinite(X3128,X3127) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3126,tc_HOL_Obool),c_Set_Oimage(X3128,X3126,esk40_4(X3125,X3126,X3127,X3128),X3127)),X3125))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3128,X3127)),c_Finite__Set_Ocard(X3126,X3125)))
| ~ c_Finite__Set_Ofinite(X3126,X3125)
| ~ c_Finite__Set_Ofinite(X3128,X3127) ) ),
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_616,plain,
! [X1760,X1761,X1762,X1763,X1764] :
( ( X1761 != X1760
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1761 != X1763
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1764),X1760)),X1762))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1760 != X1763
| X1761 = X1764
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1764)),X1762))
| X1761 = X1763
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1760 = X1763
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),X1762))
| X1761 = X1763
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1761 != X1763
| X1761 = X1763
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1760 != X1763
| X1760 = X1763
| X1761 = X1763
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),X1762))
| X1760 = X1763
| X1761 = X1763
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1760 != X1763
| X1761 != X1764
| X1761 = X1763
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),X1762))
| X1761 != X1764
| X1761 = X1763
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1760 != X1763
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1764)),X1762))
| X1761 = X1763
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),X1762))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1764)),X1762))
| X1761 = X1763
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1761 != X1763
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1764),X1760)),X1762))
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1760 != X1763
| X1760 = X1763
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1764),X1760)),X1762))
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),X1762))
| X1760 = X1763
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1764),X1760)),X1762))
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1760 != X1763
| X1761 != X1764
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1764),X1760)),X1762))
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),X1762))
| X1761 != X1764
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1764),X1760)),X1762))
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( X1760 != X1763
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1764)),X1762))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1764),X1760)),X1762))
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),X1762))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1764)),X1762))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1764),X1760)),X1762))
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1761),X1760)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1762),X1764),X1763)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1762),c_Arrow__Order__Mirabelle_OLin))
| X1764 = X1763 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_617,plain,
! [X1769,X1770,X1771,X1772,X1773] :
( ( X1770 != X1769
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1769 != X1773
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1772)),X1771))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1770 != X1773
| X1769 = X1772
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1772),X1769)),X1771))
| X1769 = X1773
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1770 = X1773
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),X1771))
| X1769 = X1773
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1769 != X1773
| X1769 = X1773
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1770 != X1773
| X1770 = X1773
| X1769 = X1773
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),X1771))
| X1770 = X1773
| X1769 = X1773
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1770 != X1773
| X1769 != X1772
| X1769 = X1773
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),X1771))
| X1769 != X1772
| X1769 = X1773
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1770 != X1773
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1772),X1769)),X1771))
| X1769 = X1773
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),X1771))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1772),X1769)),X1771))
| X1769 = X1773
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1769 != X1773
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1772)),X1771))
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1770 != X1773
| X1770 = X1773
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1772)),X1771))
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),X1771))
| X1770 = X1773
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1772)),X1771))
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1770 != X1773
| X1769 != X1772
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1772)),X1771))
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),X1771))
| X1769 != X1772
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1772)),X1771))
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( X1770 != X1773
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1772),X1769)),X1771))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1772)),X1771))
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),X1771))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1772),X1769)),X1771))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1772)),X1771))
| X1770 = X1769
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1770),X1769)),c_Arrow__Order__Mirabelle_Obelow(X1771,X1773,X1772)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1771),c_Arrow__Order__Mirabelle_OLin))
| X1773 = X1772 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_618,plain,
! [X2881,X2882] :
( ~ c_Finite__Set_Ofinite(X2882,X2881)
| c_Finite__Set_Ocard(X2882,X2881) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2882,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2882),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2881) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).
fof(i_0_619,plain,
! [X2872,X2873] :
( ( ~ c_Finite__Set_Ofinite(X2873,X2872)
| c_Finite__Set_Ocard(X2873,X2872) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2873,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2873),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2872) )
& ( c_Finite__Set_Ofinite(X2873,X2872)
| c_Finite__Set_Ocard(X2873,X2872) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])]) ).
fof(i_0_620,plain,
! [X2977,X2978,X2979,X2980,X2981] :
( ~ hBOOL(hAPP(hAPP(c_member(X2981),X2980),c_Set_Oimage(X2979,X2981,X2978,X2977)))
| hBOOL(hAPP(hAPP(c_member(X2979),hAPP(c_Hilbert__Choice_Oinv__into(X2979,X2981,X2977,X2978),X2980)),X2977)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).
cnf(i_0_621,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_622,plain,
! [X2918,X2919,X2920,X2921,X2922] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2921,tc_HOL_Obool),c_Set_Oimage(X2922,X2921,X2920,X2919)),c_Set_Oimage(X2922,X2921,X2920,X2918)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2922,tc_HOL_Obool),X2919),X2918))
| ~ c_Fun_Oinj__on(X2922,X2921,X2920,c_Orderings_Otop__class_Otop(tc_fun(X2922,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2922,tc_HOL_Obool),X2919),X2918))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2921,tc_HOL_Obool),c_Set_Oimage(X2922,X2921,X2920,X2919)),c_Set_Oimage(X2922,X2921,X2920,X2918)))
| ~ c_Fun_Oinj__on(X2922,X2921,X2920,c_Orderings_Otop__class_Otop(tc_fun(X2922,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_623,plain,
! [X2471,X2472,X2473] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2473,tc_HOL_Obool)),X2472),X2471))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2473,tc_HOL_Obool),tc_fun(X2473,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2473,tc_HOL_Obool),tc_fun(X2473,tc_HOL_Obool)),X2472),X2471)),c_Wellfounded_Ofinite__psubset(X2473))) )
& ( c_Finite__Set_Ofinite(X2473,X2471)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2473,tc_HOL_Obool),tc_fun(X2473,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2473,tc_HOL_Obool),tc_fun(X2473,tc_HOL_Obool)),X2472),X2471)),c_Wellfounded_Ofinite__psubset(X2473))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2473,tc_HOL_Obool)),X2472),X2471))
| ~ c_Finite__Set_Ofinite(X2473,X2471)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2473,tc_HOL_Obool),tc_fun(X2473,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2473,tc_HOL_Obool),tc_fun(X2473,tc_HOL_Obool)),X2472),X2471)),c_Wellfounded_Ofinite__psubset(X2473))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).
fof(i_0_624,plain,
! [X3108,X3109,X3110,X3111,X3112] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3112,X3111)),X3110),c_FuncSet_OPi(X3112,X3111,X3109,hAPP(c_COMBK(tc_fun(X3111,tc_HOL_Obool),X3112),X3108))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3111,tc_HOL_Obool),c_Set_Oimage(X3112,X3111,X3110,X3109)),X3108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_625,plain,
! [X2971,X2972,X2973,X2974,X2975,X2976] :
( hAPP(c_Hilbert__Choice_Oinv__into(X2976,X2975,X2974,X2973),X2972) != hAPP(c_Hilbert__Choice_Oinv__into(X2976,X2975,X2974,X2973),X2971)
| ~ hBOOL(hAPP(hAPP(c_member(X2975),X2972),c_Set_Oimage(X2976,X2975,X2973,X2974)))
| ~ hBOOL(hAPP(hAPP(c_member(X2975),X2971),c_Set_Oimage(X2976,X2975,X2973,X2974)))
| X2972 = X2971 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).
fof(i_0_626,plain,
! [X2825,X2826] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2826),c_Groups_Oone__class_Oone(X2826)),X2825)),X2825)),c_Groups_Ozero__class_Ozero(X2826)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2826),X2825),c_Groups_Ozero__class_Ozero(X2826)))
| ~ hBOOL(hAPP(hAPP(c_member(X2826),X2825),c_Int_Oring__1__class_OInts(X2826)))
| ~ class_Rings_Olinordered__idom(X2826) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2826),X2825),c_Groups_Ozero__class_Ozero(X2826)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2826),c_Groups_Oone__class_Oone(X2826)),X2825)),X2825)),c_Groups_Ozero__class_Ozero(X2826)))
| ~ hBOOL(hAPP(hAPP(c_member(X2826),X2825),c_Int_Oring__1__class_OInts(X2826)))
| ~ class_Rings_Olinordered__idom(X2826) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).
fof(i_0_627,plain,
! [X2900,X2901,X2902,X2903,X2905,X2906] :
( ( X2900 = hAPP(X2901,esk34_4(X2900,X2901,X2902,X2903))
| ~ hBOOL(hAPP(hAPP(c_member(X2902),X2900),c_Set_Oimage(X2903,X2902,X2901,c_Orderings_Otop__class_Otop(tc_fun(X2903,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2903,X2902,X2901,c_Orderings_Otop__class_Otop(tc_fun(X2903,tc_HOL_Obool))) )
& ( X2900 != hAPP(X2901,X2905)
| X2905 = esk34_4(X2900,X2901,X2902,X2903)
| ~ hBOOL(hAPP(hAPP(c_member(X2902),X2900),c_Set_Oimage(X2903,X2902,X2901,c_Orderings_Otop__class_Otop(tc_fun(X2903,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2903,X2902,X2901,c_Orderings_Otop__class_Otop(tc_fun(X2903,tc_HOL_Obool))) )
& ( X2900 = hAPP(X2901,esk35_5(X2900,X2901,X2902,X2903,X2906))
| X2900 != hAPP(X2901,X2906)
| hBOOL(hAPP(hAPP(c_member(X2902),X2900),c_Set_Oimage(X2903,X2902,X2901,c_Orderings_Otop__class_Otop(tc_fun(X2903,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2903,X2902,X2901,c_Orderings_Otop__class_Otop(tc_fun(X2903,tc_HOL_Obool))) )
& ( esk35_5(X2900,X2901,X2902,X2903,X2906) != X2906
| X2900 != hAPP(X2901,X2906)
| hBOOL(hAPP(hAPP(c_member(X2902),X2900),c_Set_Oimage(X2903,X2902,X2901,c_Orderings_Otop__class_Otop(tc_fun(X2903,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2903,X2902,X2901,c_Orderings_Otop__class_Otop(tc_fun(X2903,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_628,plain,
! [X2923,X2924,X2925,X2926] :
( ~ c_Finite__Set_Ofinite(X2926,X2925)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2924,c_Set_Oimage(X2926,X2924,X2923,X2925))),c_Finite__Set_Ocard(X2926,X2925))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_629,plain,
! [X3009,X3010,X3011,X3012,X3013] :
( ~ c_Fun_Oinj__on(X3013,X3012,X3011,X3010)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3013,tc_HOL_Obool)),X3009),X3010))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3012,tc_HOL_Obool)),c_Set_Oimage(X3013,X3012,X3011,X3009)),c_Set_Oimage(X3013,X3012,X3011,X3010))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_630,plain,
! [X2911,X2912,X2913] :
( ~ c_Finite__Set_Ofinite(X2913,X2912)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2913,tc_HOL_Obool),c_Set_Oimage(X2913,X2913,X2911,X2912)),X2912))
| ~ c_Fun_Oinj__on(X2913,X2913,X2911,X2912)
| c_Set_Oimage(X2913,X2913,X2911,X2912) = X2912 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_631,plain,
! [X3119,X3120,X3121,X3122,X3123] :
( ~ c_Fun_Oinj__on(X3123,X3122,X3121,X3120)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3122,tc_HOL_Obool),c_Set_Oimage(X3123,X3122,X3121,X3120)),X3119))
| ~ c_Finite__Set_Ofinite(X3122,X3119)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3123,X3120)),c_Finite__Set_Ocard(X3122,X3119))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).
cnf(i_0_632,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_633,plain,
! [X3025,X3026,X3027,X3028,X3029,X3031,X3032,X3033,X3034,X3035,X3036] :
( ( hBOOL(hAPP(hAPP(c_member(X3027),esk37_4(X3025,X3026,X3027,X3028)),X3025))
| ~ hBOOL(hAPP(hAPP(c_member(X3029),X3028),c_Set_Oimage(X3027,X3029,X3026,X3025))) )
& ( X3028 = hAPP(X3026,esk37_4(X3025,X3026,X3027,X3028))
| ~ hBOOL(hAPP(hAPP(c_member(X3029),X3028),c_Set_Oimage(X3027,X3029,X3026,X3025))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3033),X3035),X3031))
| X3034 != hAPP(X3032,X3035)
| hBOOL(hAPP(hAPP(c_member(X3036),X3034),c_Set_Oimage(X3033,X3036,X3032,X3031))) ) ),
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_634,plain,
! [X1753,X1754,X1755] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1754),X1753)),X1755))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1753),X1754)),X1755))
| X1754 = X1753
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1755),c_Arrow__Order__Mirabelle_OLin)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1753),X1754)),X1755))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1754),X1753)),X1755))
| X1754 = X1753
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1755),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])])]) ).
fof(i_0_635,plain,
! [X1756,X1757,X1758] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1758),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),X1757),X1756)),X1758))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1756),X1757)),X1758)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])]) ).
fof(i_0_636,plain,
! [X2422,X2423,X2424,X2425,X2426] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2426,X2425)),X2424),c_FuncSet_OPi(X2426,X2425,X2423,hAPP(c_COMBK(tc_fun(X2425,tc_HOL_Obool),X2426),X2422))))
| ~ c_Fun_Oinj__on(X2426,X2425,X2424,X2423)
| ~ c_Finite__Set_Ofinite(X2425,X2422)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2426,X2423)),c_Finite__Set_Ocard(X2425,X2422))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj])]) ).
fof(i_0_637,plain,
! [X2203,X2204,X2205,X2206,X2207] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2207,tc_HOL_Obool),X2206),X2205))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2207,X2204),tc_HOL_Obool),c_FuncSet_OPi(X2207,X2204,X2205,X2203)),c_FuncSet_OPi(X2207,X2204,X2206,X2203))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_638,plain,
! [X3079,X3080,X3081,X3082,X3083] :
( ~ c_Finite__Set_Ofinite(X3083,c_Set_Oimage(X3082,X3083,X3081,c_Orderings_Otop__class_Otop(tc_fun(X3082,tc_HOL_Obool))))
| c_Finite__Set_Ofinite(X3080,c_Set_Oimage(X3082,X3080,hAPP(c_COMBB(X3083,X3080,X3082,X3079),X3081),c_Orderings_Otop__class_Otop(tc_fun(X3082,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).
fof(i_0_639,plain,
! [X1759] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1759),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),X1759)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_640,plain,
! [X1974,X1975,X1976,X1977,X1978,X1979] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1979,X1978)),X1977),c_FuncSet_OPi(X1979,X1978,X1976,hAPP(c_COMBK(tc_fun(X1978,tc_HOL_Obool),X1979),X1975))))
| ~ hBOOL(hAPP(hAPP(c_member(X1979),X1974),X1976))
| hBOOL(hAPP(hAPP(c_member(X1978),hAPP(X1977,X1974)),X1975)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
cnf(i_0_641,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_642,plain,
! [X3055,X3056,X3057,X3058,X3059] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3059,tc_HOL_Obool),X3058),X3057))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3056,tc_HOL_Obool),c_Set_Oimage(X3059,X3056,X3055,X3058)),c_Set_Oimage(X3059,X3056,X3055,X3057))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
cnf(i_0_643,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_644,plain,
! [X1998,X1999,X2000,X2001,X2002] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2002,X2001)),hAPP(X2002,X2000)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1999,X1999)),hAPP(hAPP(c_Product__Type_OPair(X1999,X1999),X2001),X2000)),X1998))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1999,X1999)),hAPP(hAPP(c_Product__Type_OPair(X1999,X1999),X2001),X2000)),c_Wellfounded_Omlex__prod(X1999,X2002,X1998))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_645,plain,
! [X1635,X1636,X1637,X1638,X1639] :
( ( ~ c_FunDef_Oin__rel(X1639,X1638,X1637,X1636,X1635)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1639,X1638)),hAPP(hAPP(c_Product__Type_OPair(X1639,X1638),X1636),X1635)),X1637)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1639,X1638)),hAPP(hAPP(c_Product__Type_OPair(X1639,X1638),X1636),X1635)),X1637))
| c_FunDef_Oin__rel(X1639,X1638,X1637,X1636,X1635) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_646,plain,
! [X2982,X2983,X2984,X2985,X2986] :
( ~ hBOOL(hAPP(hAPP(c_member(X2986),X2985),c_Set_Oimage(X2984,X2986,X2983,X2982)))
| hAPP(X2983,hAPP(c_Hilbert__Choice_Oinv__into(X2984,X2986,X2982,X2983),X2985)) = X2985 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).
fof(i_0_647,plain,
! [X3001,X3002,X3003,X3004,X3005,X3006,X3007] :
( ( c_Set_Oimage(X3003,X3002,X3001,c_Orderings_Otop__class_Otop(tc_fun(X3003,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3002,tc_HOL_Obool))
| hAPP(X3001,hAPP(c_Hilbert__Choice_Oinv__into(X3003,X3002,c_Orderings_Otop__class_Otop(tc_fun(X3003,tc_HOL_Obool)),X3001),X3004)) = X3004 )
& ( hAPP(X3005,hAPP(c_Hilbert__Choice_Oinv__into(X3007,X3006,c_Orderings_Otop__class_Otop(tc_fun(X3007,tc_HOL_Obool)),X3005),esk36_3(X3005,X3006,X3007))) != esk36_3(X3005,X3006,X3007)
| c_Set_Oimage(X3007,X3006,X3005,c_Orderings_Otop__class_Otop(tc_fun(X3007,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3006,tc_HOL_Obool)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__iff__all])])])])]) ).
fof(i_0_648,plain,
! [X3089,X3090,X3091,X3092,X3093] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3093,tc_HOL_Obool),X3092),c_Set_Oimage(X3091,X3093,X3090,X3089)))
| c_Fun_Oinj__on(X3093,X3091,c_Hilbert__Choice_Oinv__into(X3091,X3093,X3089,X3090),X3092) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).
cnf(i_0_649,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____ ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_650,plain,
! [X1622,X1623,X1624,X1625] :
( ( X1624 != X1622
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1623),X1622))) )
& ( X1625 != X1622
| X1625 != X1624
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1623),X1622))) )
& ( X1625 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),X1623))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1623),X1622))) )
& ( X1625 != X1622
| X1625 = X1622
| X1624 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1623),X1622))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),X1623))
| X1625 = X1622
| X1624 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1623),X1622))) )
& ( X1625 != X1622
| X1625 = X1624
| X1624 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1623),X1622))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),X1623))
| X1625 = X1624
| X1624 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1623),X1622))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_651,plain,
! [X1626,X1627,X1628,X1629] :
( ( X1629 != X1626
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1627),X1626))) )
& ( X1628 != X1626
| X1629 != X1628
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1627),X1626))) )
& ( X1628 = X1626
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),X1627))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1627),X1626))) )
& ( X1628 != X1626
| X1628 = X1626
| X1629 = X1626
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1627),X1626))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),X1627))
| X1628 = X1626
| X1629 = X1626
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1627),X1626))) )
& ( X1628 != X1626
| X1629 = X1628
| X1629 = X1626
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1627),X1626))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),X1627))
| X1629 = X1628
| X1629 = X1626
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1629),X1628)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1627),X1626))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_652,plain,
! [X3200,X3201,X3202,X3203,X3204,X3205] : hAPP(c_COMBS(X3205,X3204,X3203,X3202,X3201),X3200) = hAPP(hAPP(X3202,X3200),hAPP(X3201,X3200)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_653,plain,
! [X1980,X1981,X1982,X1983,X1984,X1985] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1985,X1984)),X1983),c_FuncSet_OPi(X1985,X1984,X1982,X1981)))
| ~ hBOOL(hAPP(hAPP(c_member(X1985),X1980),X1982))
| hBOOL(hAPP(hAPP(c_member(X1984),hAPP(X1983,X1980)),hAPP(X1981,X1980))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_654,plain,
! [X1968,X1969,X1970,X1971,X1972,X1973] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1973,X1972)),X1971),c_FuncSet_OPi(X1973,X1972,X1970,X1969)))
| hBOOL(hAPP(hAPP(c_member(X1972),hAPP(X1971,X1968)),hAPP(X1969,X1968)))
| ~ hBOOL(hAPP(hAPP(c_member(X1973),X1968),X1970)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])]) ).
fof(i_0_655,plain,
! [X2895,X2896,X2897,X2898,X2899] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2898),hAPP(X2897,X2896)),c_Set_Oimage(X2899,X2898,X2897,X2895)))
| hBOOL(hAPP(hAPP(c_member(X2899),X2896),X2895))
| ~ c_Fun_Oinj__on(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2899),X2896),X2895))
| hBOOL(hAPP(hAPP(c_member(X2898),hAPP(X2897,X2896)),c_Set_Oimage(X2899,X2898,X2897,X2895)))
| ~ c_Fun_Oinj__on(X2899,X2898,X2897,c_Orderings_Otop__class_Otop(tc_fun(X2899,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_656,plain,
! [X2993,X2994,X2995,X2996] :
( c_Set_Oimage(X2996,X2995,X2994,c_Orderings_Otop__class_Otop(tc_fun(X2996,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2995,tc_HOL_Obool))
| c_Set_Oimage(X2996,X2995,X2994,c_Set_Oimage(X2995,X2996,c_Hilbert__Choice_Oinv__into(X2996,X2995,c_Orderings_Otop__class_Otop(tc_fun(X2996,tc_HOL_Obool)),X2994),X2993)) = X2993 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).
fof(i_0_657,plain,
! [X2987,X2988,X2989,X2990,X2991,X2992] :
( c_Set_Oimage(X2992,X2991,X2990,X2989) != X2988
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2991,tc_HOL_Obool),X2987),X2988))
| c_Set_Oimage(X2992,X2991,X2990,c_Set_Oimage(X2991,X2992,c_Hilbert__Choice_Oinv__into(X2992,X2991,X2989,X2990),X2987)) = X2987 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).
fof(i_0_658,plain,
! [X1858,X1859,X1860,X1861,X1862,X1863,X1864,X1865,X1866,X1867] :
( ( ~ c_Fun_Oinj__on(X1861,X1860,X1859,X1858)
| ~ hBOOL(hAPP(hAPP(c_member(X1861),X1862),X1858))
| ~ hBOOL(hAPP(hAPP(c_member(X1861),X1863),X1858))
| hAPP(X1859,X1862) != hAPP(X1859,X1863)
| X1862 = X1863 )
& ( hBOOL(hAPP(hAPP(c_member(X1867),esk11_4(X1864,X1865,X1866,X1867)),X1864))
| c_Fun_Oinj__on(X1867,X1866,X1865,X1864) )
& ( hBOOL(hAPP(hAPP(c_member(X1867),esk12_4(X1864,X1865,X1866,X1867)),X1864))
| c_Fun_Oinj__on(X1867,X1866,X1865,X1864) )
& ( hAPP(X1865,esk11_4(X1864,X1865,X1866,X1867)) = hAPP(X1865,esk12_4(X1864,X1865,X1866,X1867))
| c_Fun_Oinj__on(X1867,X1866,X1865,X1864) )
& ( esk11_4(X1864,X1865,X1866,X1867) != esk12_4(X1864,X1865,X1866,X1867)
| c_Fun_Oinj__on(X1867,X1866,X1865,X1864) ) ),
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])])])])])]) ).
cnf(i_0_659,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_b____),v_a____)),v_Lab____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_660,plain,
! [X1746,X1747,X1748] :
( X1748 = X1747
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1746),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,X1746),X1748),X1747)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
cnf(i_0_661,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) ),
inference(split_conjunct,[status(thm)],[i_0_526]) ).
fof(i_0_662,plain,
! [X3042,X3043,X3044,X3045,X3046] : c_Set_Oimage(X3046,X3045,hAPP(c_COMBB(X3044,X3045,X3046,X3043),X3042),c_Orderings_Otop__class_Otop(tc_fun(X3046,tc_HOL_Obool))) = c_Set_Oimage(X3044,X3045,X3043,c_Set_Oimage(X3046,X3044,X3042,c_Orderings_Otop__class_Otop(tc_fun(X3046,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_range__composition]) ).
fof(i_0_663,plain,
! [X2908,X2909,X2910] :
( ~ c_Finite__Set_Ofinite(X2910,X2909)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2910,tc_HOL_Obool),X2909),c_Set_Oimage(X2910,X2910,X2908,X2909)))
| c_Fun_Oinj__on(X2910,X2910,X2908,X2909) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_664,plain,
! [X2208,X2209,X2210,X2211,X2212] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2209,X2208)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2210),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2209,X2210) = hAPP(X2210,X2208) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk17_2(X2211,X2212)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2212,X2211) )
& ( hAPP(X2212,esk17_2(X2211,X2212)) != hAPP(esk17_2(X2211,X2212),X2211)
| c_Arrow__Order__Mirabelle_Odictator(X2212,X2211) ) ),
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_665,plain,
! [X1788,X1789,X1790,X1791] :
( ~ c_Fun_Oinj__on(X1791,X1790,X1789,c_Orderings_Otop__class_Otop(tc_fun(X1791,tc_HOL_Obool)))
| c_Fun_Oinj__on(X1791,tc_fun(X1788,X1790),hAPP(c_COMBB(X1790,tc_fun(X1788,X1790),X1791,c_COMBK(X1790,X1788)),X1789),c_Orderings_Otop__class_Otop(tc_fun(X1791,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).
fof(i_0_666,plain,
! [X1989,X1990] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1990,X1990)),c_COMBI(X1990)),c_FuncSet_OPi(X1990,X1990,X1989,hAPP(c_COMBK(tc_fun(X1990,tc_HOL_Obool),X1990),X1989)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_667,plain,
! [X3049,X3050,X3051,X3052,X3053,X3054] : c_Set_Oimage(X3054,X3053,X3052,c_Set_Oimage(X3051,X3054,X3050,X3049)) = c_Set_Oimage(X3051,X3053,hAPP(c_COMBB(X3054,X3053,X3051,X3052),X3050),X3049),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_668,plain,
! [X1965,X1966,X1967] :
( X1967 = X1966
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1965),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(X1965,X1967,X1966)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_669,plain,
! [X1647,X1648,X1649,X1650] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1650,X1650)),hAPP(hAPP(c_Product__Type_OPair(X1650,X1650),X1649),X1648)),c_Wellfounded_Omeasure(X1650,X1647)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1647,X1649)),hAPP(X1647,X1648))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1647,X1649)),hAPP(X1647,X1648)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1650,X1650)),hAPP(hAPP(c_Product__Type_OPair(X1650,X1650),X1649),X1648)),c_Wellfounded_Omeasure(X1650,X1647))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_670,plain,
! [X3084,X3085,X3086,X3087,X3088] :
( ~ c_Fun_Oinj__on(X3088,X3087,X3086,X3085)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3088,tc_HOL_Obool),X3084),X3085))
| c_Set_Oimage(X3087,X3088,c_Hilbert__Choice_Oinv__into(X3088,X3087,X3085,X3086),c_Set_Oimage(X3088,X3087,X3086,X3084)) = X3084 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).
fof(i_0_671,plain,
! [X2953,X2954,X2955,X2956,X2957] :
( ~ c_Finite__Set_Ofinite(X2957,X2956)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2955,tc_HOL_Obool),X2954),c_Set_Oimage(X2957,X2955,X2953,X2956)))
| c_Finite__Set_Ofinite(X2955,X2954) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
fof(i_0_672,plain,
! [X1749,X1750] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1750),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,X1750),X1749)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_673,plain,
! [X1751,X1752] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1752),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,X1752),X1751)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_674,plain,
! [X3101,X3102,X3103,X3104] :
( ~ c_Fun_Oinj__on(X3104,X3103,X3102,c_Orderings_Otop__class_Otop(tc_fun(X3104,tc_HOL_Obool)))
| c_Set_Oimage(X3103,X3104,c_Hilbert__Choice_Oinv__into(X3104,X3103,c_Orderings_Otop__class_Otop(tc_fun(X3104,tc_HOL_Obool)),X3102),c_Set_Oimage(X3104,X3103,X3102,X3101)) = X3101 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).
fof(i_0_675,plain,
! [X3097,X3098,X3099,X3100] :
( ~ c_Fun_Oinj__on(X3100,X3099,X3098,c_Orderings_Otop__class_Otop(tc_fun(X3100,tc_HOL_Obool)))
| c_Set_Oimage(X3099,X3100,c_Hilbert__Choice_Oinv__into(X3100,X3099,c_Orderings_Otop__class_Otop(tc_fun(X3100,tc_HOL_Obool)),X3098),c_Set_Oimage(X3100,X3099,X3098,X3097)) = X3097 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).
fof(i_0_676,plain,
! [X2997,X2998,X2999,X3000] :
( c_Set_Oimage(X3000,X2999,X2998,c_Orderings_Otop__class_Otop(tc_fun(X3000,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2999,tc_HOL_Obool))
| hAPP(X2998,hAPP(c_Hilbert__Choice_Oinv__into(X3000,X2999,c_Orderings_Otop__class_Otop(tc_fun(X3000,tc_HOL_Obool)),X2998),X2997)) = X2997 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).
fof(i_0_677,plain,
! [X2003,X2004,X2005,X2006,X2007] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2007,X2006)),hAPP(X2007,X2005)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2004,X2004)),hAPP(hAPP(c_Product__Type_OPair(X2004,X2004),X2006),X2005)),c_Wellfounded_Omlex__prod(X2004,X2007,X2003))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_678,plain,
! [X3165,X3166] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X3166),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3165,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3165),c_Finite__Set_Ocard(tc_Nat_Onat,X3166)))))
| X3166 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3165,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3165),c_Finite__Set_Ocard(tc_Nat_Onat,X3166))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).
fof(i_0_679,plain,
! [X3105,X3106,X3107] :
( c_Set_Oimage(X3107,X3106,X3105,c_Orderings_Otop__class_Otop(tc_fun(X3107,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3106,tc_HOL_Obool))
| c_Fun_Oinj__on(X3106,X3107,c_Hilbert__Choice_Oinv__into(X3107,X3106,c_Orderings_Otop__class_Otop(tc_fun(X3107,tc_HOL_Obool)),X3105),c_Orderings_Otop__class_Otop(tc_fun(X3106,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).
fof(i_0_680,plain,
! [X2949,X2950,X2951,X2952] : hBOOL(hAPP(hAPP(c_member(X2952),hAPP(X2951,X2950)),c_Set_Oimage(X2949,X2952,X2951,c_Orderings_Otop__class_Otop(tc_fun(X2949,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_681,plain,
! [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_Orderings_Otop__class_Otop(tc_fun(X3095,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3096,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).
fof(i_0_682,plain,
! [X3020,X3021,X3022,X3023,X3024] :
( ~ hBOOL(hAPP(hAPP(c_member(X3024),X3023),X3022))
| hBOOL(hAPP(hAPP(c_member(X3021),hAPP(X3020,X3023)),c_Set_Oimage(X3024,X3021,X3020,X3022))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_683,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_684,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_685,plain,
! [X2944,X2945,X2946,X2947,X2948] :
( X2948 != hAPP(X2947,X2946)
| hBOOL(hAPP(hAPP(c_member(X2945),X2948),c_Set_Oimage(X2944,X2945,X2947,c_Orderings_Otop__class_Otop(tc_fun(X2944,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_686,plain,
! [X2885,X2886,X2887,X2888,X2889,X2890] :
( X2890 != hAPP(X2889,X2888)
| ~ hBOOL(hAPP(hAPP(c_member(X2887),X2888),X2886))
| hBOOL(hAPP(hAPP(c_member(X2885),X2890),c_Set_Oimage(X2887,X2885,X2889,X2886))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_687,plain,
! [X3014,X3015,X3016,X3017,X3018,X3019] :
( ~ hBOOL(hAPP(hAPP(c_member(X3019),X3018),X3017))
| X3016 != hAPP(X3015,X3018)
| hBOOL(hAPP(hAPP(c_member(X3014),X3016),c_Set_Oimage(X3019,X3014,X3015,X3017))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_688,plain,
! [X2962,X2963,X2964,X2965,X2966] :
( ( c_Set_Oimage(X2966,X2965,X2964,X2963) != c_Set_Oimage(X2966,X2965,X2964,X2962)
| X2963 = X2962
| ~ c_Fun_Oinj__on(X2966,X2965,X2964,c_Orderings_Otop__class_Otop(tc_fun(X2966,tc_HOL_Obool))) )
& ( X2963 != X2962
| c_Set_Oimage(X2966,X2965,X2964,X2963) = c_Set_Oimage(X2966,X2965,X2964,X2962)
| ~ c_Fun_Oinj__on(X2966,X2965,X2964,c_Orderings_Otop__class_Otop(tc_fun(X2966,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_689,plain,
! [X1929,X1930,X1931,X1932] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1932),X1931),X1930)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1932),X1929),X1930)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1932),X1931),X1929))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1932) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1932),X1931),X1929))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1932),X1931),X1930)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1932),X1929),X1930)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1932) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_690,plain,
! [X1908,X1909,X1910,X1911] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1911)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1911),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1911),X1910),X1909)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1911),X1908),X1909)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1911),X1910),X1908)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_691,plain,
! [X1925,X1926,X1927,X1928] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1928),X1927),X1926)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1928),X1927),X1925)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1928),X1926),X1925))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1928) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1928),X1926),X1925))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1928),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1928),X1927),X1926)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1928),X1927),X1925)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1928) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_692,plain,
! [X1904,X1905,X1906,X1907] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1907)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1907),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1907),X1906),X1905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1907),X1906),X1904)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1907),X1905),X1904)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_693,plain,
! [X2958,X2959,X2960,X2961] :
( ~ c_Finite__Set_Ofinite(X2961,c_Set_Oimage(X2960,X2961,X2959,X2958))
| ~ c_Fun_Oinj__on(X2960,X2961,X2959,X2958)
| c_Finite__Set_Ofinite(X2960,X2958) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_694,plain,
! [X2038,X2039,X2040,X2041] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2041,tc_HOL_Obool)),X2040),X2039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2041,tc_HOL_Obool)),X2039),X2038))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2041,tc_HOL_Obool)),X2040),X2038)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_695,plain,
! [X1896,X1897,X1898,X1899] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1899)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1899,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1899),X1898),X1897)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1899),X1896),X1897)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1899,X1898),X1896)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_696,plain,
! [X1875,X1876,X1877,X1878] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1878,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1878),X1877),X1876)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1878),X1875),X1876)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1878,X1877),X1875))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1878) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1878,X1877),X1875))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1878,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1878),X1877),X1876)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1878),X1875),X1876)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1878) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_697,plain,
! [X1900,X1901,X1902,X1903] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1903)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1903,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1903),X1902),X1901)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1903),X1902),X1900)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1903,X1901),X1900)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_698,plain,
! [X1879,X1880,X1881,X1882] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1882,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1882),X1881),X1880)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1882),X1881),X1879)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1882,X1880),X1879))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1882) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1882,X1880),X1879))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1882,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1882),X1881),X1880)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1882),X1881),X1879)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1882) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_699,plain,
! [X2557,X2558,X2559,X2560] :
( ( hBOOL(hAPP(hAPP(c_member(X2560),X2559),X2557))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2560,tc_HOL_Obool),c_Set_Oinsert(X2560,X2559,X2558)),X2557)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2560,tc_HOL_Obool),X2558),X2557))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2560,tc_HOL_Obool),c_Set_Oinsert(X2560,X2559,X2558)),X2557)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2560),X2559),X2557))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2560,tc_HOL_Obool),X2558),X2557))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2560,tc_HOL_Obool),c_Set_Oinsert(X2560,X2559,X2558)),X2557)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_700,plain,
! [X1726,X1727,X1728,X1729] :
( ~ c_Fun_Oinj__on(X1729,X1728,X1727,c_Orderings_Otop__class_Otop(tc_fun(X1729,tc_HOL_Obool)))
| hAPP(c_Hilbert__Choice_Oinv__into(X1729,X1728,c_Orderings_Otop__class_Otop(tc_fun(X1729,tc_HOL_Obool)),X1727),hAPP(X1727,X1726)) = X1726 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).
fof(i_0_701,plain,
! [X1730,X1731,X1732,X1733,X1734] :
( ~ c_Fun_Oinj__on(X1734,X1733,X1732,c_Orderings_Otop__class_Otop(tc_fun(X1734,tc_HOL_Obool)))
| hAPP(X1732,X1731) != X1730
| hAPP(c_Hilbert__Choice_Oinv__into(X1734,X1733,c_Orderings_Otop__class_Otop(tc_fun(X1734,tc_HOL_Obool)),X1732),X1730) = X1731 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).
fof(i_0_702,plain,
! [X1870,X1871,X1872] :
( ( hAPP(hAPP(c_COMBC(X1872,tc_fun(X1872,tc_HOL_Obool),tc_HOL_Obool),c_member(X1872)),X1871) != hAPP(hAPP(c_COMBC(X1872,tc_fun(X1872,tc_HOL_Obool),tc_HOL_Obool),c_member(X1872)),X1870)
| X1871 = X1870 )
& ( X1871 != X1870
| hAPP(hAPP(c_COMBC(X1872,tc_fun(X1872,tc_HOL_Obool),tc_HOL_Obool),c_member(X1872)),X1871) = hAPP(hAPP(c_COMBC(X1872,tc_fun(X1872,tc_HOL_Obool),tc_HOL_Obool),c_member(X1872)),X1870) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_703,plain,
! [X2367,X2368,X2369] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2369),X2368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2369),X2367)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2368),X2367)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2368),X2367))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2369),X2368)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2369),X2367))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_704,plain,
! [X1735,X1736,X1737,X1738,X1739] :
( ~ c_Fun_Oinj__on(X1739,X1738,X1737,X1736)
| ~ hBOOL(hAPP(hAPP(c_member(X1739),X1735),X1736))
| hAPP(c_Hilbert__Choice_Oinv__into(X1739,X1738,X1736,X1737),hAPP(X1737,X1735)) = X1735 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).
fof(i_0_705,plain,
! [X1740,X1741,X1742,X1743,X1744,X1745] :
( ~ c_Fun_Oinj__on(X1745,X1744,X1743,X1742)
| ~ hBOOL(hAPP(hAPP(c_member(X1745),X1741),X1742))
| hAPP(X1743,X1741) != X1740
| hAPP(c_Hilbert__Choice_Oinv__into(X1745,X1744,X1742,X1743),X1740) = X1741 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).
fof(i_0_706,plain,
! [X2927,X2928,X2929,X2930] :
( ~ c_Finite__Set_Ofinite(X2930,X2929)
| c_Finite__Set_Ocard(X2928,c_Set_Oimage(X2930,X2928,X2927,X2929)) != c_Finite__Set_Ocard(X2930,X2929)
| c_Fun_Oinj__on(X2930,X2928,X2927,X2929) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_707,plain,
! [X2931,X2932,X2933,X2934] :
( ( ~ c_Fun_Oinj__on(X2934,X2932,X2931,X2933)
| c_Finite__Set_Ocard(X2932,c_Set_Oimage(X2934,X2932,X2931,X2933)) = c_Finite__Set_Ocard(X2934,X2933)
| ~ c_Finite__Set_Ofinite(X2934,X2933) )
& ( c_Finite__Set_Ocard(X2932,c_Set_Oimage(X2934,X2932,X2931,X2933)) != c_Finite__Set_Ocard(X2934,X2933)
| c_Fun_Oinj__on(X2934,X2932,X2931,X2933)
| ~ c_Finite__Set_Ofinite(X2934,X2933) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).
fof(i_0_708,plain,
! [X2526,X2527,X2528,X2529] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2529,tc_HOL_Obool),X2528),X2527))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2529,tc_HOL_Obool),c_Set_Oinsert(X2529,X2526,X2528)),c_Set_Oinsert(X2529,X2526,X2527))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(i_0_709,plain,
! [X3188,X3189,X3190,X3191,X3192,X3193] : hAPP(hAPP(c_COMBB(X3193,X3192,X3191,X3190),X3189),X3188) = hAPP(X3190,hAPP(X3189,X3188)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_710,plain,
! [X1912,X1913,X1914,X1915,X1916] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1916)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1916),X1915),X1914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1916),X1913),X1912))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1916),X1915),X1913)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1916),X1914),X1912))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_711,plain,
! [X3135,X3136,X3137] : 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)),X3137),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3136,X3135)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3136),X3137),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3135),X3137)),
inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).
fof(i_0_712,plain,
! [X2394,X2395,X2396] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2396),X2395)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2396),X2394)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2395),X2394)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2395),X2394))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2396),X2395)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2396),X2394))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_713,plain,
! [X1776,X1777,X1778,X1779,X1780] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1780)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1780,X1779),X1778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1780),X1777),X1776))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1780),X1779),X1777)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1780),X1778),X1776))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_714,plain,
! [X1781,X1782,X1783,X1784,X1785] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1785),X1784),X1783))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1785,X1782),X1781))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1785),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1785),X1784),X1782)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1785),X1783),X1781))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_715,plain,
! [X2030,X2031,X2032,X2033] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2033,tc_HOL_Obool),X2032),X2031))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2033,tc_HOL_Obool)),X2031),X2030))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2033,tc_HOL_Obool)),X2032),X2030)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_716,plain,
! [X2034,X2035,X2036,X2037] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2037,tc_HOL_Obool)),X2036),X2035))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2037,tc_HOL_Obool),X2035),X2034))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2037,tc_HOL_Obool)),X2036),X2034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_717,plain,
! [X2883,X2884] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2884)),X2883))
| hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2884),X2883)) )
& ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2884),X2883))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2884)),X2883)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_718,plain,
! [X2939,X2940,X2941,X2942,X2943] :
( ~ hBOOL(hAPP(hAPP(c_member(X2943),X2942),X2941))
| c_Set_Oinsert(X2940,hAPP(X2939,X2942),c_Set_Oimage(X2943,X2940,X2939,X2941)) = c_Set_Oimage(X2943,X2940,X2939,X2941) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
fof(i_0_719,plain,
! [X2439,X2440,X2441] :
( ~ c_Finite__Set_Ofinite(X2441,X2440)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2441,tc_HOL_Obool),X2439),X2440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2441,X2439)),c_Finite__Set_Ocard(X2441,X2440)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2441,tc_HOL_Obool)),X2439),X2440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_720,plain,
! [X1891,X1892,X1893,X1894,X1895] :
( ~ class_Groups_Oordered__ab__semigroup__add(X1895)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1895,X1894),X1893))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1895,X1892),X1891))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1895,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1895),X1894),X1892)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1895),X1893),X1891))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_721,plain,
! [X2650,X2651] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2651),X2650),X2650)),c_Groups_Ozero__class_Ozero(X2651)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2651),X2650),c_Groups_Ozero__class_Ozero(X2651)))
| ~ class_Groups_Olinordered__ab__group__add(X2651) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2651),X2650),c_Groups_Ozero__class_Ozero(X2651)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2651),X2650),X2650)),c_Groups_Ozero__class_Ozero(X2651)))
| ~ class_Groups_Olinordered__ab__group__add(X2651) ) ),
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_722,plain,
! [X2710,X2711] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2711),X2710),X2710)),c_Groups_Ozero__class_Ozero(X2711)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2711),X2710),c_Groups_Ozero__class_Ozero(X2711)))
| ~ class_Rings_Olinordered__idom(X2711) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2711),X2710),c_Groups_Ozero__class_Ozero(X2711)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2711),X2710),X2710)),c_Groups_Ozero__class_Ozero(X2711)))
| ~ class_Rings_Olinordered__idom(X2711) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_723,plain,
! [X2354,X2355,X2356,X2357] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2357),X2356))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2355),X2354))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2357),X2355)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2356),X2354))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_724,plain,
! [X3037,X3038,X3039,X3040,X3041] : c_Set_Oimage(X3041,X3040,X3039,c_Set_Oinsert(X3041,X3038,X3037)) = c_Set_Oinsert(X3040,hAPP(X3039,X3038),c_Set_Oimage(X3041,X3040,X3039,X3037)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
fof(i_0_725,plain,
! [X2914,X2915] :
( ~ c_Finite__Set_Ofinite(X2915,c_Orderings_Otop__class_Otop(tc_fun(X2915,tc_HOL_Obool)))
| c_Set_Oimage(X2915,X2915,X2914,c_Orderings_Otop__class_Otop(tc_fun(X2915,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2915,tc_HOL_Obool))
| c_Fun_Oinj__on(X2915,X2915,X2914,c_Orderings_Otop__class_Otop(tc_fun(X2915,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_726,plain,
! [X1796,X1797,X1798,X1799,X1800] :
( ~ c_Fun_Oinj__on(X1800,X1799,X1798,X1797)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1800,tc_HOL_Obool),X1796),X1797))
| c_Fun_Oinj__on(X1800,X1799,X1798,X1796) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_727,plain,
! [X2967,X2968,X2969,X2970] :
( ~ c_Fun_Oinj__on(X2970,X2969,X2968,X2967)
| c_Finite__Set_Ocard(X2969,c_Set_Oimage(X2970,X2969,X2968,X2967)) = c_Finite__Set_Ocard(X2970,X2967) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_728,plain,
! [X2659,X2660,X2661] :
( ~ class_Groups_Oordered__comm__monoid__add(X2661)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2661),X2660),c_Groups_Ozero__class_Ozero(X2661)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2661),X2659),c_Groups_Ozero__class_Ozero(X2661)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2661),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2661),X2660),X2659)),c_Groups_Ozero__class_Ozero(X2661))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_729,plain,
! [X2829,X2830,X2831] :
( ~ class_Rings_Oring__1(X2831)
| ~ hBOOL(hAPP(hAPP(c_member(X2831),X2830),c_Int_Oring__1__class_OInts(X2831)))
| ~ hBOOL(hAPP(hAPP(c_member(X2831),X2829),c_Int_Oring__1__class_OInts(X2831)))
| hBOOL(hAPP(hAPP(c_member(X2831),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2831),X2830),X2829)),c_Int_Oring__1__class_OInts(X2831))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).
fof(i_0_730,plain,
! [X2916,X2917] :
( ~ c_Finite__Set_Ofinite(X2917,c_Orderings_Otop__class_Otop(tc_fun(X2917,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X2917,X2917,X2916,c_Orderings_Otop__class_Otop(tc_fun(X2917,tc_HOL_Obool)))
| c_Set_Oimage(X2917,X2917,X2916,c_Orderings_Otop__class_Otop(tc_fun(X2917,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2917,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_731,plain,
! [X1921,X1922,X1923,X1924] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1924)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1924),X1923),X1922))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1924),X1923),X1921)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1924),X1922),X1921))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_732,plain,
! [X1917,X1918,X1919,X1920] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1920)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1920),X1919),X1918))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1920),X1917),X1919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1920),X1917),X1918))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_733,plain,
! [X2629,X2630] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2630,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2630),X2629),X2629)),c_Groups_Ozero__class_Ozero(X2630)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2630,X2629),c_Groups_Ozero__class_Ozero(X2630)))
| ~ class_Groups_Olinordered__ab__group__add(X2630) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2630,X2629),c_Groups_Ozero__class_Ozero(X2630)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2630,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2630),X2629),X2629)),c_Groups_Ozero__class_Ozero(X2630)))
| ~ class_Groups_Olinordered__ab__group__add(X2630) ) ),
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_734,plain,
! [X2561,X2562,X2563,X2564] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2564,tc_HOL_Obool),X2562),c_Set_Oinsert(X2564,X2563,X2561)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2564,tc_HOL_Obool),X2562),X2561))
| hBOOL(hAPP(hAPP(c_member(X2564),X2563),X2562)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2564,tc_HOL_Obool),X2562),X2561))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2564,tc_HOL_Obool),X2562),c_Set_Oinsert(X2564,X2563,X2561)))
| hBOOL(hAPP(hAPP(c_member(X2564),X2563),X2562)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])])]) ).
fof(i_0_735,plain,
! [X2687,X2688,X2689] :
( ~ class_Groups_Oordered__comm__monoid__add(X2689)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2689,X2688),c_Groups_Ozero__class_Ozero(X2689)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2689),X2687),c_Groups_Ozero__class_Ozero(X2689)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2689),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2689),X2688),X2687)),c_Groups_Ozero__class_Ozero(X2689))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_736,plain,
! [X2684,X2685,X2686] :
( ~ class_Groups_Oordered__comm__monoid__add(X2686)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2686),X2685),c_Groups_Ozero__class_Ozero(X2686)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2686,X2684),c_Groups_Ozero__class_Ozero(X2686)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2686),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2686),X2685),X2684)),c_Groups_Ozero__class_Ozero(X2686))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_737,plain,
! [X2295,X2296,X2297,X2298] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2298),X2297))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2296),X2295))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2298),X2296)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2297),X2295))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_738,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk9_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk9_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_739,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk8_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk8_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_740,plain,
! [X2541,X2542,X2543,X2544] :
( ( c_Finite__Set_Ofinite(X2544,X2542)
| ~ c_Finite__Set_Ofinite(tc_sum(X2544,X2543),c_Sum__Type_OPlus(X2544,X2543,X2542,X2541)) )
& ( c_Finite__Set_Ofinite(X2543,X2541)
| ~ c_Finite__Set_Ofinite(tc_sum(X2544,X2543),c_Sum__Type_OPlus(X2544,X2543,X2542,X2541)) )
& ( ~ c_Finite__Set_Ofinite(X2544,X2542)
| ~ c_Finite__Set_Ofinite(X2543,X2541)
| c_Finite__Set_Ofinite(tc_sum(X2544,X2543),c_Sum__Type_OPlus(X2544,X2543,X2542,X2541)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_741,plain,
! [X2549,X2550,X2551,X2552] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2552,X2551),c_Sum__Type_OPlus(X2552,X2551,X2550,X2549))
| c_Finite__Set_Ofinite(X2552,X2550) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_742,plain,
! [X2553,X2554,X2555,X2556] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2556,X2555),c_Sum__Type_OPlus(X2556,X2555,X2554,X2553))
| c_Finite__Set_Ofinite(X2555,X2553) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_743,plain,
! [X1883,X1884,X1885,X1886] :
( ~ class_Groups_Oordered__ab__semigroup__add(X1886)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1886,X1885),X1884))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1886,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1886),X1885),X1883)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1886),X1884),X1883))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_744,plain,
! [X1887,X1888,X1889,X1890] :
( ~ class_Groups_Oordered__ab__semigroup__add(X1890)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1890,X1889),X1888))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1890,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1890),X1887),X1889)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1890),X1887),X1888))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_745,plain,
! [X2347,X2348,X2349] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2349),X2348)),X2347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2349),X2347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_746,plain,
! [X2645,X2646,X2647] :
( ~ class_Groups_Oordered__comm__monoid__add(X2647)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2647,X2646),c_Groups_Ozero__class_Ozero(X2647)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2647,X2645),c_Groups_Ozero__class_Ozero(X2647)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2647),X2646),X2645)),c_Groups_Ozero__class_Ozero(X2647))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_747,plain,
! [X2065,X2066,X2067,X2068] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2067,X2068),X2066),X2065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2067,X2068)),X2066),X2065))
| ~ class_Orderings_Oord(X2068) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2067,X2068),X2065),X2066))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2067,X2068)),X2066),X2065))
| ~ class_Orderings_Oord(X2068) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2067,X2068),X2066),X2065))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2067,X2068),X2065),X2066))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2067,X2068)),X2066),X2065))
| ~ class_Orderings_Oord(X2068) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_533])])]) ).
fof(i_0_748,plain,
! [X2020,X2021,X2022,X2023,X2024,X2025] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2025,tc_fun(X2024,tc_HOL_Obool)),X2023),X2022))
| ~ hBOOL(hAPP(hAPP(X2023,X2021),X2020))
| hBOOL(hAPP(hAPP(X2022,X2021),X2020)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_749,plain,
! [X2011,X2012,X2013,X2014,X2015,X2016] :
( ~ hBOOL(hAPP(hAPP(X2016,X2015),X2014))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2013,tc_fun(X2012,tc_HOL_Obool)),X2016),X2011))
| hBOOL(hAPP(hAPP(X2011,X2015),X2014)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_750,plain,
! [X2358,X2359,X2360] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2360),X2359))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2360),X2358)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2359),X2358))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_751,plain,
! [X1939,X1940,X1941,X1942,X1943,X1944] :
( ( hAPP(X1942,X1940) != hAPP(X1942,X1939)
| X1940 = X1939
| ~ hBOOL(hAPP(hAPP(c_member(X1944),X1939),X1941))
| ~ hBOOL(hAPP(hAPP(c_member(X1944),X1940),X1941))
| ~ c_Fun_Oinj__on(X1944,X1943,X1942,X1941) )
& ( X1940 != X1939
| hAPP(X1942,X1940) = hAPP(X1942,X1939)
| ~ hBOOL(hAPP(hAPP(c_member(X1944),X1939),X1941))
| ~ hBOOL(hAPP(hAPP(c_member(X1944),X1940),X1941))
| ~ c_Fun_Oinj__on(X1944,X1943,X1942,X1941) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_752,plain,
! [X1945,X1946,X1947,X1948,X1949,X1950] :
( ~ c_Fun_Oinj__on(X1950,X1949,X1948,X1947)
| X1946 = X1945
| ~ hBOOL(hAPP(hAPP(c_member(X1950),X1946),X1947))
| ~ hBOOL(hAPP(hAPP(c_member(X1950),X1945),X1947))
| hAPP(X1948,X1946) != hAPP(X1948,X1945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_753,plain,
! [X1933,X1934,X1935,X1936,X1937,X1938] :
( ~ c_Fun_Oinj__on(X1938,X1937,X1936,X1935)
| hAPP(X1936,X1934) != hAPP(X1936,X1933)
| ~ hBOOL(hAPP(hAPP(c_member(X1938),X1934),X1935))
| ~ hBOOL(hAPP(hAPP(c_member(X1938),X1933),X1935))
| X1934 = X1933 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_754,plain,
! [X2286,X2287,X2288] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2288),X2286))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2288),X2287)),X2286)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2287),X2286))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2288),X2287)),X2286)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_534])])]) ).
fof(i_0_755,plain,
! [X2289,X2290,X2291] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2291),X2290)),X2289))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2291),X2289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_756,plain,
! [X2292,X2293,X2294] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2294),X2293)),X2292))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2293),X2292)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_757,plain,
! [X2652,X2653,X2654] :
( ~ class_Groups_Oordered__comm__monoid__add(X2654)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2654),c_Groups_Ozero__class_Ozero(X2654)),X2653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2654),c_Groups_Ozero__class_Ozero(X2654)),X2652))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2654),c_Groups_Ozero__class_Ozero(X2654)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2654),X2653),X2652))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_758,plain,
! [X2299,X2300,X2301] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2301),X2300))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2301),X2299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2300),X2299))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_759,plain,
! [X1808,X1809,X1810,X1811] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1811,tc_HOL_Obool)),X1810),X1809))
| ~ hBOOL(hAPP(hAPP(c_member(X1811),X1808),X1810))
| hBOOL(hAPP(hAPP(c_member(X1811),X1808),X1809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_760,plain,
! [X2442,X2443,X2444] :
( ~ c_Finite__Set_Ofinite(X2444,X2443)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2444,tc_HOL_Obool)),X2442),X2443))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2444,X2442)),c_Finite__Set_Ocard(X2444,X2443))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_761,plain,
! [X2345,X2346] : 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)),X2346),X2345),
inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).
fof(i_0_762,plain,
! [X2860,X2861,X2862,X2863,X2864] :
( ~ class_Rings_Ocomm__semiring__1(X2864)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2864),X2863),X2862)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2864),X2861),X2860)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2864),X2863),X2861)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2864),X2862),X2860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_763,plain,
! [X2026,X2027,X2028,X2029] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2029,tc_HOL_Obool),X2028),X2027))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2029,tc_HOL_Obool),X2027),X2026))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2029,tc_HOL_Obool),X2028),X2026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_764,plain,
! [X2673,X2674,X2675] :
( ~ class_Groups_Oordered__comm__monoid__add(X2675)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2675,c_Groups_Ozero__class_Ozero(X2675)),X2674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2675),c_Groups_Ozero__class_Ozero(X2675)),X2673))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2675),c_Groups_Ozero__class_Ozero(X2675)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2675),X2674),X2673))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_765,plain,
! [X2670,X2671,X2672] :
( ~ class_Groups_Oordered__comm__monoid__add(X2672)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2672),c_Groups_Ozero__class_Ozero(X2672)),X2671))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2672,c_Groups_Ozero__class_Ozero(X2672)),X2670))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2672),c_Groups_Ozero__class_Ozero(X2672)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2672),X2671),X2670))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_766,plain,
! [X2372,X2373] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2373),X2372)),X2373)),
inference(variable_rename,[status(thm)],[i_0_535]) ).
fof(i_0_767,plain,
! [X2370,X2371] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2371),X2370)),X2370)),
inference(variable_rename,[status(thm)],[i_0_536]) ).
fof(i_0_768,plain,
! [X2570,X2571,X2572,X2573] :
( ( ~ c_Finite__Set_Ofinite(X2573,X2572)
| ~ c_Finite__Set_Ofinite(X2571,X2570)
| c_Finite__Set_Ocard(tc_sum(X2573,X2571),c_Sum__Type_OPlus(X2573,X2571,X2572,X2570)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2573,X2572)),c_Finite__Set_Ocard(X2571,X2570)) )
& ( c_Finite__Set_Ofinite(X2573,X2572)
| c_Finite__Set_Ocard(tc_sum(X2573,X2571),c_Sum__Type_OPlus(X2573,X2571,X2572,X2570)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X2571,X2570)
| c_Finite__Set_Ocard(tc_sum(X2573,X2571),c_Sum__Type_OPlus(X2573,X2571,X2572,X2570)) = 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_769,plain,
! [X2474,X2475,X2476,X2477] :
( ~ c_Finite__Set_Ofinite(X2477,X2476)
| ~ c_Finite__Set_Ofinite(X2475,X2474)
| c_Finite__Set_Ocard(tc_sum(X2477,X2475),c_Sum__Type_OPlus(X2477,X2475,X2476,X2474)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2477,X2476)),c_Finite__Set_Ocard(X2475,X2474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_770,plain,
! [X2655,X2656,X2657,X2658] :
( ~ class_Rings_Olinordered__semidom(X2658)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2658),c_Groups_Ozero__class_Ozero(X2658)),X2657))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2658),X2656),X2655))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2658),X2656),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2658),X2657),X2655))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_771,plain,
! [X2565,X2566,X2567] :
( ~ c_Finite__Set_Ofinite(X2567,X2566)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2567,X2566)),c_Finite__Set_Ocard(X2567,c_Set_Oinsert(X2567,X2565,X2566)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).
fof(i_0_772,plain,
! [X2835,X2836] :
( ~ class_Int_Oring__char__0(X2836)
| ~ hBOOL(hAPP(hAPP(c_member(X2836),X2835),c_Int_Oring__1__class_OInts(X2836)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2836),c_Groups_Oone__class_Oone(X2836)),X2835)),X2835) != c_Groups_Ozero__class_Ozero(X2836) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).
fof(i_0_773,plain,
! [X2648,X2649] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2649),c_Groups_Ozero__class_Ozero(X2649)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2649),X2648),X2648)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2649),c_Groups_Ozero__class_Ozero(X2649)),X2648))
| ~ class_Groups_Olinordered__ab__group__add(X2649) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2649),c_Groups_Ozero__class_Ozero(X2649)),X2648))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2649),c_Groups_Ozero__class_Ozero(X2649)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2649),X2648),X2648)))
| ~ class_Groups_Olinordered__ab__group__add(X2649) ) ),
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_774,plain,
! [X2666,X2667] :
( ( ~ 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),X2667),X2666)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2667))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2666)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2667))
| 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),X2667),X2666))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2666))
| 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),X2667),X2666))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_775,plain,
! [X2448,X2449,X2450] :
( ~ c_Finite__Set_Ofinite(X2450,X2449)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2450,tc_HOL_Obool),X2448),X2449))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2450,X2449)),c_Finite__Set_Ocard(X2450,X2448)))
| X2448 = X2449 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_776,plain,
! [X2522,X2523,X2524,X2525] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2525,tc_HOL_Obool),X2524),X2523))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2525,tc_HOL_Obool),X2524),c_Set_Oinsert(X2525,X2522,X2523))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_777,plain,
! [X2680,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),X2681),X2680))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2683),X2681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2683),X2682),X2680))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_778,plain,
! [X2676,X2677,X2678,X2679] :
( ~ class_Groups_Oordered__comm__monoid__add(X2679)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2679),c_Groups_Ozero__class_Ozero(X2679)),X2678))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2679,X2677),X2676))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2679),X2677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2679),X2678),X2676))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_779,plain,
! [X2631,X2632,X2633] :
( ~ class_Groups_Oordered__comm__monoid__add(X2633)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2633,c_Groups_Ozero__class_Ozero(X2633)),X2632))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2633,c_Groups_Ozero__class_Ozero(X2633)),X2631))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2633,c_Groups_Ozero__class_Ozero(X2633)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2633),X2632),X2631))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_780,plain,
! [X2069,X2070,X2071] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2071,tc_HOL_Obool),X2070),X2069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2071,tc_HOL_Obool)),X2070),X2069)) )
& ( X2070 != X2069
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2071,tc_HOL_Obool)),X2070),X2069)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2071,tc_HOL_Obool),X2070),X2069))
| X2070 = X2069
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2071,tc_HOL_Obool)),X2070),X2069)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_781,plain,
! [X2059,X2060,X2061] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2061,tc_HOL_Obool),X2060),X2059))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2061,tc_HOL_Obool)),X2060),X2059))
| X2060 = X2059 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2061,tc_HOL_Obool)),X2060),X2059))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2061,tc_HOL_Obool),X2060),X2059)) )
& ( X2060 != X2059
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2061,tc_HOL_Obool),X2060),X2059)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_782,plain,
! [X2046,X2047,X2048] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2048,tc_HOL_Obool)),X2047),X2046))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2048,tc_HOL_Obool),X2047),X2046)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_783,plain,
! [X2512,X2513,X2514,X2515] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2515),X2514),c_Set_Oinsert(X2515,X2513,X2512)))
| X2514 = X2513
| hBOOL(hAPP(hAPP(c_member(X2515),X2514),X2512)) )
& ( X2514 != X2513
| hBOOL(hAPP(hAPP(c_member(X2515),X2514),c_Set_Oinsert(X2515,X2513,X2512))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2515),X2514),X2512))
| hBOOL(hAPP(hAPP(c_member(X2515),X2514),c_Set_Oinsert(X2515,X2513,X2512))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_784,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_785,plain,
! [X2627,X2628] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2628,c_Groups_Ozero__class_Ozero(X2628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2628),X2627),X2627)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2628,c_Groups_Ozero__class_Ozero(X2628)),X2627))
| ~ class_Groups_Olinordered__ab__group__add(X2628) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2628,c_Groups_Ozero__class_Ozero(X2628)),X2627))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2628,c_Groups_Ozero__class_Ozero(X2628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2628),X2627),X2627)))
| ~ class_Groups_Olinordered__ab__group__add(X2628) ) ),
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_786,plain,
! [X1986,X1987,X1988] : c_FuncSet_OPi(X1988,X1987,X1986,hAPP(c_COMBK(tc_fun(X1987,tc_HOL_Obool),X1988),c_Orderings_Otop__class_Otop(tc_fun(X1987,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1988,X1987),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pi__UNIV]) ).
fof(i_0_787,plain,
! [X2637,X2638,X2639,X2640] :
( ~ class_Groups_Oordered__comm__monoid__add(X2640)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2640,c_Groups_Ozero__class_Ozero(X2640)),X2639))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2640,X2638),X2637))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2640,X2638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2640),X2639),X2637))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_788,plain,
! [X2641,X2642,X2643,X2644] :
( ~ class_Groups_Oordered__comm__monoid__add(X2644)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,c_Groups_Ozero__class_Ozero(X2644)),X2643))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,X2642),X2641))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2644,X2642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2644),X2641),X2643))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_789,plain,
! [X2545,X2546,X2547,X2548] :
( ~ c_Finite__Set_Ofinite(X2548,X2547)
| ~ c_Finite__Set_Ofinite(X2546,X2545)
| c_Finite__Set_Ofinite(tc_sum(X2548,X2546),c_Sum__Type_OPlus(X2548,X2546,X2547,X2545)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_790,plain,
! [X3194,X3195,X3196,X3197,X3198,X3199] : hAPP(hAPP(hAPP(c_COMBC(X3199,X3198,X3197),X3196),X3195),X3194) = hAPP(hAPP(X3196,X3194),X3195),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_791,plain,
! [X2062,X2063,X2064] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2062,tc_HOL_Obool),X2064),X2063))
| X2064 != X2063 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2062,tc_HOL_Obool),X2063),X2064))
| X2064 != X2063 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2062,tc_HOL_Obool),X2064),X2063))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2062,tc_HOL_Obool),X2063),X2064))
| X2064 = X2063 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_792,plain,
! [X2008,X2009,X2010] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2010,tc_HOL_Obool),X2009),X2008))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2010,tc_HOL_Obool),X2008),X2009))
| X2009 = X2008 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_793,plain,
! [X1816,X1817,X1818,X1819] :
( ~ hBOOL(hAPP(hAPP(c_member(X1819),X1818),X1817))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1819,tc_HOL_Obool),X1817),X1816))
| hBOOL(hAPP(hAPP(c_member(X1819),X1818),X1816)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_794,plain,
! [X1820,X1821,X1822,X1823] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1823,tc_HOL_Obool),X1822),X1821))
| ~ hBOOL(hAPP(hAPP(c_member(X1823),X1820),X1822))
| hBOOL(hAPP(hAPP(c_member(X1823),X1820),X1821)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_795,plain,
! [X1812,X1813,X1814,X1815] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1815,tc_HOL_Obool),X1814),X1813))
| ~ hBOOL(hAPP(hAPP(c_member(X1815),X1812),X1814))
| hBOOL(hAPP(hAPP(c_member(X1815),X1812),X1813)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_796,plain,
! [X1792,X1793,X1794,X1795] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1795,tc_HOL_Obool),X1794),X1793))
| ~ hBOOL(hAPP(hAPP(c_member(X1795),X1792),X1794))
| hBOOL(hAPP(hAPP(c_member(X1795),X1792),X1793)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_797,plain,
! [X2115,X2116,X2117,X2118,X2119] :
( ~ class_Orderings_Oord(X2119)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2118,X2119),X2117),X2116))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2119,hAPP(X2117,X2115)),hAPP(X2116,X2115))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_798,plain,
! [X2077,X2078,X2079,X2080,X2081] :
( ~ class_Orderings_Oord(X2081)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2080,X2081),X2079),X2078))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2081,hAPP(X2079,X2077)),hAPP(X2078,X2077))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_799,plain,
! [X2891,X2892,X2893,X2894] :
( ~ c_Finite__Set_Ofinite(X2894,X2893)
| c_Finite__Set_Ofinite(X2892,c_Set_Oimage(X2894,X2892,X2891,X2893)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
fof(i_0_800,plain,
! [X2445,X2446,X2447] :
( ~ c_Finite__Set_Ofinite(X2447,X2446)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2447,tc_HOL_Obool),X2445),X2446))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2447,X2445)),c_Finite__Set_Ocard(X2447,X2446))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_801,plain,
! [X2856,X2857,X2858,X2859] :
( ~ class_Rings_Ocomm__semiring__1(X2859)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2859),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2859),X2858),X2857)),X2856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2859),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2859),X2858),X2856)),X2857) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_802,plain,
! [X1951,X1952,X1953,X1954,X1955] :
( ( hAPP(X1953,X1952) != hAPP(X1953,X1951)
| X1952 = X1951
| ~ c_Fun_Oinj__on(X1955,X1954,X1953,c_Orderings_Otop__class_Otop(tc_fun(X1955,tc_HOL_Obool))) )
& ( X1952 != X1951
| hAPP(X1953,X1952) = hAPP(X1953,X1951)
| ~ c_Fun_Oinj__on(X1955,X1954,X1953,c_Orderings_Otop__class_Otop(tc_fun(X1955,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_803,plain,
! [X1956,X1957,X1958,X1959,X1960] :
( ~ c_Fun_Oinj__on(X1960,X1959,X1958,c_Orderings_Otop__class_Otop(tc_fun(X1960,tc_HOL_Obool)))
| hAPP(X1958,X1957) != hAPP(X1958,X1956)
| X1957 = X1956 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_804,plain,
! [X3150,X3151,X3152,X3153,X3154] :
( ( X3153 = X3151
| c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3153,X3152) != c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3151,X3150)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3154),X3151),X3150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3154),X3153),X3152))
| ~ class_Orderings_Olinorder(X3154) )
& ( X3152 = X3150
| c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3153,X3152) != c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3151,X3150)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3154),X3151),X3150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3154),X3153),X3152))
| ~ class_Orderings_Olinorder(X3154) )
& ( X3153 != X3151
| X3152 != X3150
| c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3153,X3152) = c_SetInterval_Oord__class_OatLeastLessThan(X3154,X3151,X3150)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3154),X3151),X3150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3154),X3153),X3152))
| ~ class_Orderings_Olinorder(X3154) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).
fof(i_0_805,plain,
! [X3155,X3156,X3157,X3158,X3159] :
( ~ class_Orderings_Olinorder(X3159)
| c_SetInterval_Oord__class_OatLeastLessThan(X3159,X3158,X3157) != c_SetInterval_Oord__class_OatLeastLessThan(X3159,X3156,X3155)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3159),X3158),X3157))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3159),X3156),X3155))
| X3158 = X3156 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).
fof(i_0_806,plain,
! [X3160,X3161,X3162,X3163,X3164] :
( ~ class_Orderings_Olinorder(X3164)
| c_SetInterval_Oord__class_OatLeastLessThan(X3164,X3163,X3162) != c_SetInterval_Oord__class_OatLeastLessThan(X3164,X3161,X3160)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3164),X3163),X3162))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3164),X3161),X3160))
| X3162 = X3160 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).
fof(i_0_807,plain,
! [X2868,X2869,X2871] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_2(X2868,X2869)),X2868))
| ~ hBOOL(hAPP(X2869,X2868))
| hBOOL(hAPP(X2869,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2871),esk33_2(X2868,X2869)))
| ~ hBOOL(hAPP(X2869,X2871))
| ~ hBOOL(hAPP(X2869,X2868))
| hBOOL(hAPP(X2869,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X2869,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk33_2(X2868,X2869)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X2869,X2868))
| hBOOL(hAPP(X2869,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_808,plain,
! [X2798,X2799] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2799),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2799),X2798)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_809,plain,
! [X2796,X2797] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2797),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2796),X2797)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_810,plain,
! [X2504,X2505,X2506,X2507] :
( ~ hBOOL(hAPP(hAPP(c_member(X2507),X2506),X2505))
| hBOOL(hAPP(hAPP(c_member(X2507),X2506),c_Set_Oinsert(X2507,X2504,X2505))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_811,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_812,plain,
! [X2732,X2733,X2734] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2734),X2733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2733),X2732))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2734)),X2732)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_813,plain,
! [X2693] :
( ~ c_Finite__Set_Ofinite(X2693,c_Orderings_Otop__class_Otop(tc_fun(X2693,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(X2693,c_Orderings_Otop__class_Otop(tc_fun(X2693,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_814,plain,
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk39_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
& c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk39_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])]) ).
fof(i_0_815,plain,
! [X2743,X2744] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2744)),hAPP(c_Nat_OSuc,X2743)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2744),X2743)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2744),X2743))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2744)),hAPP(c_Nat_OSuc,X2743))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_816,plain,
! [X2726,X2727] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2727)),hAPP(c_Nat_OSuc,X2726)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2727),X2726)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_817,plain,
! [X2712,X2713] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2713,X2712),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2713,X2712),tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2712,c_Orderings_Otop__class_Otop(tc_fun(X2712,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Finite__Set_Ofinite(X2713,c_Orderings_Otop__class_Otop(tc_fun(X2713,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_818,plain,
! [X2189,X2190,X2191,X2192] :
( ~ class_Orderings_Opreorder(X2192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2192),X2191),X2190))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2192),X2190),X2189))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2192),X2191),X2189)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_819,plain,
! [X2193,X2194,X2195,X2196] :
( ~ class_Orderings_Oorder(X2196)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2196),X2195),X2194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2196),X2193),X2195))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2196),X2193),X2194)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_820,plain,
! [X3133,X3134] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3134,X3133)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3134),hAPP(c_Nat_OSuc,X3133)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).
fof(i_0_821,plain,
! [X2634,X2635,X2636] :
( ( X2635 = c_Groups_Ozero__class_Ozero(X2636)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2636),X2635),X2634) != c_Groups_Ozero__class_Ozero(X2636)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),X2634))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),X2635))
| ~ class_Groups_Oordered__comm__monoid__add(X2636) )
& ( X2634 = c_Groups_Ozero__class_Ozero(X2636)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2636),X2635),X2634) != c_Groups_Ozero__class_Ozero(X2636)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),X2634))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),X2635))
| ~ class_Groups_Oordered__comm__monoid__add(X2636) )
& ( X2635 != c_Groups_Ozero__class_Ozero(X2636)
| X2634 != c_Groups_Ozero__class_Ozero(X2636)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2636),X2635),X2634) = c_Groups_Ozero__class_Ozero(X2636)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),X2634))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2636,c_Groups_Ozero__class_Ozero(X2636)),X2635))
| ~ class_Groups_Oordered__comm__monoid__add(X2636) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_822,plain,
! [X2568,X2569] : c_Sum__Type_OPlus(X2569,X2568,c_Orderings_Otop__class_Otop(tc_fun(X2569,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2568,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2569,X2568),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_823,plain,
! [X2364,X2365,X2366] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2366),X2365))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2365),X2364))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_824,plain,
! [X1664,X1665,X1666] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1666),X1665))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1665),X1664))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_825,plain,
! [X2361,X2362,X2363] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2363),X2362))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2363),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2361),X2362))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_826,plain,
! [X1661,X1662,X1663] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1663),X1662))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1661),X1662))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_827,plain,
! [X2780,X2781,X2783,X2784,X2785] :
( ( X2781 = hAPP(c_Nat_OSuc,esk31_2(X2780,X2781))
| X2781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2781),hAPP(c_Nat_OSuc,X2780))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk31_2(X2780,X2781)),X2780))
| X2781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2781),hAPP(c_Nat_OSuc,X2780))) )
& ( X2784 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2784),hAPP(c_Nat_OSuc,X2783))) )
& ( X2784 != hAPP(c_Nat_OSuc,X2785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2785),X2783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2784),hAPP(c_Nat_OSuc,X2783))) ) ),
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_828,plain,
! [X2852,X2853,X2854,X2855] :
( ~ class_Rings_Ocomm__semiring__1(X2855)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2855),X2854),X2853)),X2852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2855),X2854),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2855),X2853),X2852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_829,plain,
! [X1832,X1833,X1834,X1835] :
( ~ class_Groups_Oab__semigroup__add(X1835)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1835),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1835),X1834),X1833)),X1832) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1835),X1834),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1835),X1833),X1832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_830,plain,
! [X2848,X2849,X2850,X2851] :
( ~ class_Rings_Ocomm__semiring__1(X2851)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),X2850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),X2849),X2848)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),X2850),X2849)),X2848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_831,plain,
! [X2537,X2538,X2539,X2540] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2540,X2539,X2538),X2537))
| X2539 = X2537
| hBOOL(hAPP(X2538,X2537)) )
& ( X2539 != X2537
| hBOOL(hAPP(c_Set_Oinsert(X2540,X2539,X2538),X2537)) )
& ( ~ hBOOL(hAPP(X2538,X2537))
| hBOOL(hAPP(c_Set_Oinsert(X2540,X2539,X2538),X2537)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_832,plain,
! [X2690] :
( ~ class_Rings_Olinordered__semidom(X2690)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2690),c_Groups_Ozero__class_Ozero(X2690)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2690),c_Groups_Oone__class_Oone(X2690)),c_Groups_Oone__class_Oone(X2690)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_833,plain,
! [X2754,X2755] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2755)),hAPP(c_Nat_OSuc,X2754)))
| 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),X2754))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2755)),hAPP(c_Nat_OSuc,X2754))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_834,plain,
! [X2273,X2274,X2275,X2276] :
( ~ class_Orderings_Opreorder(X2276)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2276,X2275),X2274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2276),X2274),X2273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2276),X2275),X2273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_835,plain,
! [X2265,X2266,X2267,X2268] :
( ~ class_Orderings_Opreorder(X2268)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2268),X2267),X2266))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2268,X2266),X2265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2268),X2267),X2265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_836,plain,
! [X2277,X2278,X2279,X2280] :
( ~ class_Orderings_Oorder(X2280)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2280,X2279),X2278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2280),X2277),X2279))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2280),X2277),X2278)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_837,plain,
! [X2269,X2270,X2271,X2272] :
( ~ class_Orderings_Oorder(X2272)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2272),X2271),X2270))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2272,X2269),X2271))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2272),X2269),X2270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_838,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_839,plain,
! [X2464,X2465] :
( ~ c_Finite__Set_Ofinite(X2465,c_Orderings_Otop__class_Otop(tc_fun(X2465,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2464,c_Orderings_Otop__class_Otop(tc_fun(X2464,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_prod(X2465,X2464),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2465,X2464),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_840,plain,
! [X2350,X2351,X2352,X2353] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2353),X2352))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2351),X2352) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2353),X2350)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2351),X2350)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_841,plain,
! [X2519,X2520,X2521] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2521,tc_HOL_Obool),X2520),c_Set_Oinsert(X2521,X2519,X2520))),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_842,plain,
! [X2508,X2509,X2510,X2511] :
( ( c_Set_Oinsert(X2511,X2510,X2509) != c_Set_Oinsert(X2511,X2510,X2508)
| X2509 = X2508
| hBOOL(hAPP(hAPP(c_member(X2511),X2510),X2508))
| hBOOL(hAPP(hAPP(c_member(X2511),X2510),X2509)) )
& ( X2509 != X2508
| c_Set_Oinsert(X2511,X2510,X2509) = c_Set_Oinsert(X2511,X2510,X2508)
| hBOOL(hAPP(hAPP(c_member(X2511),X2510),X2508))
| hBOOL(hAPP(hAPP(c_member(X2511),X2510),X2509)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])])]) ).
fof(i_0_843,plain,
! [X2728,X2729] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2729)),X2728))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2729),X2728)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_844,plain,
! [X2750,X2751] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2751),X2750))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2750)),X2751)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2750)),X2751))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2751),X2750)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])]) ).
fof(i_0_845,plain,
! [X2717,X2718] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2718),X2717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2718)),hAPP(c_Nat_OSuc,X2717))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_846,plain,
! [X2305,X2306,X2307] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2307),X2306))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2307),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2306),X2305))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_847,plain,
! [X1655,X1656,X1657] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1657),X1656))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1657),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1656),X1655))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_848,plain,
! [X2302,X2303,X2304] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2304),X2303))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2304),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2302),X2303))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_849,plain,
! [X1658,X1659,X1660] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1660),X1659))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1660),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1658),X1659))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_850,plain,
! [X2469,X2470] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2470,X2469),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2470,X2469),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2469,c_Orderings_Otop__class_Otop(tc_fun(X2469,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_851,plain,
! [X2747,X2748] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2748),X2747))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2747),hAPP(c_Nat_OSuc,X2748))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2747),hAPP(c_Nat_OSuc,X2748)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2748),X2747)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])]) ).
fof(i_0_852,plain,
! [X2326,X2327,X2328] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2328),X2327)),X2326) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2328),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2327),X2326)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_853,plain,
! [X2812,X2813] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2813),X2812))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2813)),X2812)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2813)),X2812))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2813),X2812)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_854,plain,
! [X2808,X2809] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2809)),X2808))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2809),X2808)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2809),X2808))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2809)),X2808)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_855,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)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_856,plain,
! [X2042,X2043,X2044,X2045] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2045,tc_HOL_Obool),X2044),X2043))
| ~ hBOOL(hAPP(X2044,X2042))
| hBOOL(hAPP(X2043,X2042)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_857,plain,
! [X2055,X2056,X2057,X2058] :
( ~ hBOOL(hAPP(X2058,X2057))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2056,tc_HOL_Obool),X2058),X2055))
| hBOOL(hAPP(X2055,X2057)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_858,plain,
! [X2089,X2090,X2091,X2092] :
( ~ class_Orderings_Opreorder(X2092)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2092,X2091),X2090))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2092,X2090),X2089))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2092,X2091),X2089)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_859,plain,
! [X2082,X2083,X2084,X2085] :
( ~ class_Orderings_Oorder(X2085)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2085,X2084),X2083))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2085,X2082),X2084))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2085,X2082),X2083)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_860,plain,
! [X2735,X2736] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2736),X2735))
| hAPP(c_Nat_OSuc,X2736) = X2735
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2736)),X2735)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_861,plain,
! [X2170,X2171,X2172] :
( ~ class_Orderings_Oorder(X2172)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2172),X2171),X2170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2172),X2170),X2171)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])]) ).
fof(i_0_862,plain,
! [X2140,X2141,X2142] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2142),X2141),X2140))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2142),X2140),X2141))
| X2141 = X2140
| ~ class_Orderings_Olinorder(X2142) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2142),X2140),X2141))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2142),X2141),X2140))
| ~ class_Orderings_Olinorder(X2142) )
& ( X2141 != X2140
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2142),X2141),X2140))
| ~ class_Orderings_Olinorder(X2142) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])])]) ).
fof(i_0_863,plain,
! [X2197,X2198,X2199] :
( ~ class_Orderings_Opreorder(X2199)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2199),X2198),X2197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2199),X2197),X2198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])]) ).
fof(i_0_864,plain,
! [X2167,X2168,X2169] :
( ~ class_Orderings_Opreorder(X2169)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2169),X2168),X2167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2169),X2167),X2168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])]) ).
fof(i_0_865,plain,
! [X2158,X2159,X2160] :
( ~ class_Orderings_Opreorder(X2160)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2160),X2159),X2158))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2160),X2158),X2159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])]) ).
fof(i_0_866,plain,
! [X2155,X2156,X2157] :
( ~ class_Orderings_Opreorder(X2157)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2157),X2156),X2155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2157),X2155),X2156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])]) ).
fof(i_0_867,plain,
! [X1774,X1775] :
( ~ class_Rings_Olinordered__semidom(X1775)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1775),X1774),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1775),X1774),c_Groups_Oone__class_Oone(X1775)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_868,plain,
! [X2802,X2803] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2802),hAPP(c_Nat_OSuc,X2803)))
| X2802 = X2803
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2803),X2802)) )
& ( X2802 != X2803
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2802),hAPP(c_Nat_OSuc,X2803)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2803),X2802)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_869,plain,
! [X2760,X2761] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2761)),X2760))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2761),X2760)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_870,plain,
! [X2478,X2479,X2480] :
( ~ c_Finite__Set_Ofinite(X2480,X2479)
| hBOOL(hAPP(hAPP(c_member(X2480),X2478),X2479))
| c_Finite__Set_Ocard(X2480,c_Set_Oinsert(X2480,X2478,X2479)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X2480,X2479)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])]) ).
fof(i_0_871,plain,
! [X2226,X2227,X2228] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2228,X2227),X2226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2228),X2227),X2226))
| ~ class_Orderings_Opreorder(X2228) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2228,X2226),X2227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2228),X2227),X2226))
| ~ class_Orderings_Opreorder(X2228) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2228,X2227),X2226))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2228,X2226),X2227))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2228),X2227),X2226))
| ~ class_Orderings_Opreorder(X2228) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])])]) ).
fof(i_0_872,plain,
! [X2818,X2819,X2820] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2820),X2818),X2819))
| c_Finite__Set_Ocard(X2820,c_Set_Oinsert(X2820,X2818,X2819)) = c_Finite__Set_Ocard(X2820,X2819)
| ~ c_Finite__Set_Ofinite(X2820,X2819) )
& ( hBOOL(hAPP(hAPP(c_member(X2820),X2818),X2819))
| c_Finite__Set_Ocard(X2820,c_Set_Oinsert(X2820,X2818,X2819)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2820,X2819))
| ~ c_Finite__Set_Ofinite(X2820,X2819) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])])]) ).
fof(i_0_873,plain,
! [X3138,X3140,X3141,X3142] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3138)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3140),X3138))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3140),esk41_1(X3138))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_2(X3141,X3142)),X3141))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3141) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk42_2(X3141,X3142)),X3142))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3141) ) ),
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_874,plain,
! [X2533,X2534,X2535,X2536] : c_Set_Oinsert(X2536,X2535,c_Set_Oinsert(X2536,X2534,X2533)) = c_Set_Oinsert(X2536,X2534,c_Set_Oinsert(X2536,X2535,X2533)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_875,plain,
! [X2516,X2517,X2518] : hBOOL(hAPP(hAPP(c_member(X2518),X2517),c_Set_Oinsert(X2518,X2517,X2516))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_876,plain,
! [X2745,X2746] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2746),hAPP(c_Nat_OSuc,X2745)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2746),X2745))
| X2746 = X2745 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2746),X2745))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2746),hAPP(c_Nat_OSuc,X2745))) )
& ( X2746 != X2745
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2746),hAPP(c_Nat_OSuc,X2745))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_877,plain,
! [X2741,X2742] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2742),hAPP(c_Nat_OSuc,X2741)))
| X2742 = X2741
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2742),X2741)) )
& ( X2742 != X2741
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2742),hAPP(c_Nat_OSuc,X2741)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2742),X2741)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])])]) ).
fof(i_0_878,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),X2740),hAPP(c_Nat_OSuc,X2739)))
| X2739 = X2740 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])]) ).
fof(i_0_879,plain,
! [X2730,X2731] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2731),hAPP(c_Nat_OSuc,X2730)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2731),X2730))
| X2731 = X2730 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])]) ).
fof(i_0_880,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)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_881,plain,
! [X2844,X2845,X2846,X2847] :
( ~ class_Rings_Ocomm__semiring__1(X2847)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2847),X2846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2847),X2845),X2844)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2847),X2845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2847),X2846),X2844)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_882,plain,
! [X2340,X2341,X2342] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2342),X2341))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2341),X2340))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2342),X2340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_883,plain,
! [X2458,X2459,X2460] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2460,tc_HOL_Obool),X2459),X2458))
| ~ c_Finite__Set_Ofinite(X2460,X2458)
| c_Finite__Set_Ofinite(X2460,X2459) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_884,plain,
! [X2455,X2456,X2457] :
( ~ c_Finite__Set_Ofinite(X2457,X2456)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2457,tc_HOL_Obool),X2455),X2456))
| c_Finite__Set_Ofinite(X2457,X2455) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_885,plain,
! [X2253,X2254,X2255] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2255),X2254),X2253))
| X2254 = X2253
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2255,X2254),X2253))
| ~ class_Orderings_Olinorder(X2255) )
& ( X2254 != X2253
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2255),X2254),X2253))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2255,X2254),X2253))
| ~ class_Orderings_Olinorder(X2255) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])])]) ).
fof(i_0_886,plain,
! [X2247,X2248,X2249] :
( ~ class_Orderings_Olinorder(X2249)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2249,X2248),X2247))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2249),X2247),X2248)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])]) ).
fof(i_0_887,plain,
! [X2214,X2215,X2216] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2216),X2215),X2214))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2216,X2214),X2215))
| ~ class_Orderings_Olinorder(X2216) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2216,X2214),X2215))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2216),X2215),X2214))
| ~ class_Orderings_Olinorder(X2216) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).
fof(i_0_888,plain,
! [X2217,X2218,X2219] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2219,X2218),X2217))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2219),X2217),X2218))
| ~ class_Orderings_Olinorder(X2219) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2219),X2217),X2218))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2219,X2218),X2217))
| ~ class_Orderings_Olinorder(X2219) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])])]) ).
fof(i_0_889,plain,
! [X2790,X2791,X2793,X2794,X2795] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2791),X2790))
| X2790 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2791),esk32_2(X2790,X2791))) )
& ( X2793 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2794),X2795))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2794),X2793)) ) ),
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_890,plain,
! [X2810,X2811] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2811),hAPP(c_Nat_OSuc,X2810)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2811),X2810)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2811),X2810))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2811),hAPP(c_Nat_OSuc,X2810))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_891,plain,
! [X3144,X3146,X3147,X3148] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3144)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3146),X3144))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3146),esk43_1(X3144))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk44_2(X3147,X3148)),X3147))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3147) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk44_2(X3147,X3148)),X3148))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3147) ) ),
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_892,plain,
! [X2815,X2816,X2817] :
( ~ c_Finite__Set_Ofinite(X2817,X2816)
| hBOOL(hAPP(hAPP(c_member(X2817),X2815),X2816))
| c_Finite__Set_Ocard(X2817,c_Set_Oinsert(X2817,X2815,X2816)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2817,X2816)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).
fof(i_0_893,plain,
! [X2737,X2738] :
( ~ 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))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_894,plain,
! [X2833,X2834] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2834),X2833),X2833) != c_Groups_Ozero__class_Ozero(X2834)
| X2833 = c_Groups_Ozero__class_Ozero(X2834)
| ~ hBOOL(hAPP(hAPP(c_member(X2834),X2833),c_Int_Oring__1__class_OInts(X2834)))
| ~ class_Int_Oring__char__0(X2834) )
& ( X2833 != c_Groups_Ozero__class_Ozero(X2834)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2834),X2833),X2833) = c_Groups_Ozero__class_Ozero(X2834)
| ~ hBOOL(hAPP(hAPP(c_member(X2834),X2833),c_Int_Oring__1__class_OInts(X2834)))
| ~ class_Int_Oring__char__0(X2834) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).
fof(i_0_895,plain,
! [X3072,X3073,X3074,X3075] : c_Nat_Onat_Onat__case(X3075,X3074,X3073,hAPP(c_Nat_OSuc,X3072)) = hAPP(X3073,X3072),
inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).
fof(i_0_896,plain,
! [X2758,X2759] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2759),hAPP(c_Nat_OSuc,X2758)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2759),X2758))
| X2759 = hAPP(c_Nat_OSuc,X2758) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])]) ).
fof(i_0_897,plain,
! [X2752,X2753] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2753),hAPP(c_Nat_OSuc,X2752)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2753),X2752))
| 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),hAPP(c_Nat_OSuc,X2752))) )
& ( X2753 != hAPP(c_Nat_OSuc,X2752)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2753),hAPP(c_Nat_OSuc,X2752))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_898,plain,
! [X1824,X1825] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1825,tc_HOL_Obool),X1824),c_Orderings_Otop__class_Otop(tc_fun(X1825,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_899,plain,
! [X2308,X2309,X2310] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2309),X2310))
| hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| X2310 = X2309
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2310),X2309)) )
& ( ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| X2310 = X2309
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2310),X2309)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2309),X2310))
| hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2310),X2309)) )
& ( ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2310),X2309)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2309),X2310))
| hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| X2310 = X2309
| ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310)) )
& ( ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| X2310 = X2309
| ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2309),X2310))
| hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310)) )
& ( ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310))
| ~ hBOOL(hAPP(hAPP(X2308,X2309),X2310)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_900,plain,
! [X2323,X2324,X2325] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2325),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2324),X2323)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2324),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2325),X2323)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_901,plain,
! [X2123,X2124,X2125] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2124),X2123))
| X2124 != X2123
| ~ class_Orderings_Oorder(X2125) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2123),X2124))
| X2124 != X2123
| ~ class_Orderings_Oorder(X2125) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2124),X2123))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2123),X2124))
| X2124 = X2123
| ~ class_Orderings_Oorder(X2125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_902,plain,
! [X2112,X2113,X2114] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2114,X2112),X2113))
| X2112 = X2113
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2114,X2113),X2112))
| ~ class_Orderings_Oorder(X2114) )
& ( X2112 != X2113
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2114,X2112),X2113))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2114,X2113),X2112))
| ~ class_Orderings_Oorder(X2114) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_903,plain,
! [X2093,X2094,X2095] :
( ~ class_Orderings_Oorder(X2095)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2095,X2094),X2093))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2095,X2093),X2094))
| X2094 = X2093 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_904,plain,
! [X2086,X2087,X2088] :
( ~ class_Orderings_Oorder(X2088)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2088,X2087),X2086))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2088,X2086),X2087))
| X2086 = X2087 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_905,plain,
! [X2691,X2692] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2692,X2691)))
| c_Finite__Set_Ofinite(X2692,X2691) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
fof(i_0_906,plain,
! [X2749] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2749)),X2749)),
inference(variable_rename,[status(thm)],[i_0_560]) ).
fof(i_0_907,plain,
! [X2806,X2807] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2807),X2806))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2807),hAPP(c_Nat_OSuc,X2806))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_908,plain,
! [X2467,X2468] :
( ~ c_Finite__Set_Ofinite(X2468,c_Orderings_Otop__class_Otop(tc_fun(X2468,tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2468,X2467) != c_Finite__Set_Ocard(X2468,c_Orderings_Otop__class_Otop(tc_fun(X2468,tc_HOL_Obool)))
| X2467 = c_Orderings_Otop__class_Otop(tc_fun(X2468,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_909,plain,
! [X2229,X2230,X2231] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2231,X2230),X2229))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2231),X2230),X2229))
| X2230 = X2229
| ~ class_Orderings_Oorder(X2231) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2231),X2230),X2229))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2231,X2230),X2229))
| ~ class_Orderings_Oorder(X2231) )
& ( X2230 != X2229
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2231,X2230),X2229))
| ~ class_Orderings_Oorder(X2231) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_910,plain,
! [X2223,X2224,X2225] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2225,X2224),X2223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2225),X2224),X2223))
| ~ class_Orderings_Oorder(X2225) )
& ( X2224 != X2223
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2225),X2224),X2223))
| ~ class_Orderings_Oorder(X2225) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2225,X2224),X2223))
| X2224 = X2223
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2225),X2224),X2223))
| ~ class_Orderings_Oorder(X2225) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_911,plain,
! [X2250,X2251,X2252] :
( ~ class_Orderings_Opreorder(X2252)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2252),X2251),X2250))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2252,X2251),X2250)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_912,plain,
! [X2386,X2387] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2387),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2387),X2386))),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_913,plain,
! [X2384,X2385] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2385),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2384),X2385))),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_914,plain,
! [X3047,X3048] : c_Set_Oimage(X3048,X3048,c_COMBI(X3048),X3047) = X3047,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_915,plain,
! [X1873,X1874] : c_Fun_Oinj__on(X1874,X1874,c_COMBI(X1874),X1873),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_916,plain,
! [X3076,X3077,X3078] : c_Nat_Onat_Onat__case(X3078,X3077,X3076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3077,
inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).
fof(i_0_917,plain,
! [X2262,X2263,X2264] :
( ~ class_Orderings_Oorder(X2264)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2264,X2263),X2262))
| X2262 = X2263
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2264),X2263),X2262)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_918,plain,
! [X2259,X2260,X2261] :
( ~ class_Orderings_Oorder(X2261)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2261,X2260),X2259))
| X2260 = X2259
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2261),X2260),X2259)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_919,plain,
! [X2256,X2257,X2258] :
( ~ class_Orderings_Oorder(X2258)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2258,X2257),X2256))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2258),X2257),X2256))
| X2257 = X2256 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_920,plain,
! [X2241,X2242,X2243] :
( ~ class_Orderings_Oorder(X2243)
| X2242 = X2241
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2243,X2242),X2241))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2243),X2242),X2241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_921,plain,
! [X2238,X2239,X2240] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2240,X2239),X2238))
| X2239 = X2238
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2240),X2239),X2238))
| ~ class_Orderings_Olinorder(X2240) )
& ( X2239 != X2238
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2240,X2239),X2238))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2240),X2239),X2238))
| ~ class_Orderings_Olinorder(X2240) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])])]) ).
fof(i_0_922,plain,
! [X2244,X2245,X2246] :
( ~ class_Orderings_Oorder(X2246)
| X2245 = X2244
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2246,X2244),X2245))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2246),X2244),X2245)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_923,plain,
! [X2779] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2779),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X2779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2779 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2779),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_924,plain,
! [X2774] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2774),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_925,plain,
! [X2343,X2344] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2344),X2343))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2343),X2344))
| X2344 = X2343 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_926,plain,
! [X1826,X1827,X1828] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1828),X1827),hAPP(c_fequal,X1826)))
| X1827 = X1826 )
& ( X1827 != X1826
| hBOOL(hAPP(hAPP(c_member(X1828),X1827),hAPP(c_fequal,X1826))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_927,plain,
! [X2756,X2757] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2757),X2756))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2757),hAPP(c_Nat_OSuc,X2756))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_928,plain,
! [X2664] :
( ~ class_Rings_Olinordered__semidom(X2664)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2664),c_Groups_Oone__class_Oone(X2664)),c_Groups_Ozero__class_Ozero(X2664))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])]) ).
fof(i_0_929,plain,
! [X2382,X2383] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2383),X2382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2383),X2382)) )
& ( X2383 != X2382
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2383),X2382)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2383),X2382))
| X2383 = X2382
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2383),X2382)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_930,plain,
! [X2380,X2381] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2381),X2380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2381),X2380))
| X2381 = X2380 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2381),X2380))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2381),X2380)) )
& ( X2381 != X2380
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2381),X2380)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_931,plain,
! [X2378,X2379] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2379),X2378))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2379),X2378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_932,plain,
! [X2374,X2375] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2375),X2374))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2375),X2374)) )
& ( X2375 != X2374
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2375),X2374)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_933,plain,
! [X1667,X1668] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1668),X1667))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1668),X1667)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_934,plain,
! [X2501,X2502,X2503] :
( ~ hBOOL(hAPP(hAPP(c_member(X2503),X2502),X2501))
| c_Set_Oinsert(X2503,X2502,X2501) = X2501 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_935,plain,
! [X2137,X2138,X2139] :
( ( X2138 = X2137
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2139),X2138),X2137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2139),X2137),X2138))
| ~ class_Orderings_Olinorder(X2139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2139),X2138),X2137))
| X2138 != X2137
| ~ class_Orderings_Olinorder(X2139) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2139),X2137),X2138))
| X2138 != X2137
| ~ class_Orderings_Olinorder(X2139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_936,plain,
! [X2200,X2201,X2202] :
( ~ class_Orderings_Olinorder(X2202)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2202),X2201),X2200))
| X2201 = X2200
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2202),X2200),X2201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_937,plain,
! [X2149,X2150,X2151] :
( ~ class_Orderings_Olinorder(X2151)
| X2150 = X2149
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2151),X2150),X2149))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2151),X2149),X2150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])]) ).
fof(i_0_938,plain,
! [X2146,X2147,X2148] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2148),X2146),X2147))
| X2146 = X2147
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2148),X2147),X2146))
| ~ class_Orderings_Olinorder(X2148) )
& ( X2146 != X2147
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2148),X2146),X2147))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2148),X2147),X2146))
| ~ class_Orderings_Olinorder(X2148) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])])]) ).
fof(i_0_939,plain,
! [X2143,X2144,X2145] :
( ~ class_Orderings_Olinorder(X2145)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2145),X2144),X2143))
| X2144 = X2143
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2145),X2143),X2144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_940,plain,
! [X1829,X1830,X1831] :
( ~ class_Rings_Olinordered__idom(X1831)
| X1830 = X1829
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1831),X1830),X1829))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1831),X1829),X1830)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])]) ).
fof(i_0_941,plain,
! [X2461] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X2461),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2461),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2461,c_Orderings_Otop__class_Otop(tc_fun(X2461,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2461,c_Orderings_Otop__class_Otop(tc_fun(X2461,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X2461),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2461),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_942,plain,
! [X2376,X2377] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2377),X2376))
| X2377 = X2376
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2377),X2376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_943,plain,
! [X2530,X2531,X2532] : c_Set_Oinsert(X2532,X2531,c_Set_Oinsert(X2532,X2531,X2530)) = c_Set_Oinsert(X2532,X2531,X2530),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
fof(i_0_944,plain,
! [X2420,X2421] : hBOOL(hAPP(hAPP(c_member(X2421),X2420),c_Orderings_Otop__class_Otop(tc_fun(X2421,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_945,plain,
! [X1652,X1653] : hBOOL(hAPP(hAPP(c_member(X1653),X1652),c_Orderings_Otop__class_Otop(tc_fun(X1653,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_946,plain,
! [X2498,X2499,X2500] :
( ( ~ c_Finite__Set_Ofinite(X2500,c_Set_Oinsert(X2500,X2499,X2498))
| c_Finite__Set_Ofinite(X2500,X2498) )
& ( ~ c_Finite__Set_Ofinite(X2500,X2498)
| c_Finite__Set_Ofinite(X2500,c_Set_Oinsert(X2500,X2499,X2498)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).
fof(i_0_947,plain,
! [X1681,X1682,X1683] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1683),X1682),X1681))
| hBOOL(hAPP(X1681,X1682)) )
& ( ~ hBOOL(hAPP(X1681,X1682))
| hBOOL(hAPP(hAPP(c_member(X1683),X1682),X1681)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_948,plain,
! [X2235,X2236,X2237] :
( ~ class_Orderings_Olinorder(X2237)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2237,X2236),X2235))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2237),X2235),X2236)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_949,plain,
! [X2220,X2221,X2222] :
( ~ class_Orderings_Olinorder(X2222)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2222,X2221),X2220))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2222),X2220),X2221)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_950,plain,
! [X2232,X2233,X2234] :
( ~ class_Orderings_Olinorder(X2234)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2234),X2233),X2232))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2234,X2232),X2233)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_951,plain,
! [X2770,X2771] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2771)),X2770) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2771),X2770)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_952,plain,
! [X2662] :
( ~ class_Rings_Olinordered__semidom(X2662)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2662,c_Groups_Oone__class_Oone(X2662)),c_Groups_Ozero__class_Ozero(X2662))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_953,plain,
! [X2388,X2389,X2391,X2392,X2393] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2389),X2388))
| X2388 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2389),esk18_2(X2388,X2389)) )
& ( X2391 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2392),X2393)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2392),X2391)) ) ),
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_954,plain,
! [X2318,X2319] :
( ( X2319 = X2318
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2319),X2318))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2318),X2319)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2319),X2318))
| X2319 != X2318 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2318),X2319))
| X2319 != X2318 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_955,plain,
! [X2316,X2317] :
( X2317 = X2316
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2317),X2316))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2316),X2317)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])]) ).
fof(i_0_956,plain,
! [X2775,X2777,X2778] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2775))
| X2775 = hAPP(c_Nat_OSuc,esk30_1(X2775)) )
& ( X2777 != hAPP(c_Nat_OSuc,X2778)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2777)) ) ),
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_957,plain,
! [X2164,X2165,X2166] :
( ~ class_Orderings_Oorder(X2166)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2166),X2165),X2164))
| X2164 != X2165 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_958,plain,
! [X2161,X2162,X2163] :
( ~ class_Orderings_Oorder(X2163)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2163),X2162),X2161))
| X2162 != X2161 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_959,plain,
! [X2152,X2153,X2154] :
( ~ class_Orderings_Oorder(X2154)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2154),X2153),X2152))
| X2153 != X2152 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_960,plain,
! [X2017,X2018,X2019] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2017,tc_HOL_Obool),X2019),X2018))
| X2019 != X2018 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2017,tc_HOL_Obool),X2018),X2019))
| X2019 != X2018 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])])]) ).
fof(i_0_961,plain,
! [X2052,X2053,X2054] :
( X2054 != X2053
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2052,tc_HOL_Obool),X2054),X2053)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_962,plain,
! [X2049,X2050,X2051] :
( X2051 != X2050
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2049,tc_HOL_Obool),X2050),X2051)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_963,plain,
! [X2135,X2136] :
( ~ class_Orderings_Opreorder(X2136)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2136),X2135),X2135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).
fof(i_0_964,plain,
! [X2072,X2073] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2073,tc_HOL_Obool),X2072),X2072)),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_965,plain,
! [X2618] :
( ( X2618 = 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)),X2618)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2618))
| X2618 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_966,plain,
! [X1852,X1853,X1854,X1855] :
( ~ class_Groups_Ocancel__semigroup__add(X1855)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1855),X1854),X1853) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1855),X1852),X1853)
| X1854 = X1852 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_967,plain,
! [X1840,X1841,X1842,X1843] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1843),X1842),X1841) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1843),X1840),X1841)
| X1842 = X1840
| ~ class_Groups_Ocancel__semigroup__add(X1843) )
& ( X1842 != X1840
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1843),X1842),X1841) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1843),X1840),X1841)
| ~ class_Groups_Ocancel__semigroup__add(X1843) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_968,plain,
! [X1848,X1849,X1850,X1851] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X1851)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1851),X1850),X1849) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1851),X1850),X1848)
| X1849 = X1848 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_969,plain,
! [X1844,X1845,X1846,X1847] :
( ~ class_Groups_Ocancel__semigroup__add(X1847)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1847),X1846),X1845) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1847),X1846),X1844)
| X1845 = X1844 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_970,plain,
! [X1836,X1837,X1838,X1839] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1839),X1838),X1837) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1839),X1838),X1836)
| X1837 = X1836
| ~ class_Groups_Ocancel__semigroup__add(X1839) )
& ( X1837 != X1836
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1839),X1838),X1837) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1839),X1838),X1836)
| ~ class_Groups_Ocancel__semigroup__add(X1839) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_971,plain,
! [X2126,X2127,X2128] :
( ~ class_Orderings_Olinorder(X2128)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2128,X2127),X2126))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2128,X2126),X2127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_972,plain,
! [X2074,X2075,X2076] :
( ~ class_Orderings_Olinorder(X2076)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2076,X2075),X2074))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2076,X2074),X2075)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_573])]) ).
fof(i_0_973,plain,
! [X2772,X2773] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2773),hAPP(c_Nat_OSuc,X2772)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2773),X2772)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_974,plain,
! [X2768,X2769] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2769)),X2768) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2769),hAPP(c_Nat_OSuc,X2768)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_975,plain,
! [X2619] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2619),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_574]) ).
fof(i_0_976,plain,
! [X2617] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2617),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_575]) ).
fof(i_0_977,plain,
! [X2590] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2590),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_576]) ).
fof(i_0_978,plain,
! [X2824] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2824)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2824)),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_979,plain,
! [X2615,X2616] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2616),X2615))
| X2615 != 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_980,plain,
! [X2336,X2337] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2337),X2336))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2336),X2337)) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_981,plain,
! [X2719] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2719))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_982,plain,
! [X2313,X2314] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2314),X2313))
| X2313 != X2314 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_983,plain,
! [X2311,X2312] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2312),X2311))
| X2312 != X2311 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_984,plain,
! [X2665] :
( ~ class_Rings_Olinordered__semidom(X2665)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2665),c_Groups_Ozero__class_Ozero(X2665)),c_Groups_Oone__class_Oone(X2665))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_985,plain,
! [X2828] :
( ~ class_Rings_Oring__1(X2828)
| hBOOL(hAPP(hAPP(c_member(X2828),c_Groups_Ozero__class_Ozero(X2828)),c_Int_Oring__1__class_OInts(X2828))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).
fof(i_0_986,plain,
! [X2832] :
( ~ class_Rings_Oring__1(X2832)
| hBOOL(hAPP(hAPP(c_member(X2832),c_Groups_Oone__class_Oone(X2832)),c_Int_Oring__1__class_OInts(X2832))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).
fof(i_0_987,plain,
! [X2320] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2320),X2320)),
inference(variable_rename,[status(thm)],[i_0_577]) ).
fof(i_0_988,plain,
! [X2315] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2315),X2315)),
inference(variable_rename,[status(thm)],[i_0_578]) ).
fof(i_0_989,plain,
! [X2332,X2333,X2334] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2334),X2333) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2332),X2333)
| X2334 = X2332 )
& ( X2334 != X2332
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2334),X2333) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2332),X2333) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_990,plain,
! [X2329,X2330,X2331] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2331),X2330) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2331),X2329)
| X2330 = X2329 )
& ( X2330 != X2329
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2331),X2330) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2331),X2329) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_991,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_992,plain,
! [X2716] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2716),hAPP(c_Nat_OSuc,X2716))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_993,plain,
! [X1786,X1787] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1787,tc_HOL_Obool)),X1786)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_994,plain,
! [X2599] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2599),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X2599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2599 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2599),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_995,plain,
! [X2788,X2789] :
( ( X2789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2789 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2789),X2788) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2788 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2789 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2789),X2788) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2789),X2788) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2788 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2789),X2788) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2789 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2789),X2788) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2789 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2788 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2789),X2788) = 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_996,plain,
! [X2786,X2787] :
( ( X2787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2787 = 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),X2787),X2786) )
& ( X2786 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2787 = 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),X2787),X2786) )
& ( X2787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2786 = 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),X2787),X2786) )
& ( X2786 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2786 = 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),X2787),X2786) )
& ( X2787 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2786 != 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),X2787),X2786) )
& ( X2787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2786 != 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),X2787),X2786) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_997,plain,
! [X1618,X1619] :
( hAPP(X1619,esk1_2(X1618,X1619)) != hAPP(X1618,esk1_2(X1618,X1619))
| X1619 = X1618 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_998,plain,
! [X2663] :
( ~ class_Rings_Olinordered__semidom(X2663)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2663,c_Groups_Ozero__class_Ozero(X2663)),c_Groups_Oone__class_Oone(X2663))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_999,plain,
! [X3206,X3207] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X3207),X3206))
| X3207 = X3206 ),
inference(variable_rename,[status(thm)],[i_0_579]) ).
fof(i_0_1000,plain,
! [X3131,X3132] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3132,X3131)),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).
fof(i_0_1001,plain,
! [X2823] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X2823)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X2823)),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_1002,plain,
! [X2841,X2842,X2843] :
( ~ class_Rings_Ocomm__semiring__1(X2843)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2843),X2842),X2841) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2843),X2841),X2842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_1003,plain,
! [X2614] :
( X2614 = 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)),X2614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_1004,plain,
! [X2281,X2282] :
( ~ class_Orderings_Otop(X2282)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2282,X2281),c_Orderings_Otop__class_Otop(X2282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_1005,plain,
! [X2714,X2715] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2715),X2714),X2714) != c_Groups_Ozero__class_Ozero(X2715)
| X2714 = c_Groups_Ozero__class_Ozero(X2715)
| ~ class_Groups_Olinordered__ab__group__add(X2715) )
& ( X2714 != c_Groups_Ozero__class_Ozero(X2715)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2715),X2714),X2714) = c_Groups_Ozero__class_Ozero(X2715)
| ~ class_Groups_Olinordered__ab__group__add(X2715) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_1006,plain,
! [X2608,X2609] :
( ( c_Groups_Ozero__class_Ozero(X2609) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2609),X2608),X2608)
| X2608 = c_Groups_Ozero__class_Ozero(X2609)
| ~ class_Groups_Olinordered__ab__group__add(X2609) )
& ( X2608 != c_Groups_Ozero__class_Ozero(X2609)
| c_Groups_Ozero__class_Ozero(X2609) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2609),X2608),X2608)
| ~ class_Groups_Olinordered__ab__group__add(X2609) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_1007,plain,
! [X2865,X2866,X2867] :
( ( X2866 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2867),X2866),X2865)
| X2865 = c_Groups_Ozero__class_Ozero(X2867)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2867) )
& ( X2865 != c_Groups_Ozero__class_Ozero(X2867)
| X2866 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2867),X2866),X2865)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2867) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_1008,plain,
! [X2120,X2121,X2122] :
( ~ class_Orderings_Opreorder(X2122)
| X2121 != X2120
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2122,X2121),X2120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1009,plain,
! [X3184,X3185,X3186,X3187] : hAPP(hAPP(c_COMBK(X3187,X3186),X3185),X3184) = X3185,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_1010,plain,
! [X2321,X2322] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2322),X2321) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2321),X2322),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_1011,plain,
! [X1991,X1992] :
( ~ class_Orderings_Opreorder(X1992)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1992,X1991),X1991)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1012,plain,
! [X2598] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2598)),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_1013,plain,
! [X2591] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2591)),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_1014,plain,
! [X2283,X2284,X2285] :
( ~ class_Orderings_Otop(X2285)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X2284,X2285)),X2283) = c_Orderings_Otop__class_Otop(X2285) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_1015,plain,
! [X2594,X2595] :
( ( X2595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2595),X2594) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2594 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2595),X2594) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2595 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2594 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2595),X2594) = 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_1016,plain,
! [X2338,X2339] :
( X2339 != X2338
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2339),X2338)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1017,plain,
! [X3208,X3209] :
( X3209 != X3208
| hBOOL(hAPP(hAPP(c_fequal,X3209),X3208)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1018,plain,
! [X2596,X2597] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2597),X2596) != X2597
| X2596 = 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_1019,plain,
! [X2335] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2335),X2335)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1020,plain,
! [X2466] :
( ~ class_Finite__Set_Ofinite(X2466)
| c_Finite__Set_Ofinite(X2466,c_Orderings_Otop__class_Otop(tc_fun(X2466,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_1021,plain,
! [X2837,X2838] :
( ~ class_Rings_Ocomm__semiring__1(X2838)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2838),c_Groups_Ozero__class_Ozero(X2838)),X2837) = X2837 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_1022,plain,
! [X2612,X2613] :
( ~ class_Groups_Omonoid__add(X2613)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2613),c_Groups_Ozero__class_Ozero(X2613)),X2612) = X2612 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_1023,plain,
! [X2610,X2611] :
( ~ class_Groups_Ocomm__monoid__add(X2611)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2611),c_Groups_Ozero__class_Ozero(X2611)),X2610) = X2610 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_1024,plain,
! [X2839,X2840] :
( ~ class_Rings_Ocomm__semiring__1(X2840)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2840),X2839),c_Groups_Ozero__class_Ozero(X2840)) = X2839 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_1025,plain,
! [X2606,X2607] :
( ~ class_Groups_Omonoid__add(X2607)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2607),X2606),c_Groups_Ozero__class_Ozero(X2607)) = X2606 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_1026,plain,
! [X2604,X2605] :
( ~ class_Groups_Ocomm__monoid__add(X2605)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2605),X2604),c_Groups_Ozero__class_Ozero(X2605)) = X2604 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_1027,plain,
! [X2821] : hAPP(c_Nat_OSuc,X2821) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2821),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1028,plain,
! [X2822] : hAPP(c_Nat_OSuc,X2822) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2822),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1029,plain,
! [X2592] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2592) = X2592,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_1030,plain,
! [X2814] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2814) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2814)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(i_0_1031,plain,
! [X2593] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2593),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2593,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_1032,plain,
! [X3177,X3178] :
( ~ class_Finite__Set_Ofinite(X3178)
| ~ class_Finite__Set_Ofinite(X3177)
| class_Finite__Set_Ofinite(tc_sum(X3178,X3177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_1033,plain,
! [X3169,X3170] :
( ~ class_Finite__Set_Ofinite(X3170)
| ~ class_Finite__Set_Ofinite(X3169)
| class_Finite__Set_Ofinite(tc_fun(X3170,X3169)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_1034,plain,
! [X3180,X3181] :
( ~ class_Finite__Set_Ofinite(X3181)
| ~ class_Finite__Set_Ofinite(X3180)
| class_Finite__Set_Ofinite(tc_prod(X3181,X3180)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_1035,plain,
! [X2766,X2767] :
( hAPP(c_Nat_OSuc,X2767) != hAPP(c_Nat_OSuc,X2766)
| X2767 = X2766 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1036,plain,
! [X2764,X2765] :
( ( hAPP(c_Nat_OSuc,X2765) != hAPP(c_Nat_OSuc,X2764)
| X2765 = X2764 )
& ( X2765 != X2764
| hAPP(c_Nat_OSuc,X2765) = hAPP(c_Nat_OSuc,X2764) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1037,plain,
! [X3173,X3174] :
( ~ class_Orderings_Otop(X3174)
| class_Orderings_Otop(tc_fun(X3173,X3174)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_1038,plain,
! [X3171,X3172] :
( ~ class_Orderings_Oorder(X3172)
| class_Orderings_Oorder(tc_fun(X3171,X3172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1039,plain,
! [X3175,X3176] :
( ~ class_Orderings_Oord(X3176)
| class_Orderings_Oord(tc_fun(X3175,X3176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1040,plain,
! [X3167,X3168] :
( ~ class_Orderings_Opreorder(X3168)
| class_Orderings_Opreorder(tc_fun(X3167,X3168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1041,plain,
! [X2668,X2669] :
( c_Finite__Set_Ofinite(X2669,X2668)
| c_Finite__Set_Ocard(X2669,X2668) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_580])]) ).
fof(i_0_1042,plain,
! [X2723] : hAPP(c_Nat_OSuc,X2723) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1043,plain,
! [X2722] : hAPP(c_Nat_OSuc,X2722) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1044,plain,
! [X2720] : hAPP(c_Nat_OSuc,X2720) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1045,plain,
! [X2725] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2725),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1046,plain,
! [X2724] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2724),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1047,plain,
! [X2721] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2721),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1048,plain,
! [X2453,X2454] :
( ~ class_Finite__Set_Ofinite(X2454)
| c_Finite__Set_Ofinite(X2454,X2453) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_1049,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])]) ).
fof(i_0_1050,plain,
! [X2763] : hAPP(c_Nat_OSuc,X2763) != X2763,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1051,plain,
! [X2762] : X2762 != hAPP(c_Nat_OSuc,X2762),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1052,plain,
! [X3182,X3183] : hAPP(c_COMBI(X3183),X3182) = X3182,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1053,plain,
! [X2603] :
( ~ class_Rings_Ozero__neq__one(X2603)
| c_Groups_Oone__class_Oone(X2603) != c_Groups_Ozero__class_Ozero(X2603) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_1054,plain,
! [X2602] :
( ~ class_Rings_Ozero__neq__one(X2602)
| c_Groups_Ozero__class_Ozero(X2602) != c_Groups_Oone__class_Oone(X2602) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_1055,plain,
! [X3179] :
( ~ class_Finite__Set_Ofinite(X3179)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X3179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_1056,plain,
! [X2827] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X2827) = X2827,
inference(variable_rename,[status(thm)],[fact_nat__size]) ).
fof(i_0_1057,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
cnf(i_0_1058,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_e____)),hAPP(v_F,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))))) ),
inference(split_conjunct,[status(thm)],[i_0_581]),
[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_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_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,c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_582]),
[final] ).
cnf(i_0_1062,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_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_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_1064,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk10_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_583]),
[final] ).
cnf(i_0_1065,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_584]),
[final] ).
cnf(i_0_1066,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[fact_n_I3_J]),
[final] ).
cnf(i_0_1067,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_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_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),esk10_0)) ),
inference(split_conjunct,[status(thm)],[i_0_583]),
[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_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1))),v_Lab____)),v_Lba____))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk7_0)) ),
inference(split_conjunct,[status(thm)],[i_0_584]),
[final] ).
cnf(i_0_1070,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_586]),
[final] ).
cnf(i_0_1071,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_587]),
[final] ).
cnf(i_0_1072,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_587]),
[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),X4),X5)),hAPP(v_F,X6)))
| X5 = X1
| X4 = X2
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1074,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
| X2 = X4
| X1 = X5
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1075,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(v_F,X4)))
| X2 = X6
| X1 = X5
| X6 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk5_6(X4,X3,X5,X6,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(X4,esk5_6(X4,X3,X5,X6,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_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)))
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk3_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk3_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_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)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk3_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk3_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[final] ).
cnf(i_0_1078,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_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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X3,X6,X2,X1,X5,X4))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X3,X6,X2,X1,X5,X4))))
| X5 = X1
| X4 = X2
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1080,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk6_6(X6,X3,X5,X4,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk6_6(X6,X3,X5,X4,X2,X1))))
| X2 = X4
| X1 = X5
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1081,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk5_6(X4,X3,X5,X6,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(X4,esk5_6(X4,X3,X5,X6,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(v_F,X4)))
| X2 = X6
| X1 = X5
| X6 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[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,esk3_6(X3,X6,X2,X1,X5,X4))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk3_6(X3,X6,X2,X1,X5,X4))))
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_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,esk3_6(X6,X3,X5,X4,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk3_6(X6,X3,X5,X4,X2,X1))))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[final] ).
cnf(i_0_1084,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X1),tc_HOL_Obool),c_FuncSet_OPi(X5,X1,X4,X2)),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(X2,esk28_5(X3,X2,X1,X4,X5))),hAPP(X3,esk28_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1085,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk29_5(X3,X2,X1,X4,X5))),hAPP(X3,esk29_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[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),X1),X2)),hAPP(X3,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk19_5(X3,X4,X5,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk19_5(X3,X4,X5,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1087,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk19_5(X3,X5,X4,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk19_5(X3,X5,X4,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1088,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),hAPP(v_F,X5)))
| X1 = X4
| X2 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk4_5(X5,X3,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),hAPP(X5,esk4_5(X5,X3,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_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),X4),X1)),hAPP(v_F,X5)))
| X4 = X2
| X1 = X2
| X4 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),hAPP(X5,esk4_5(X3,X5,X2,X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk4_5(X3,X5,X2,X1,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[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(X4,esk19_5(X3,X4,X5,X1,X2))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk19_5(X3,X4,X5,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[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),X1),X2)),hAPP(X3,X5)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X5,esk19_5(X3,X5,X4,X1,X2))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk19_5(X3,X5,X4,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X3) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[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),X2),X4)),hAPP(v_F,X5)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk4_5(X5,X3,X4,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),hAPP(X5,esk4_5(X5,X3,X4,X2,X1))))
| X1 = X4
| X2 = X4
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[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),X4),X1)),hAPP(v_F,X5)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X1)),hAPP(X5,esk4_5(X3,X5,X2,X1,X4))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk4_5(X3,X5,X2,X1,X4))))
| X4 = X2
| X1 = X2
| X4 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X5),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[final] ).
cnf(i_0_1094,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),esk14_2(X1,X2)),esk15_2(X1,X2))),hAPP(X2,esk13_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_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),esk14_2(X1,X2)),esk15_2(X1,X2))),hAPP(esk13_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_596]),
[final] ).
cnf(i_0_1096,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))),esk13_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_596]),
[final] ).
cnf(i_0_1097,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk14_2(X1,X2) != esk15_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_596]),
[final] ).
cnf(i_0_1098,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_597]),
[final] ).
cnf(i_0_1099,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(X4,esk2_4(X3,X4,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk2_4(X3,X4,X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1100,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk2_4(X4,X3,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(X4,esk2_4(X4,X3,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1101,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_599]),
[final] ).
cnf(i_0_1102,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_597]),
[final] ).
cnf(i_0_1103,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk28_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X5,X3)),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1104,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(X4,esk2_4(X3,X4,X1,X2))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk2_4(X3,X4,X1,X2))))
| X2 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1105,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk2_4(X4,X3,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(X4,esk2_4(X4,X3,X2,X1))))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1106,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk38_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_600]),
[final] ).
cnf(i_0_1107,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk29_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1108,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_601]),
[final] ).
cnf(i_0_1109,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_1110,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_597]),
[final] ).
cnf(i_0_1111,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_597]),
[final] ).
cnf(i_0_1112,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,esk16_4(X3,X2,X4,X1))),hAPP(X3,esk16_4(X3,X2,X4,X1))))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1113,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_603]),
[final] ).
cnf(i_0_1114,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_604]),
[final] ).
cnf(i_0_1115,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_605]),
[final] ).
cnf(i_0_1116,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_606]),
[final] ).
cnf(i_0_1117,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_607]),
[final] ).
cnf(i_0_1118,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_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1119,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_608]),
[final] ).
cnf(i_0_1120,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1121,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(X1,X2)))
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(X2,esk24_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1122,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_610]),
[final] ).
cnf(i_0_1123,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[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_610]),
[final] ).
cnf(i_0_1125,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_611]),
[final] ).
cnf(i_0_1126,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_612]),
[final] ).
cnf(i_0_1127,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_613]),
[final] ).
cnf(i_0_1128,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1129,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_614]),
[final] ).
cnf(i_0_1130,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_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____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[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,esk40_4(X3,X1,X4,X2),X4)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2,X4)),c_Finite__Set_Ocard(X1,X3)))
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[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_616]),
[final] ).
cnf(i_0_1133,negated_conjecture,
( hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1134,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_617]),
[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_618]),
[final] ).
cnf(i_0_1136,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_619]),
[final] ).
cnf(i_0_1137,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_610]),
[final] ).
cnf(i_0_1138,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_620]),
[final] ).
cnf(i_0_1139,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[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_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_610]),
[final] ).
cnf(i_0_1141,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[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____))
| 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_610]),
[final] ).
cnf(i_0_1143,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____))) ),
inference(cn,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1144,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_1145,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_622]),
[final] ).
cnf(i_0_1146,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_610]),
[final] ).
cnf(i_0_1147,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_623]),
[final] ).
cnf(i_0_1148,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_613]),
[final] ).
cnf(i_0_1149,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_624]),
[final] ).
cnf(i_0_1150,negated_conjecture,
( hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1151,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1152,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_613]),
[final] ).
cnf(i_0_1153,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1154,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_610]),
[final] ).
cnf(i_0_1155,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_623]),
[final] ).
cnf(i_0_1156,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_625]),
[final] ).
cnf(i_0_1157,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_616]),
[final] ).
cnf(i_0_1158,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_616]),
[final] ).
cnf(i_0_1159,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_616]),
[final] ).
cnf(i_0_1160,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_616]),
[final] ).
cnf(i_0_1161,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_610]),
[final] ).
cnf(i_0_1162,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_617]),
[final] ).
cnf(i_0_1163,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_617]),
[final] ).
cnf(i_0_1164,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_617]),
[final] ).
cnf(i_0_1165,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_617]),
[final] ).
cnf(i_0_1166,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_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1167,negated_conjecture,
( hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(split_conjunct,[status(thm)],[i_0_526]),
[final] ).
cnf(i_0_1168,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_612]),
[final] ).
cnf(i_0_1169,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_613]),
[final] ).
cnf(i_0_1170,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk38_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_600]),
[final] ).
cnf(i_0_1171,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_610]),
[final] ).
cnf(i_0_1172,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_626]),
[final] ).
cnf(i_0_1173,plain,
( X1 = hAPP(X2,esk35_5(X1,X2,X3,X4,X5))
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| X1 != hAPP(X2,X5)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1174,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_628]),
[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_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_610]),
[final] ).
cnf(i_0_1176,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_629]),
[final] ).
cnf(i_0_1177,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_610]),
[final] ).
cnf(i_0_1178,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_610]),
[final] ).
cnf(i_0_1179,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_615]),
[final] ).
cnf(i_0_1180,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_630]),
[final] ).
cnf(i_0_1181,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_631]),
[final] ).
cnf(i_0_1182,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hAPP(v_h____,esk45_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____))) ),
inference(cn,[status(thm)],[i_0_632]),
[final] ).
cnf(i_0_1183,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_622]),
[final] ).
cnf(i_0_1184,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_610]),
[final] ).
cnf(i_0_1185,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk37_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_633]),
[final] ).
cnf(i_0_1186,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_616]),
[final] ).
cnf(i_0_1187,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_616]),
[final] ).
cnf(i_0_1188,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_616]),
[final] ).
cnf(i_0_1189,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_634]),
[final] ).
cnf(i_0_1190,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_635]),
[final] ).
cnf(i_0_1191,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_636]),
[final] ).
cnf(i_0_1192,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_623]),
[final] ).
cnf(i_0_1193,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| esk35_5(X1,X2,X3,X4,X5) != X5
| X1 != hAPP(X2,X5)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1194,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_610]),
[final] ).
cnf(i_0_1195,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_637]),
[final] ).
cnf(i_0_1196,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_616]),
[final] ).
cnf(i_0_1197,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_616]),
[final] ).
cnf(i_0_1198,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_616]),
[final] ).
cnf(i_0_1199,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_616]),
[final] ).
cnf(i_0_1200,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_616]),
[final] ).
cnf(i_0_1201,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_617]),
[final] ).
cnf(i_0_1202,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_638]),
[final] ).
cnf(i_0_1203,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),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_617]),
[final] ).
cnf(i_0_1204,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_617]),
[final] ).
cnf(i_0_1205,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____))
| ~ 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_610]),
[final] ).
cnf(i_0_1206,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_613]),
[final] ).
cnf(i_0_1207,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_639]),
[final] ).
cnf(i_0_1208,plain,
( c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(X1,esk20_1(X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(X1,esk21_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1209,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_640]),
[final] ).
cnf(i_0_1210,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_610]),
[final] ).
cnf(i_0_1211,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_617]),
[final] ).
cnf(i_0_1212,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_617]),
[final] ).
cnf(i_0_1213,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_617]),
[final] ).
cnf(i_0_1214,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_617]),
[final] ).
cnf(i_0_1215,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_617]),
[final] ).
cnf(i_0_1216,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__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_610]),
[final] ).
cnf(i_0_1217,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(cn,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1218,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_642]),
[final] ).
cnf(i_0_1219,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(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_610]),
[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____))
| ~ 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_610]),
[final] ).
cnf(i_0_1221,negated_conjecture,
( hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____))) ),
inference(cn,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1222,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_610]),
[final] ).
cnf(i_0_1223,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_610]),
[final] ).
cnf(i_0_1224,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_1225,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_610]),
[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(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_613]),
[final] ).
cnf(i_0_1227,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_610]),
[final] ).
cnf(i_0_1228,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_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_613]),
[final] ).
cnf(i_0_1229,plain,
( X1 = hAPP(X2,esk34_4(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1230,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_613]),
[final] ).
cnf(i_0_1231,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_626]),
[final] ).
cnf(i_0_1232,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X3))
| ~ c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_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_616]),
[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_613]),
[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),esk22_1(X1)),esk23_1(X1))),hAPP(esk21_1(X1),X2)))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(esk20_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[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),esk22_1(X1)),esk23_1(X1))),hAPP(esk20_1(X1),X2)))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(esk21_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[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_645]),
[final] ).
cnf(i_0_1238,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_613]),
[final] ).
cnf(i_0_1239,plain,
( X3 = esk34_4(X1,X2,X4,X5)
| X1 != hAPP(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_627]),
[final] ).
cnf(i_0_1240,plain,
( hAPP(X4,hAPP(c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)) = X2
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_646]),
[final] ).
cnf(i_0_1241,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_634]),
[final] ).
cnf(i_0_1242,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_617]),
[final] ).
cnf(i_0_1243,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),esk36_3(X1,X3,X2))) != esk36_3(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1244,plain,
( c_Fun_Oinj__on(X1,X3,c_Hilbert__Choice_Oinv__into(X3,X1,X5,X4),X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1245,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____)))
| hAPP(v_h____,esk45_0) != v_n____ ),
inference(cn,[status(thm)],[i_0_649]),
[final] ).
cnf(i_0_1246,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_650]),
[final] ).
cnf(i_0_1247,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_651]),
[final] ).
cnf(i_0_1248,plain,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1249,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_653]),
[final] ).
cnf(i_0_1250,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_654]),
[final] ).
cnf(i_0_1251,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_655]),
[final] ).
cnf(i_0_1252,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_656]),
[final] ).
cnf(i_0_1253,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_651]),
[final] ).
cnf(i_0_1254,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_650]),
[final] ).
cnf(i_0_1255,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_650]),
[final] ).
cnf(i_0_1256,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_651]),
[final] ).
cnf(i_0_1257,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_657]),
[final] ).
cnf(i_0_1258,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk12_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[final] ).
cnf(i_0_1259,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk11_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[final] ).
cnf(i_0_1260,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_b____),v_a____)),v_Lab____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)) ),
inference(cn,[status(thm)],[i_0_659]),
[final] ).
cnf(i_0_1261,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(X1,esk20_1(X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk22_1(X1)),esk23_1(X1))),hAPP(X1,esk21_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1262,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_660]),
[final] ).
cnf(i_0_1263,plain,
( X1 = hAPP(X2,esk37_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_633]),
[final] ).
cnf(i_0_1264,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_616]),
[final] ).
cnf(i_0_1265,negated_conjecture,
( hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____,esk45_0)),v_e____))) ),
inference(cn,[status(thm)],[i_0_661]),
[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_662]),
[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_663]),
[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_664]),
[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_617]),
[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_665]),
[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_666]),
[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_667]),
[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_668]),
[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_669]),
[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_670]),
[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_671]),
[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_672]),
[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_673]),
[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_655]),
[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_600]),
[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_674]),
[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_675]),
[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),esk26_1(X1)),esk27_1(X1))),hAPP(X1,esk25_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[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_647]),
[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_676]),
[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_677]),
[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_650]),
[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_651]),
[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_651]),
[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_650]),
[final] ).
cnf(i_0_1291,plain,
( X1 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Finite__Set_Ocard(tc_Nat_Onat,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X1),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Finite__Set_Ocard(tc_Nat_Onat,X1))))) ),
inference(split_conjunct,[status(thm)],[i_0_678]),
[final] ).
cnf(i_0_1292,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_669]),
[final] ).
cnf(i_0_1293,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_679]),
[final] ).
cnf(i_0_1294,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk17_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1295,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_680]),
[final] ).
cnf(i_0_1296,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_681]),
[final] ).
cnf(i_0_1297,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_682]),
[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_683]),
[final] ).
cnf(i_0_1299,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_684]),
[final] ).
cnf(i_0_1300,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_685]),
[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))),esk21_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[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))),esk20_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1303,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk25_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1304,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_686]),
[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_633]),
[final] ).
cnf(i_0_1306,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_687]),
[final] ).
cnf(i_0_1307,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_1308,plain,
( hAPP(X1,esk11_4(X2,X1,X3,X4)) = hAPP(X1,esk12_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[final] ).
cnf(i_0_1309,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_688]),
[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_689]),
[final] ).
cnf(i_0_1311,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_690]),
[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_691]),
[final] ).
cnf(i_0_1313,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_692]),
[final] ).
cnf(i_0_1314,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_693]),
[final] ).
cnf(i_0_1315,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_694]),
[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_695]),
[final] ).
cnf(i_0_1317,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_696]),
[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_697]),
[final] ).
cnf(i_0_1319,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_698]),
[final] ).
cnf(i_0_1320,plain,
( c_Fun_Oinj__on(X1,X2,esk40_4(X3,X2,X4,X1),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X3)))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1321,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X1)),esk27_1(X1))),hAPP(esk25_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1322,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_699]),
[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),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_700]),
[final] ).
cnf(i_0_1324,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_701]),
[final] ).
cnf(i_0_1325,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_702]),
[final] ).
cnf(i_0_1326,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_703]),
[final] ).
cnf(i_0_1327,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_704]),
[final] ).
cnf(i_0_1328,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_705]),
[final] ).
cnf(i_0_1329,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_706]),
[final] ).
cnf(i_0_1330,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_707]),
[final] ).
cnf(i_0_1331,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_708]),
[final] ).
cnf(i_0_1332,plain,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_709]),
[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_710]),
[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_711]),
[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_699]),
[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_650]),
[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_651]),
[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_712]),
[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_699]),
[final] ).
cnf(i_0_1340,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk11_4(X1,X2,X3,X4) != esk12_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_658]),
[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_713]),
[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_714]),
[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_715]),
[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_716]),
[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_717]),
[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_718]),
[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_719]),
[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_720]),
[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_721]),
[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_722]),
[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_707]),
[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_723]),
[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_724]),
[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_725]),
[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_726]),
[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_727]),
[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_728]),
[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_729]),
[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_730]),
[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_689]),
[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_731]),
[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_691]),
[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_732]),
[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_733]),
[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_734]),
[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_735]),
[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_736]),
[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_737]),
[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_b____),v_a____)),esk9_0)),
inference(split_conjunct,[status(thm)],[i_0_738]),
[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_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_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_a____),v_b____)),esk8_0)),
inference(split_conjunct,[status(thm)],[i_0_739]),
[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_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_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_740]),
[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_740]),
[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_741]),
[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_742]),
[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_743]),
[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_696]),
[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_744]),
[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_698]),
[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_745]),
[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_746]),
[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_717]),
[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_747]),
[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_747]),
[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_748]),
[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_749]),
[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_750]),
[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_703]),
[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_751]),
[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_752]),
[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_753]),
[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_658]),
[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_734]),
[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_754]),
[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_754]),
[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_755]),
[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_756]),
[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_757]),
[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_758]),
[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_712]),
[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_759]),
[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_760]),
[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_761]),
[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_762]),
[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_721]),
[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_722]),
[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_763]),
[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_764]),
[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_765]),
[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_766]),
[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_767]),
[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_768]),
[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_769]),
[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_770]),
[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_747]),
[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_771]),
[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_772]),
[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_773]),
[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_774]),
[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_775]),
[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_776]),
[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_733]),
[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_777]),
[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_778]),
[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_779]),
[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_780]),
[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_781]),
[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_782]),
[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_783]),
[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_784]),
[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_785]),
[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_786]),
[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)),esk9_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_738]),
[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)),esk8_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_739]),
[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_787]),
[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_788]),
[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_789]),
[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_740]),
[final] ).
cnf(i_0_1443,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1444,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_781]),
[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_790]),
[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_768]),
[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_768]),
[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_773]),
[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_791]),
[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_792]),
[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_793]),
[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_794]),
[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_795]),
[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_796]),
[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_797]),
[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_798]),
[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_602]),
[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_799]),
[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_800]),
[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_801]),
[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_802]),
[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_803]),
[final] ).
cnf(i_0_1463,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) != c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X4))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1464,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) != c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X4),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1465,plain,
( X2 = X4
| ~ class_Orderings_Olinorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_805]),
[final] ).
cnf(i_0_1466,plain,
( X3 = X5
| ~ class_Orderings_Olinorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_806]),
[final] ).
cnf(i_0_1467,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk33_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_807]),
[final] ).
cnf(i_0_1468,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_808]),
[final] ).
cnf(i_0_1469,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_809]),
[final] ).
cnf(i_0_1470,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_783]),
[final] ).
cnf(i_0_1471,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_1472,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_811]),
[final] ).
cnf(i_0_1473,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_785]),
[final] ).
cnf(i_0_1474,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_812]),
[final] ).
cnf(i_0_1475,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_813]),
[final] ).
cnf(i_0_1476,plain,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk39_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1477,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_1478,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3,tc_HOL_Obool)),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1479,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_1480,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_816]),
[final] ).
cnf(i_0_1481,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_817]),
[final] ).
cnf(i_0_1482,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_774]),
[final] ).
cnf(i_0_1483,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_774]),
[final] ).
cnf(i_0_1484,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_818]),
[final] ).
cnf(i_0_1485,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_819]),
[final] ).
cnf(i_0_1486,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_820]),
[final] ).
cnf(i_0_1487,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_821]),
[final] ).
cnf(i_0_1488,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_821]),
[final] ).
cnf(i_0_1489,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_822]),
[final] ).
cnf(i_0_1490,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_1491,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_824]),
[final] ).
cnf(i_0_1492,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_1493,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_826]),
[final] ).
cnf(i_0_1494,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk31_2(X1,X2)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_827]),
[final] ).
cnf(i_0_1495,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_828]),
[final] ).
cnf(i_0_1496,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_829]),
[final] ).
cnf(i_0_1497,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_830]),
[final] ).
cnf(i_0_1498,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1499,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_821]),
[final] ).
cnf(i_0_1500,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_832]),
[final] ).
cnf(i_0_1501,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_833]),
[final] ).
cnf(i_0_1502,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_834]),
[final] ).
cnf(i_0_1503,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_835]),
[final] ).
cnf(i_0_1504,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_836]),
[final] ).
cnf(i_0_1505,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_837]),
[final] ).
cnf(i_0_1506,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_838]),
[final] ).
cnf(i_0_1507,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_839]),
[final] ).
cnf(i_0_1508,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_840]),
[final] ).
cnf(i_0_1509,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_841]),
[final] ).
cnf(i_0_1510,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_842]),
[final] ).
cnf(i_0_1511,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_843]),
[final] ).
cnf(i_0_1512,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_844]),
[final] ).
cnf(i_0_1513,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_815]),
[final] ).
cnf(i_0_1514,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_845]),
[final] ).
cnf(i_0_1515,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_1516,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_847]),
[final] ).
cnf(i_0_1517,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_1518,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_849]),
[final] ).
cnf(i_0_1519,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_838]),
[final] ).
cnf(i_0_1520,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_838]),
[final] ).
cnf(i_0_1521,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_850]),
[final] ).
cnf(i_0_1522,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_851]),
[final] ).
cnf(i_0_1523,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_852]),
[final] ).
cnf(i_0_1524,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_1525,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_1526,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_855]),
[final] ).
cnf(i_0_1527,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_856]),
[final] ).
cnf(i_0_1528,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_857]),
[final] ).
cnf(i_0_1529,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_858]),
[final] ).
cnf(i_0_1530,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_859]),
[final] ).
cnf(i_0_1531,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_860]),
[final] ).
cnf(i_0_1532,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_861]),
[final] ).
cnf(i_0_1533,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_862]),
[final] ).
cnf(i_0_1534,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_1535,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_1536,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_1537,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_866]),
[final] ).
cnf(i_0_1538,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_867]),
[final] ).
cnf(i_0_1539,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_868]),
[final] ).
cnf(i_0_1540,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_869]),
[final] ).
cnf(i_0_1541,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk33_2(X2,X3)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_807]),
[final] ).
cnf(i_0_1542,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_833]),
[final] ).
cnf(i_0_1543,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_870]),
[final] ).
cnf(i_0_1544,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_871]),
[final] ).
cnf(i_0_1545,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_872]),
[final] ).
cnf(i_0_1546,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk42_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1547,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_783]),
[final] ).
cnf(i_0_1548,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1549,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_874]),
[final] ).
cnf(i_0_1550,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1551,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_876]),
[final] ).
cnf(i_0_1552,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_877]),
[final] ).
cnf(i_0_1553,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_878]),
[final] ).
cnf(i_0_1554,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_879]),
[final] ).
cnf(i_0_1555,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk10_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_583]),
[final] ).
cnf(i_0_1556,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk7_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_584]),
[final] ).
cnf(i_0_1557,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_1558,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_1559,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_854]),
[final] ).
cnf(i_0_1560,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_880]),
[final] ).
cnf(i_0_1561,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_881]),
[final] ).
cnf(i_0_1562,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_882]),
[final] ).
cnf(i_0_1563,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_827]),
[final] ).
cnf(i_0_1564,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_883]),
[final] ).
cnf(i_0_1565,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_884]),
[final] ).
cnf(i_0_1566,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_885]),
[final] ).
cnf(i_0_1567,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_886]),
[final] ).
cnf(i_0_1568,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_1569,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_888]),
[final] ).
cnf(i_0_1570,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_871]),
[final] ).
cnf(i_0_1571,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk32_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1572,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_890]),
[final] ).
cnf(i_0_1573,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk44_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1574,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1575,plain,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk39_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1576,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_1577,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_872]),
[final] ).
cnf(i_0_1578,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_892]),
[final] ).
cnf(i_0_1579,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_876]),
[final] ).
cnf(i_0_1580,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_893]),
[final] ).
cnf(i_0_1581,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_894]),
[final] ).
cnf(i_0_1582,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_895]),
[final] ).
cnf(i_0_1583,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_2(X1,X2)),X1))
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_807]),
[final] ).
cnf(i_0_1584,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_1585,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_897]),
[final] ).
cnf(i_0_1586,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_898]),
[final] ).
cnf(i_0_1587,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk41_1(X1)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1588,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_899]),
[final] ).
cnf(i_0_1589,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_900]),
[final] ).
cnf(i_0_1590,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_1591,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_902]),
[final] ).
cnf(i_0_1592,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_903]),
[final] ).
cnf(i_0_1593,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_904]),
[final] ).
cnf(i_0_1594,plain,
( X1 = hAPP(c_Nat_OSuc,esk31_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_827]),
[final] ).
cnf(i_0_1595,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_868]),
[final] ).
cnf(i_0_1596,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_905]),
[final] ).
cnf(i_0_1597,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_906]),
[final] ).
cnf(i_0_1598,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_890]),
[final] ).
cnf(i_0_1599,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_907]),
[final] ).
cnf(i_0_1600,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_894]),
[final] ).
cnf(i_0_1601,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_908]),
[final] ).
cnf(i_0_1602,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_889]),
[final] ).
cnf(i_0_1603,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk43_1(X1)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1604,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_909]),
[final] ).
cnf(i_0_1605,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_910]),
[final] ).
cnf(i_0_1606,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_911]),
[final] ).
cnf(i_0_1607,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_871]),
[final] ).
cnf(i_0_1608,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_912]),
[final] ).
cnf(i_0_1609,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_913]),
[final] ).
cnf(i_0_1610,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1611,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1612,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_916]),
[final] ).
cnf(i_0_1613,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_831]),
[final] ).
cnf(i_0_1614,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_917]),
[final] ).
cnf(i_0_1615,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_918]),
[final] ).
cnf(i_0_1616,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_919]),
[final] ).
cnf(i_0_1617,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_920]),
[final] ).
cnf(i_0_1618,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_909]),
[final] ).
cnf(i_0_1619,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_910]),
[final] ).
cnf(i_0_1620,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_885]),
[final] ).
cnf(i_0_1621,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_921]),
[final] ).
cnf(i_0_1622,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_922]),
[final] ).
cnf(i_0_1623,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_844]),
[final] ).
cnf(i_0_1624,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_923]),
[final] ).
cnf(i_0_1625,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_924]),
[final] ).
cnf(i_0_1626,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_925]),
[final] ).
cnf(i_0_1627,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1628,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_927]),
[final] ).
cnf(i_0_1629,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_897]),
[final] ).
cnf(i_0_1630,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_877]),
[final] ).
cnf(i_0_1631,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_851]),
[final] ).
cnf(i_0_1632,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_928]),
[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_929]),
[final] ).
cnf(i_0_1634,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_1635,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_1636,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_1637,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_933]),
[final] ).
cnf(i_0_1638,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_934]),
[final] ).
cnf(i_0_1639,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_935]),
[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_936]),
[final] ).
cnf(i_0_1641,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_1642,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_1643,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_1644,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_862]),
[final] ).
cnf(i_0_1645,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_940]),
[final] ).
cnf(i_0_1646,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_941]),
[final] ).
cnf(i_0_1647,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_929]),
[final] ).
cnf(i_0_1648,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_930]),
[final] ).
cnf(i_0_1649,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_942]),
[final] ).
cnf(i_0_1650,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_943]),
[final] ).
cnf(i_0_1651,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk44_2(X1,X2)),X1))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1652,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_2(X1,X2)),X1))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1653,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_1654,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_945]),
[final] ).
cnf(i_0_1655,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_946]),
[final] ).
cnf(i_0_1656,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_941]),
[final] ).
cnf(i_0_1657,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_921]),
[final] ).
cnf(i_0_1658,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1659,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_1660,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_949]),
[final] ).
cnf(i_0_1661,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_888]),
[final] ).
cnf(i_0_1662,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_950]),
[final] ).
cnf(i_0_1663,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_1664,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_951]),
[final] ).
cnf(i_0_1665,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_952]),
[final] ).
cnf(i_0_1666,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X2,X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_953]),
[final] ).
cnf(i_0_1667,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_1668,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_955]),
[final] ).
cnf(i_0_1669,plain,
( X1 = hAPP(c_Nat_OSuc,esk30_1(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1670,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_910]),
[final] ).
cnf(i_0_1671,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_862]),
[final] ).
cnf(i_0_1672,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_957]),
[final] ).
cnf(i_0_1673,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_1674,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_959]),
[final] ).
cnf(i_0_1675,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_935]),
[final] ).
cnf(i_0_1676,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_935]),
[final] ).
cnf(i_0_1677,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_791]),
[final] ).
cnf(i_0_1678,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_791]),
[final] ).
cnf(i_0_1679,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_960]),
[final] ).
cnf(i_0_1680,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_960]),
[final] ).
cnf(i_0_1681,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_781]),
[final] ).
cnf(i_0_1682,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_961]),
[final] ).
cnf(i_0_1683,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_962]),
[final] ).
cnf(i_0_1684,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1685,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_964]),
[final] ).
cnf(i_0_1686,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_965]),
[final] ).
cnf(i_0_1687,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_1688,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_967]),
[final] ).
cnf(i_0_1689,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_968]),
[final] ).
cnf(i_0_1690,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_1691,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_970]),
[final] ).
cnf(i_0_1692,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_1693,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_972]),
[final] ).
cnf(i_0_1694,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_973]),
[final] ).
cnf(i_0_1695,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_974]),
[final] ).
cnf(i_0_1696,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_923]),
[final] ).
cnf(i_0_1697,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_1698,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_1699,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_977]),
[final] ).
cnf(i_0_1700,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_978]),
[final] ).
cnf(i_0_1701,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1702,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1703,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_979]),
[final] ).
cnf(i_0_1704,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_980]),
[final] ).
cnf(i_0_1705,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_981]),
[final] ).
cnf(i_0_1706,plain,
( 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_1707,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1708,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1709,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1710,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1711,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_953]),
[final] ).
cnf(i_0_1712,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_984]),
[final] ).
cnf(i_0_1713,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_985]),
[final] ).
cnf(i_0_1714,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_986]),
[final] ).
cnf(i_0_1715,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_1716,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1717,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_989]),
[final] ).
cnf(i_0_1718,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_990]),
[final] ).
cnf(i_0_1719,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_827]),
[final] ).
cnf(i_0_1720,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_946]),
[final] ).
cnf(i_0_1721,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_991]),
[final] ).
cnf(i_0_1722,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_876]),
[final] ).
cnf(i_0_1723,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_897]),
[final] ).
cnf(i_0_1724,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk17_2(X2,X1)) != hAPP(esk17_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1725,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_992]),
[final] ).
cnf(i_0_1726,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1727,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_994]),
[final] ).
cnf(i_0_1728,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_995]),
[final] ).
cnf(i_0_1729,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_996]),
[final] ).
cnf(i_0_1730,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_956]),
[final] ).
cnf(i_0_1731,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_997]),
[final] ).
cnf(i_0_1732,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_998]),
[final] ).
cnf(i_0_1733,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1734,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_995]),
[final] ).
cnf(i_0_1735,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_995]),
[final] ).
cnf(i_0_1736,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_996]),
[final] ).
cnf(i_0_1737,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_996]),
[final] ).
cnf(i_0_1738,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_1000]),
[final] ).
cnf(i_0_1739,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_1001]),
[final] ).
cnf(i_0_1740,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_1002]),
[final] ).
cnf(i_0_1741,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_965]),
[final] ).
cnf(i_0_1742,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_1003]),
[final] ).
cnf(i_0_1743,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_995]),
[final] ).
cnf(i_0_1744,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_996]),
[final] ).
cnf(i_0_1745,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_1004]),
[final] ).
cnf(i_0_1746,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_1005]),
[final] ).
cnf(i_0_1747,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_1006]),
[final] ).
cnf(i_0_1748,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_1007]),
[final] ).
cnf(i_0_1749,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_995]),
[final] ).
cnf(i_0_1750,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_995]),
[final] ).
cnf(i_0_1751,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_996]),
[final] ).
cnf(i_0_1752,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_996]),
[final] ).
cnf(i_0_1753,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_901]),
[final] ).
cnf(i_0_1754,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_901]),
[final] ).
cnf(i_0_1755,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_1008]),
[final] ).
cnf(i_0_1756,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_909]),
[final] ).
cnf(i_0_1757,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_1009]),
[final] ).
cnf(i_0_1758,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_1010]),
[final] ).
cnf(i_0_1759,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1011]),
[final] ).
cnf(i_0_1760,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_1761,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_1013]),
[final] ).
cnf(i_0_1762,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_994]),
[final] ).
cnf(i_0_1763,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_1014]),
[final] ).
cnf(i_0_1764,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_1015]),
[final] ).
cnf(i_0_1765,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_1015]),
[final] ).
cnf(i_0_1766,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1767,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1768,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1769,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1770,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_1018]),
[final] ).
cnf(i_0_1771,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1019]),
[final] ).
cnf(i_0_1772,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_1020]),
[final] ).
cnf(i_0_1773,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_1021]),
[final] ).
cnf(i_0_1774,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_1775,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_1023]),
[final] ).
cnf(i_0_1776,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_1005]),
[final] ).
cnf(i_0_1777,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_1006]),
[final] ).
cnf(i_0_1778,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_1007]),
[final] ).
cnf(i_0_1779,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_1024]),
[final] ).
cnf(i_0_1780,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_1781,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_1026]),
[final] ).
cnf(i_0_1782,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_1027]),
[final] ).
cnf(i_0_1783,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_1028]),
[final] ).
cnf(i_0_1784,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_1785,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_1015]),
[final] ).
cnf(i_0_1786,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_1787,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_1029]),
[final] ).
cnf(i_0_1788,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_1030]),
[final] ).
cnf(i_0_1789,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_1031]),
[final] ).
cnf(i_0_1790,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_1032]),
[final] ).
cnf(i_0_1791,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_1033]),
[final] ).
cnf(i_0_1792,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_1034]),
[final] ).
cnf(i_0_1793,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_1794,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1795,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1796,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1797,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1798,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1799,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_619]),
[final] ).
cnf(i_0_1800,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_1041]),
[final] ).
cnf(i_0_1801,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_1802,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_1803,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1044]),
[final] ).
cnf(i_0_1804,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_1805,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_1806,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1807,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1808,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1809,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1810,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1811,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1052]),
[final] ).
cnf(i_0_1812,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_1813,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_1054]),
[final] ).
cnf(i_0_1814,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_1815,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_1816,plain,
( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1055]),
[final] ).
cnf(i_0_1817,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1818,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_1819,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_1057]),
[final] ).
cnf(i_0_1820,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_1821,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_1822,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_1823,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_1824,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_1825,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_1826,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_1827,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_1828,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_1829,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_1830,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1831,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1832,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1833,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1834,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1835,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1836,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1837,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_1838,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_1839,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_1840,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_1841,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_1842,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_1843,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_1844,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_1845,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1846,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1847,plain,
v_c____ != v_d____,
inference(split_conjunct,[status(thm)],[fact__096c_A_126_061_Ad_096]),
[final] ).
cnf(i_0_1848,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1849,axiom,
X1 = X1 ).
cnf(i_0_1850,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1851,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1852,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1853,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1854,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1855,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1856,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1857,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1858,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1859,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1860,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1861,axiom,
( X1 != X2
| esk14_2(X1,X3) = esk14_2(X2,X3) ) ).
cnf(i_0_1862,axiom,
( X1 != X2
| esk14_2(X3,X1) = esk14_2(X3,X2) ) ).
cnf(i_0_1863,axiom,
( X1 != X2
| esk15_2(X1,X3) = esk15_2(X2,X3) ) ).
cnf(i_0_1864,axiom,
( X1 != X2
| esk15_2(X3,X1) = esk15_2(X3,X2) ) ).
cnf(i_0_1865,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_1866,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_1867,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_1868,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_1869,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_1870,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_1871,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| esk35_5(X1,X3,X4,X5,X6) = esk35_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| esk35_5(X3,X1,X4,X5,X6) = esk35_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| esk35_5(X3,X4,X1,X5,X6) = esk35_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| esk35_5(X3,X4,X5,X1,X6) = esk35_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| esk35_5(X3,X4,X5,X6,X1) = esk35_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| esk34_4(X1,X3,X4,X5) = esk34_4(X2,X3,X4,X5) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| esk34_4(X3,X1,X4,X5) = esk34_4(X3,X2,X4,X5) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| esk34_4(X3,X4,X1,X5) = esk34_4(X3,X4,X2,X5) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| esk34_4(X3,X4,X5,X1) = esk34_4(X3,X4,X5,X2) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| esk36_3(X1,X3,X4) = esk36_3(X2,X3,X4) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| esk36_3(X3,X1,X4) = esk36_3(X3,X2,X4) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| esk36_3(X3,X4,X1) = esk36_3(X3,X4,X2) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| esk12_4(X1,X3,X4,X5) = esk12_4(X2,X3,X4,X5) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| esk12_4(X3,X1,X4,X5) = esk12_4(X3,X2,X4,X5) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| esk12_4(X3,X4,X1,X5) = esk12_4(X3,X4,X2,X5) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| esk12_4(X3,X4,X5,X1) = esk12_4(X3,X4,X5,X2) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| esk11_4(X1,X3,X4,X5) = esk11_4(X2,X3,X4,X5) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| esk11_4(X3,X1,X4,X5) = esk11_4(X3,X2,X4,X5) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| esk11_4(X3,X4,X1,X5) = esk11_4(X3,X4,X2,X5) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| esk11_4(X3,X4,X5,X1) = esk11_4(X3,X4,X5,X2) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1925,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1926,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1938,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1939,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1940,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(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
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1943,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1944,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1945,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1946,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1947,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1948,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1949,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_1950,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_1951,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_1952,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_1953,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_1954,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_1955,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1956,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1957,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1958,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_1959,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_1960,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_1961,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_1962,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_1963,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_1964,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1965,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1966,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1967,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1968,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1849_001,axiom,
X1 = X1 ).
cnf(i_0_1850_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1851_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1852_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1853_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1854_006,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1855_007,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1856_008,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1857_009,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1858_010,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1859_011,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1860_012,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1861_013,axiom,
( X1 != X2
| esk14_2(X1,X3) = esk14_2(X2,X3) ) ).
cnf(i_0_1862_014,axiom,
( X1 != X2
| esk14_2(X3,X1) = esk14_2(X3,X2) ) ).
cnf(i_0_1863_015,axiom,
( X1 != X2
| esk15_2(X1,X3) = esk15_2(X2,X3) ) ).
cnf(i_0_1864_016,axiom,
( X1 != X2
| esk15_2(X3,X1) = esk15_2(X3,X2) ) ).
cnf(i_0_1865_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_1866_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_1867_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_1868_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_1869_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_1870_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_1871_023,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1872_024,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1873_025,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1874_026,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1875_027,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1876_028,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1877_029,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1878_030,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1879_031,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1880_032,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1881_033,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1882_034,axiom,
( X1 != X2
| esk35_5(X1,X3,X4,X5,X6) = esk35_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1883_035,axiom,
( X1 != X2
| esk35_5(X3,X1,X4,X5,X6) = esk35_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1884_036,axiom,
( X1 != X2
| esk35_5(X3,X4,X1,X5,X6) = esk35_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1885_037,axiom,
( X1 != X2
| esk35_5(X3,X4,X5,X1,X6) = esk35_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1886_038,axiom,
( X1 != X2
| esk35_5(X3,X4,X5,X6,X1) = esk35_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1887_039,axiom,
( X1 != X2
| esk34_4(X1,X3,X4,X5) = esk34_4(X2,X3,X4,X5) ) ).
cnf(i_0_1888_040,axiom,
( X1 != X2
| esk34_4(X3,X1,X4,X5) = esk34_4(X3,X2,X4,X5) ) ).
cnf(i_0_1889_041,axiom,
( X1 != X2
| esk34_4(X3,X4,X1,X5) = esk34_4(X3,X4,X2,X5) ) ).
cnf(i_0_1890_042,axiom,
( X1 != X2
| esk34_4(X3,X4,X5,X1) = esk34_4(X3,X4,X5,X2) ) ).
cnf(i_0_1891_043,axiom,
( X1 != X2
| esk36_3(X1,X3,X4) = esk36_3(X2,X3,X4) ) ).
cnf(i_0_1892_044,axiom,
( X1 != X2
| esk36_3(X3,X1,X4) = esk36_3(X3,X2,X4) ) ).
cnf(i_0_1893_045,axiom,
( X1 != X2
| esk36_3(X3,X4,X1) = esk36_3(X3,X4,X2) ) ).
cnf(i_0_1894_046,axiom,
( X1 != X2
| esk12_4(X1,X3,X4,X5) = esk12_4(X2,X3,X4,X5) ) ).
cnf(i_0_1895_047,axiom,
( X1 != X2
| esk12_4(X3,X1,X4,X5) = esk12_4(X3,X2,X4,X5) ) ).
cnf(i_0_1896_048,axiom,
( X1 != X2
| esk12_4(X3,X4,X1,X5) = esk12_4(X3,X4,X2,X5) ) ).
cnf(i_0_1897_049,axiom,
( X1 != X2
| esk12_4(X3,X4,X5,X1) = esk12_4(X3,X4,X5,X2) ) ).
cnf(i_0_1898_050,axiom,
( X1 != X2
| esk11_4(X1,X3,X4,X5) = esk11_4(X2,X3,X4,X5) ) ).
cnf(i_0_1899_051,axiom,
( X1 != X2
| esk11_4(X3,X1,X4,X5) = esk11_4(X3,X2,X4,X5) ) ).
cnf(i_0_1900_052,axiom,
( X1 != X2
| esk11_4(X3,X4,X1,X5) = esk11_4(X3,X4,X2,X5) ) ).
cnf(i_0_1901_053,axiom,
( X1 != X2
| esk11_4(X3,X4,X5,X1) = esk11_4(X3,X4,X5,X2) ) ).
cnf(i_0_1902_054,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1903_055,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1904_056,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1905_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_1906_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_1907_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_1908_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_1909_061,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1910_062,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1911_063,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1912_064,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1913_065,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1914_066,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1915_067,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1916_068,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1917_069,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1918_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_1919_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_1920_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_1921_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_1922_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_1923_075,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1924_076,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1925_077,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1926_078,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1927_079,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1928_080,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1929_081,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1930_082,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1931_083,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1932_084,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1933_085,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1934_086,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1935_087,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1936_088,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1937_089,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1938_090,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1939_091,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1940_092,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1941_093,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1942_094,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1943_095,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1944_096,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1945_097,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1946_098,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1947_099,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1948_100,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1949_101,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X1,X3,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_1950_102,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X1,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_1951_103,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X1,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_1952_104,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X1,X6,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_1953_105,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X1,X7)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_1954_106,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X1)
| c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_1955_107,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1956_108,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1957_109,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1958_110,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_1959_111,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_1960_112,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_1961_113,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_1962_114,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_1963_115,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_1964_116,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1965_117,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1966_118,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1967_119,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1968_120,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1969,plain,
X1 = X1,
inference(equality_inference,[],[1078]) ).
cnf(i_0_1970,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,[],[1110]) ).
cnf(i_0_1971,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,[],[1156]) ).
cnf(i_0_1972,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,[],[1157]) ).
cnf(i_0_1973,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,[],[1158]) ).
cnf(i_0_1974,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,[],[1162]) ).
cnf(i_0_1975,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,[],[1163]) ).
cnf(i_0_1976,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,[],[1186]) ).
cnf(i_0_1977,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,[],[1188]) ).
cnf(i_0_1978,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,[],[1197]) ).
cnf(i_0_1979,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,[],[1198]) ).
cnf(i_0_1980,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,[],[1200]) ).
cnf(i_0_1981,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,[],[1201]) ).
cnf(i_0_1982,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,[],[1204]) ).
cnf(i_0_1983,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,[],[1212]) ).
cnf(i_0_1984,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,[],[1213]) ).
cnf(i_0_1985,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,[],[1215]) ).
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)),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_1987,plain,
( X1 = esk34_4(hAPP(X2,X1),X2,X3,X4)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))) ),
inference(equality_inference,[],[1239]) ).
cnf(i_0_1988,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,[],[1242]) ).
cnf(i_0_1989,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,[],[1257]) ).
cnf(i_0_1990,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_1991,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1992,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1993,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,[],[1300]) ).
cnf(i_0_1994,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,[],[1306]) ).
cnf(i_0_1995,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1309]) ).
cnf(i_0_1996,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,[],[1324]) ).
cnf(i_0_1997,plain,
X1 = X1,
inference(equality_inference,[],[1325]) ).
cnf(i_0_1998,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,[],[1328]) ).
cnf(i_0_1999,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_2000,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_2001,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_2002,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_2003,plain,
( X1 = X1
| ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3)) ),
inference(equality_inference,[],[1465]) ).
cnf(i_0_2004,plain,
( X1 = X1
| ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1)) ),
inference(equality_inference,[],[1466]) ).
cnf(i_0_2005,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[1478]) ).
cnf(i_0_2006,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(equality_inference,[],[1510]) ).
cnf(i_0_2007,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(equality_inference,[],[1548]) ).
cnf(i_0_2008,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,[],[1563]) ).
cnf(i_0_2009,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,[],[1600]) ).
cnf(i_0_2010,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,[],[1601]) ).
cnf(i_0_2011,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,[],[1602]) ).
cnf(i_0_2012,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(equality_inference,[],[1613]) ).
cnf(i_0_2013,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,[],[1657]) ).
cnf(i_0_2014,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1672]) ).
cnf(i_0_2015,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1674]) ).
cnf(i_0_2016,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1675]) ).
cnf(i_0_2017,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1676]) ).
cnf(i_0_2018,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1682]) ).
cnf(i_0_2019,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1683]) ).
cnf(i_0_2020,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[1688]) ).
cnf(i_0_2021,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[1689]) ).
cnf(i_0_2022,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[1691]) ).
cnf(i_0_2023,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1701]) ).
cnf(i_0_2024,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[1703]) ).
cnf(i_0_2025,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1709]) ).
cnf(i_0_2026,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1710]) ).
cnf(i_0_2027,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,[],[1711]) ).
cnf(i_0_2028,plain,
X1 = X1,
inference(equality_inference,[],[1717]) ).
cnf(i_0_2029,plain,
X1 = X1,
inference(equality_inference,[],[1718]) ).
cnf(i_0_2030,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,[],[1719]) ).
cnf(i_0_2031,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[1722]) ).
cnf(i_0_2032,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,[],[1730]) ).
cnf(i_0_2033,plain,
X1 = X1,
inference(equality_inference,[],[1731]) ).
cnf(i_0_2034,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1754]) ).
cnf(i_0_2035,plain,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1755]) ).
cnf(i_0_2036,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1756]) ).
cnf(i_0_2037,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(equality_inference,[],[1768]) ).
cnf(i_0_2038,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1769]) ).
cnf(i_0_2039,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,[],[1776]) ).
cnf(i_0_2040,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,[],[1777]) ).
cnf(i_0_2041,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,[],[1778]) ).
cnf(i_0_2042,plain,
X1 = X1,
inference(equality_inference,[],[1794]) ).
cnf(i_0_2043,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____))) ),
inference(scs_inference,[],[i_0_1371,i_0_1143]) ).
cnf(i_0_2044,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_1299,i_0_1146]) ).
cnf(i_0_2045,plain,
( hAPP(v_h____,esk45_0) != v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk45_0)),v_c____),v_e____))) ),
inference(scs_inference,[],[i_0_1371,i_0_1182]) ).
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)),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_1299,i_0_1184]) ).
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)),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_1373,i_0_1194]) ).
cnf(i_0_2048,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_1373,i_0_1219]) ).
cnf(i_0_2049,plain,
( hAPP(v_h____,esk45_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_e____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk45_0)),v_e____))) ),
inference(scs_inference,[],[i_0_1371,i_0_1221]) ).
cnf(i_0_2050,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_1373,i_0_1222]) ).
cnf(i_0_2051,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk45_0)),v_n____)),
inference(scs_inference,[],[i_0_1298,i_0_1991,i_0_1260]) ).
cnf(i_0_2052,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_1991,i_0_1232]) ).
cnf(i_0_2053,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_1232]) ).
cnf(i_0_2054,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
inference(scs_inference,[],[i_0_1991,i_0_1509,i_0_1232,i_0_1335]) ).
cnf(i_0_2055,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_1509]) ).
cnf(i_0_2056,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_2057,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_1991,i_0_1509,i_0_1413,i_0_1232,i_0_1335,i_0_1491]) ).
cnf(i_0_2058,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_2059,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_1491]) ).
cnf(i_0_2060,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_1991,i_0_1509,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493]) ).
cnf(i_0_2061,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_2062,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_1493]) ).
cnf(i_0_2063,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_1991,i_0_1509,i_0_1705,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514]) ).
cnf(i_0_2064,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(rename_variables,[],[i_0_1514]) ).
cnf(i_0_2065,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_1991,i_0_1509,i_0_1705,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522]) ).
cnf(i_0_2066,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_1522]) ).
cnf(i_0_2067,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk32_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1991,i_0_1509,i_0_1705,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571]) ).
cnf(i_0_2068,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk32_2(X2,X1))) ),
inference(rename_variables,[],[i_0_1571]) ).
cnf(i_0_2069,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_1991,i_0_1509,i_0_1705,i_0_1725,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580]) ).
cnf(i_0_2070,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_1580]) ).
cnf(i_0_2071,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1991,i_0_1509,i_0_1705,i_0_1725,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637]) ).
cnf(i_0_2072,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_1637]) ).
cnf(i_0_2073,plain,
hBOOL(hAPP(v_Lba____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____))),
inference(scs_inference,[],[i_0_1991,i_0_1371,i_0_1509,i_0_1705,i_0_1725,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658]) ).
cnf(i_0_2074,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1658]) ).
cnf(i_0_2075,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_1991,i_0_1371,i_0_1509,i_0_1705,i_0_1725,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702]) ).
cnf(i_0_2076,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1702]) ).
cnf(i_0_2077,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_1991,i_0_1371,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703]) ).
cnf(i_0_2078,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_1703]) ).
cnf(i_0_2079,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_1991,i_0_1371,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709]) ).
cnf(i_0_2080,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_1709]) ).
cnf(i_0_2081,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_1991,i_0_1371,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710]) ).
cnf(i_0_2082,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1710]) ).
cnf(i_0_2083,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
inference(scs_inference,[],[i_0_1991,i_0_1371,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722]) ).
cnf(i_0_2084,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_2085,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_1722]) ).
cnf(i_0_2086,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_1991,i_0_1371,i_0_1782,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731]) ).
cnf(i_0_2087,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_1782]) ).
cnf(i_0_2088,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2089,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk32_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1991,i_0_1371,i_0_1782,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794]) ).
cnf(i_0_2090,plain,
( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1794]) ).
cnf(i_0_2091,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(scs_inference,[],[i_0_1991,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850]) ).
cnf(i_0_2092,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_2005,i_0_1991,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147]) ).
cnf(i_0_2093,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_1147]) ).
cnf(i_0_2094,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_2005,i_0_1991,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_1705,i_0_1725,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149]) ).
cnf(i_0_2095,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_1149]) ).
cnf(i_0_2096,plain,
c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk38_5(X4,X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_1705,i_0_1725,i_0_1685,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170]) ).
cnf(i_0_2097,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1685]) ).
cnf(i_0_2098,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,esk38_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_1170]) ).
cnf(i_0_2099,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_2005,i_0_1991,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195]) ).
cnf(i_0_2100,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_1195]) ).
cnf(i_0_2101,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_2005,i_0_1991,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218]) ).
cnf(i_0_2102,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_1218]) ).
cnf(i_0_2103,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_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237]) ).
cnf(i_0_2104,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2023]) ).
cnf(i_0_2105,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_2106,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_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240]) ).
cnf(i_0_2107,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_1240]) ).
cnf(i_0_2108,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_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_2097,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244]) ).
cnf(i_0_2109,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1685]) ).
cnf(i_0_2110,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_1244]) ).
cnf(i_0_2111,plain,
hAPP(X1,X2) = hAPP(X1,esk37_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_2097,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263]) ).
cnf(i_0_2112,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
| X2 = hAPP(X4,esk37_4(X5,X4,X3,X2)) ),
inference(rename_variables,[],[i_0_1263]) ).
cnf(i_0_2113,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_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274]) ).
cnf(i_0_2114,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1716]) ).
cnf(i_0_2115,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_2116,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,esk9_0),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277]) ).
cnf(i_0_2117,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_2118,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,esk9_0),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278]) ).
cnf(i_0_2119,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_2120,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_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1803,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285]) ).
cnf(i_0_2121,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1803]) ).
cnf(i_0_2122,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_2123,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_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1803,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286]) ).
cnf(i_0_2124,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2125,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_2126,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_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1803,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292]) ).
cnf(i_0_2127,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2128,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_1292]) ).
cnf(i_0_2129,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_2005,i_0_1991,i_0_2023,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293]) ).
cnf(i_0_2130,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1610]) ).
cnf(i_0_2131,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_1293]) ).
cnf(i_0_2132,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297]) ).
cnf(i_0_2133,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_1297]) ).
cnf(i_0_2134,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331]) ).
cnf(i_0_2135,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_1331]) ).
cnf(i_0_2136,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346]) ).
cnf(i_0_2137,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_2138,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347]) ).
cnf(i_0_2139,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_2140,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382]) ).
cnf(i_0_2141,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_1469]) ).
cnf(i_0_2142,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_2143,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384]) ).
cnf(i_0_2144,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1771]) ).
cnf(i_0_2145,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_2146,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1608,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398]) ).
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),X1),X2))),
inference(rename_variables,[],[i_0_1608]) ).
cnf(i_0_2148,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_2149,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1608,i_0_2147,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399]) ).
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),X1),X2))),
inference(rename_variables,[],[i_0_1608]) ).
cnf(i_0_2151,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_2152,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1608,i_0_2147,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423]) ).
cnf(i_0_2153,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_2154,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,hAPP(c_fequal,X2)))),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1608,i_0_2147,i_0_1557,i_0_1271,i_0_1412,i_0_1413,i_0_2058,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472]) ).
cnf(i_0_2155,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_1472]) ).
cnf(i_0_2156,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))),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1608,i_0_2147,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480]) ).
cnf(i_0_2157,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_1480]) ).
cnf(i_0_2158,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1608,i_0_2147,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511]) ).
cnf(i_0_2159,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(rename_variables,[],[i_0_1468]) ).
cnf(i_0_2160,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_1511]) ).
cnf(i_0_2161,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512]) ).
cnf(i_0_2162,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_1608]) ).
cnf(i_0_2163,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_1512]) ).
cnf(i_0_2164,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516]) ).
cnf(i_0_2165,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1597]) ).
cnf(i_0_2166,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_1516]) ).
cnf(i_0_2167,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_2165,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518]) ).
cnf(i_0_2168,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1597]) ).
cnf(i_0_2169,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_1518]) ).
cnf(i_0_2170,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_2165,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526]) ).
cnf(i_0_2171,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_1608]) ).
cnf(i_0_2172,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_1526]) ).
cnf(i_0_2173,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_2165,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540]) ).
cnf(i_0_2174,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_1608]) ).
cnf(i_0_2175,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_1540]) ).
cnf(i_0_2176,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_2165,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542]) ).
cnf(i_0_2177,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_1542]) ).
cnf(i_0_2178,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,X1))),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_2165,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572]) ).
cnf(i_0_2179,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_1572]) ).
cnf(i_0_2180,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_1597,i_0_2165,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599]) ).
cnf(i_0_2181,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_1599]) ).
cnf(i_0_2182,plain,
X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602]) ).
cnf(i_0_2183,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_1602]) ).
cnf(i_0_2184,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629]) ).
cnf(i_0_2185,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1597]) ).
cnf(i_0_2186,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_1629]) ).
cnf(i_0_2187,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631]) ).
cnf(i_0_2188,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
inference(rename_variables,[],[i_0_1631]) ).
cnf(i_0_2189,plain,
c_Set_Oinsert(X1,X2,hAPP(c_fequal,X2)) = hAPP(c_fequal,X2),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638]) ).
cnf(i_0_2190,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Set_Oinsert(X1,X2,X3) = X3 ),
inference(rename_variables,[],[i_0_1638]) ).
cnf(i_0_2191,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X1,X1)),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666]) ).
cnf(i_0_2192,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X2,X1)) ),
inference(rename_variables,[],[i_0_1666]) ).
cnf(i_0_2193,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,esk30_1(hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669]) ).
cnf(i_0_2194,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 = hAPP(c_Nat_OSuc,esk30_1(X1)) ),
inference(rename_variables,[],[i_0_1669]) ).
cnf(i_0_2195,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704]) ).
cnf(i_0_2196,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_1704]) ).
cnf(i_0_2197,plain,
X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711]) ).
cnf(i_0_2198,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_1711]) ).
cnf(i_0_2199,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719]) ).
cnf(i_0_2200,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_2201,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_1719]) ).
cnf(i_0_2202,plain,
~ class_Orderings_Otop(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745]) ).
cnf(i_0_2203,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1597]) ).
cnf(i_0_2204,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_1745]) ).
cnf(i_0_2205,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768]) ).
cnf(i_0_2206,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2207,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808]) ).
cnf(i_0_2208,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1808]) ).
cnf(i_0_2209,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_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989]) ).
cnf(i_0_2210,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1685]) ).
cnf(i_0_2211,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_1989]) ).
cnf(i_0_2212,plain,
hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X1,X2))) != X1,
inference(scs_inference,[],[i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852]) ).
cnf(i_0_2213,plain,
hAPP(c_Set_Oinsert(X1,X2,X3),X2) != hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X5),X5),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1817,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916]) ).
cnf(i_0_2214,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_2012,i_0_2005,i_0_1991,i_0_2023,i_0_2104,i_0_1371,i_0_1809,i_0_1817,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246]) ).
cnf(i_0_2215,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1991]) ).
cnf(i_0_2216,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1246]) ).
cnf(i_0_2217,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2023,i_0_2104,i_0_1371,i_0_1809,i_0_1817,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247]) ).
cnf(i_0_2218,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1991]) ).
cnf(i_0_2219,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1247]) ).
cnf(i_0_2220,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_1809,i_0_1817,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251]) ).
cnf(i_0_2221,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2222,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_1251]) ).
cnf(i_0_2223,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(esk9_0,hAPP(c_Nat_OSuc,X1),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_1809,i_0_1817,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273]) ).
cnf(i_0_2224,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_2225,plain,
X1 = esk38_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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_1809,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309]) ).
cnf(i_0_2226,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1625]) ).
cnf(i_0_2227,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_1309]) ).
cnf(i_0_2228,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324]) ).
cnf(i_0_2229,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1810]) ).
cnf(i_0_2230,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2231,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_1324]) ).
cnf(i_0_2232,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450]) ).
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_1509]) ).
cnf(i_0_2234,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_1586]) ).
cnf(i_0_2235,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_2236,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Set_Oinsert(X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1610,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454]) ).
cnf(i_0_2237,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_2238,plain,
hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X3)),hAPP(hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X3),X4)) = X4,
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462]) ).
cnf(i_0_2239,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_2240,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_2241,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508]) ).
cnf(i_0_2242,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_1508]) ).
cnf(i_0_2243,plain,
~ hBOOL(hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1),hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X3)),X3)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528]) ).
cnf(i_0_2244,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_1528]) ).
cnf(i_0_2245,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532]) ).
cnf(i_0_2246,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_1532]) ).
cnf(i_0_2247,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533]) ).
cnf(i_0_2248,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_1533]) ).
cnf(i_0_2249,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),esk7_0)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537]) ).
cnf(i_0_2250,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_1537]) ).
cnf(i_0_2251,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553]) ).
cnf(i_0_2252,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_1553]) ).
cnf(i_0_2253,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554]) ).
cnf(i_0_2254,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1412]) ).
cnf(i_0_2255,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_1554]) ).
cnf(i_0_2256,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563]) ).
cnf(i_0_2257,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1716]) ).
cnf(i_0_2258,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_1563]) ).
cnf(i_0_2259,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569]) ).
cnf(i_0_2260,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_1569]) ).
cnf(i_0_2261,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570]) ).
cnf(i_0_2262,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_1570]) ).
cnf(i_0_2263,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605]) ).
cnf(i_0_2264,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_1605]) ).
cnf(i_0_2265,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk7_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607]) ).
cnf(i_0_2266,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_1607]) ).
cnf(i_0_2267,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649]) ).
cnf(i_0_2268,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_2269,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_1649]) ).
cnf(i_0_2270,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668]) ).
cnf(i_0_2271,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_2272,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_1668]) ).
cnf(i_0_2273,plain,
c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != esk7_0,
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672]) ).
cnf(i_0_2274,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1672]) ).
cnf(i_0_2275,plain,
esk7_0 != c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674]) ).
cnf(i_0_2276,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1674]) ).
cnf(i_0_2277,plain,
esk10_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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675]) ).
cnf(i_0_2278,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1675]) ).
cnf(i_0_2279,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))) != esk10_0,
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676]) ).
cnf(i_0_2280,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1676]) ).
cnf(i_0_2281,plain,
X1 = esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689]) ).
cnf(i_0_2282,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_1689]) ).
cnf(i_0_2283,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754]) ).
cnf(i_0_2284,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1754]) ).
cnf(i_0_2285,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755]) ).
cnf(i_0_2286,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2287,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != X2,
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756]) ).
cnf(i_0_2288,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1756]) ).
cnf(i_0_2289,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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,esk9_0),hAPP(c_Nat_OSuc,X2)),X2))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986]) ).
cnf(i_0_2290,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_1986]) ).
cnf(i_0_2291,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)),c_Arrow__Order__Mirabelle_Obelow(esk9_0,hAPP(c_Nat_OSuc,X2),X2))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988]) ).
cnf(i_0_2292,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_1988]) ).
cnf(i_0_2293,plain,
hAPP(c_Nat_OSuc,X1) != c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851]) ).
cnf(i_0_2294,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2295,plain,
class_Groups_Oordered__ab__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1837,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925]) ).
cnf(i_0_2296,plain,
class_Groups_Oordered__comm__monoid__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1822,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1837,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927]) ).
cnf(i_0_2297,plain,
class_Rings_Ocomm__semiring__1(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1837,i_0_1840,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929]) ).
cnf(i_0_2298,plain,
class_Rings_Olinordered__semidom(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1837,i_0_1840,i_0_1844,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930]) ).
cnf(i_0_2299,plain,
c_Arrow__Order__Mirabelle_OIIA(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_F),esk18_2(v_F,v_F))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1837,i_0_1840,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931]) ).
cnf(i_0_2300,plain,
class_Orderings_Olinorder(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1831,i_0_1832,i_0_1836,i_0_1837,i_0_1840,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,i_0_1933]) ).
cnf(i_0_2301,plain,
class_Orderings_Opreorder(esk38_5(tc_HOL_Obool,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_HOL_Obool),tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,i_0_1933,i_0_1934]) ).
cnf(i_0_2302,plain,
class_Orderings_Oorder(esk38_5(tc_HOL_Obool,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_HOL_Obool),tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,i_0_1933,i_0_1934,i_0_1935]) ).
cnf(i_0_2303,plain,
class_Groups_Oab__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,i_0_1933,i_0_1934,i_0_1935,i_0_1936]) ).
cnf(i_0_2304,plain,
class_Groups_Ocancel__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937]) ).
cnf(i_0_2305,plain,
class_Groups_Ocancel__ab__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938]) ).
cnf(i_0_2306,plain,
tc_HOL_Obool != tc_Nat_Onat,
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1821,i_0_1822,i_0_1827,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,i_0_1933,i_0_1934,i_0_1935,i_0_1936,i_0_1937,i_0_1938,i_0_1939]) ).
cnf(i_0_2307,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1827,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_2308,plain,
class_Finite__Set_Ofinite(esk32_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Product__Type_Ounit)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1827,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941]) ).
cnf(i_0_2309,plain,
class_Groups_Omonoid__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1827,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944]) ).
cnf(i_0_2310,plain,
class_Groups_Ocomm__monoid__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1827,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945]) ).
cnf(i_0_2311,plain,
class_Rings_Ozero__neq__one(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946]) ).
cnf(i_0_2312,plain,
class_Groups_Ozero(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947]) ).
cnf(i_0_2313,plain,
class_Groups_Oone(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948]) ).
cnf(i_0_2314,plain,
class_Orderings_Oord(esk38_5(tc_HOL_Obool,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_HOL_Obool),tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957]) ).
cnf(i_0_2315,plain,
c_Arrow__Order__Mirabelle_Ounanimity(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_F),esk18_2(v_F,v_F))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1610,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968]) ).
cnf(i_0_2316,plain,
~ c_Finite__Set_Ofolding__image__simple__idem(X1,tc_Nat_Onat,c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X3,c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7),c_Set_Oinsert(X4,c_Set_Oinsert(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6)),X7)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1610,i_0_1738,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116]) ).
cnf(i_0_2317,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_1116]) ).
cnf(i_0_2318,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk9_0)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1610,i_0_1738,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190]) ).
cnf(i_0_2319,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_1190]) ).
cnf(i_0_2320,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2))),c_Wellfounded_Omlex__prod(X1,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1610,i_0_1738,i_0_1405,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224]) ).
cnf(i_0_2321,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_2322,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_1609]) ).
cnf(i_0_2323,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_1224]) ).
cnf(i_0_2324,plain,
hAPP(hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2) = hAPP(hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),esk34_4(hAPP(hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229]) ).
cnf(i_0_2325,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_1295]) ).
cnf(i_0_2326,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_2327,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))
| X2 = hAPP(X4,esk34_4(X2,X4,X1,X3))
| ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1229]) ).
cnf(i_0_2328,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250]) ).
cnf(i_0_2329,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2023]) ).
cnf(i_0_2330,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1991]) ).
cnf(i_0_2331,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_1250]) ).
cnf(i_0_2332,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257]) ).
cnf(i_0_2333,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_1509]) ).
cnf(i_0_2334,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_1257]) ).
cnf(i_0_2335,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268]) ).
cnf(i_0_2336,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_2337,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275]) ).
cnf(i_0_2338,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_1509]) ).
cnf(i_0_2339,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2340,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_2341,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_1809,i_0_1810,i_0_1817,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276]) ).
cnf(i_0_2342,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1685]) ).
cnf(i_0_2343,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_2344,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280]) ).
cnf(i_0_2345,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2346,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_2347,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306]) ).
cnf(i_0_2348,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2349,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_1306]) ).
cnf(i_0_2350,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317]) ).
cnf(i_0_2351,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_1317]) ).
cnf(i_0_2352,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327]) ).
cnf(i_0_2353,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2023]) ).
cnf(i_0_2354,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2355,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_1327]) ).
cnf(i_0_2356,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360]) ).
cnf(i_0_2357,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_2358,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457]) ).
cnf(i_0_2359,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_2360,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459]) ).
cnf(i_0_2361,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_1509]) ).
cnf(i_0_2362,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_2363,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545]) ).
cnf(i_0_2364,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(rename_variables,[],[i_0_1550]) ).
cnf(i_0_2365,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_1545]) ).
cnf(i_0_2366,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),X1)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562]) ).
cnf(i_0_2367,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1597]) ).
cnf(i_0_2368,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_1562]) ).
cnf(i_0_2369,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_1586,i_0_2234,i_0_1654,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565]) ).
cnf(i_0_2370,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_1586]) ).
cnf(i_0_2371,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_1565]) ).
cnf(i_0_2372,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587]) ).
cnf(i_0_2373,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_2374,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1716]) ).
cnf(i_0_2375,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk41_1(X2)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(rename_variables,[],[i_0_1587]) ).
cnf(i_0_2376,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,esk31_2(hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Product__Type_Ounit)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_1295,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594]) ).
cnf(i_0_2377,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1803]) ).
cnf(i_0_2378,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 = hAPP(c_Nat_OSuc,esk31_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1594]) ).
cnf(i_0_2379,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603]) ).
cnf(i_0_2380,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_1295]) ).
cnf(i_0_2381,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1597]) ).
cnf(i_0_2382,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk43_1(X2)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(rename_variables,[],[i_0_1603]) ).
cnf(i_0_2383,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663]) ).
cnf(i_0_2384,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_1663]) ).
cnf(i_0_2385,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693]) ).
cnf(i_0_2386,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_1693]) ).
cnf(i_0_2387,plain,
esk18_2(v_F,v_F) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748]) ).
cnf(i_0_2388,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_1748]) ).
cnf(i_0_2389,plain,
X1 = esk34_4(hAPP(c_COMBI(X2),X1),c_COMBI(X2),X2,X2),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987]) ).
cnf(i_0_2390,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2391,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_1295]) ).
cnf(i_0_2392,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))
| X4 = esk34_4(hAPP(X3,X4),X3,X2,X1) ),
inference(rename_variables,[],[i_0_1987]) ).
cnf(i_0_2393,plain,
~ c_FunDef_Oin__rel(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),hAPP(c_Nat_OSuc,tc_Nat_Onat)),hAPP(c_Nat_OSuc,tc_Nat_Onat),X2),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918]) ).
cnf(i_0_2394,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2395,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),hAPP(c_Nat_OSuc,tc_Nat_Onat)),hAPP(c_Nat_OSuc,tc_Nat_Onat),X2),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919]) ).
cnf(i_0_2396,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2397,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),hAPP(c_Nat_OSuc,tc_Nat_Onat))),hAPP(c_Nat_OSuc,tc_Nat_Onat),X2),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920]) ).
cnf(i_0_2398,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2399,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),hAPP(c_Nat_OSuc,tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat)),X2),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921]) ).
cnf(i_0_2400,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2401,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923]) ).
cnf(i_0_2402,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924]) ).
cnf(i_0_2403,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk9_0),hAPP(c_Nat_OSuc,tc_Nat_Onat)),tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233]) ).
cnf(i_0_2404,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2405,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_2406,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(esk9_0,hAPP(c_Nat_OSuc,X2),X2))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242]) ).
cnf(i_0_2407,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_1242]) ).
cnf(i_0_2408,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328]) ).
cnf(i_0_2409,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1654]) ).
cnf(i_0_2410,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1810]) ).
cnf(i_0_2411,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(rename_variables,[],[i_0_1757]) ).
cnf(i_0_2412,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_1328]) ).
cnf(i_0_2413,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425]) ).
cnf(i_0_2414,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_2415,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)))),esk10_0)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484]) ).
cnf(i_0_2416,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1716]) ).
cnf(i_0_2417,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_1484]) ).
cnf(i_0_2418,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485]) ).
cnf(i_0_2419,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1716]) ).
cnf(i_0_2420,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_1485]) ).
cnf(i_0_2421,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),esk7_0)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502]) ).
cnf(i_0_2422,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1716]) ).
cnf(i_0_2423,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_1502]) ).
cnf(i_0_2424,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503]) ).
cnf(i_0_2425,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2426,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_1503]) ).
cnf(i_0_2427,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)))),esk10_0)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504]) ).
cnf(i_0_2428,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1716]) ).
cnf(i_0_2429,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_1504]) ).
cnf(i_0_2430,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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)))),X1)),v_n____)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505]) ).
cnf(i_0_2431,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_1608]) ).
cnf(i_0_2432,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_1505]) ).
cnf(i_0_2433,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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593]) ).
cnf(i_0_2434,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_1609]) ).
cnf(i_0_2435,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_1593]) ).
cnf(i_0_2436,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657]) ).
cnf(i_0_2437,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_1699]) ).
cnf(i_0_2438,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_1789]) ).
cnf(i_0_2439,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_1657]) ).
cnf(i_0_2440,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk9_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977]) ).
cnf(i_0_2441,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1810]) ).
cnf(i_0_2442,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_1977]) ).
cnf(i_0_2443,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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(esk9_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982]) ).
cnf(i_0_2444,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2445,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_1982]) ).
cnf(i_0_2446,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181]) ).
cnf(i_0_2447,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_1509]) ).
cnf(i_0_2448,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2449,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_1181]) ).
cnf(i_0_2450,plain,
X1 = esk34_4(hAPP(c_COMBI(X2),hAPP(c_COMBI(X2),X1)),c_COMBI(X2),X2,X2),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239]) ).
cnf(i_0_2451,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_1295]) ).
cnf(i_0_2452,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2453,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1811]) ).
cnf(i_0_2454,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)))))
| ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))
| X2 != hAPP(X4,X5)
| X5 = esk34_4(X2,X4,X1,X3) ),
inference(rename_variables,[],[i_0_1239]) ).
cnf(i_0_2455,plain,
c_Fun_Oinj__on(tc_Product__Type_Ounit,tc_Product__Type_Ounit,esk40_4(c_Set_Oinsert(tc_Product__Type_Ounit,X1,c_Set_Oimage(tc_Product__Type_Ounit,tc_Product__Type_Ounit,c_COMBI(tc_Product__Type_Ounit),c_Set_Oimage(tc_Nat_Onat,tc_Product__Type_Ounit,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4)))),tc_Product__Type_Ounit,c_Set_Oimage(tc_Nat_Onat,tc_Product__Type_Ounit,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4)),tc_Product__Type_Ounit),c_Set_Oimage(tc_Nat_Onat,tc_Product__Type_Ounit,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320]) ).
cnf(i_0_2456,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X4)))
| c_Fun_Oinj__on(X1,X3,esk40_4(X4,X3,X2,X1),X2)
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1320]) ).
cnf(i_0_2457,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439]) ).
cnf(i_0_2458,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_2459,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440]) ).
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)),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_2461,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_Product__Type_Ounit)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529]) ).
cnf(i_0_2462,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1597]) ).
cnf(i_0_2463,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_1529]) ).
cnf(i_0_2464,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530]) ).
cnf(i_0_2465,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_1530]) ).
cnf(i_0_2466,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,v_a____))),v_b____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,esk9_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188]) ).
cnf(i_0_2467,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1810]) ).
cnf(i_0_2468,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2469,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),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_1188]) ).
cnf(i_0_2470,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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(esk9_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204]) ).
cnf(i_0_2471,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2472,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1817]) ).
cnf(i_0_2473,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_1204]) ).
cnf(i_0_2474,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_Product__Type_Ounit))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465]) ).
cnf(i_0_2475,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2476,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_1705]) ).
cnf(i_0_2477,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
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),X4),X5))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| X2 = X4
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1465]) ).
cnf(i_0_2479,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466]) ).
cnf(i_0_2480,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2481,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2482,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| X3 = X5
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1466]) ).
cnf(i_0_2483,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487]) ).
cnf(i_0_2484,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_1609]) ).
cnf(i_0_2485,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_1487]) ).
cnf(i_0_2486,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),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488]) ).
cnf(i_0_2487,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)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1488]) ).
cnf(i_0_2488,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk9_0),hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,X1)),X1))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_1992,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187]) ).
cnf(i_0_2489,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1992]) ).
cnf(i_0_2490,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_1187]) ).
cnf(i_0_2491,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk9_0),hAPP(c_Nat_OSuc,X1)),X1,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1435,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203]) ).
cnf(i_0_2492,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1992]) ).
cnf(i_0_2493,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2494,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2495,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_1203]) ).
cnf(i_0_2496,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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,esk8_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973]) ).
cnf(i_0_2497,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1810]) ).
cnf(i_0_2498,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_1973]) ).
cnf(i_0_2499,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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(esk8_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_2494,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973,i_0_1975]) ).
cnf(i_0_2500,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2501,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_1975]) ).
cnf(i_0_2502,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),c_Arrow__Order__Mirabelle_Obelow(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,esk9_0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2330,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_2494,i_0_2500,i_0_2493,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_2377,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973,i_0_1975,i_0_1981]) ).
cnf(i_0_2503,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1991]) ).
cnf(i_0_2504,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2505,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1809]) ).
cnf(i_0_2506,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1803]) ).
cnf(i_0_2507,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_1981]) ).
cnf(i_0_2508,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_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2330,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_2494,i_0_2500,i_0_2493,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_2377,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_2438,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_2431,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973,i_0_1975,i_0_1981,i_0_1499]) ).
cnf(i_0_2509,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_1608]) ).
cnf(i_0_2510,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_1789]) ).
cnf(i_0_2511,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_1499]) ).
cnf(i_0_2512,plain,
c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_COMBI(tc_Arrow__Order__Mirabelle_Oindi),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2330,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_2452,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_2494,i_0_2500,i_0_2493,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_2377,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_2438,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_2342,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_2370,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_2431,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973,i_0_1975,i_0_1981,i_0_1499,i_0_1119]) ).
cnf(i_0_2513,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1685]) ).
cnf(i_0_2514,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_1586]) ).
cnf(i_0_2515,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2516,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X6,X5)),X4))
| c_Finite__Set_Ocard(X2,X4) = c_Finite__Set_Ocard(X1,X5)
| ~ c_Finite__Set_Ofinite(X2,X4)
| ~ c_Finite__Set_Ofinite(X1,X5)
| ~ c_Fun_Oinj__on(X2,X1,X3,X4)
| ~ c_Fun_Oinj__on(X1,X2,X6,X5) ),
inference(rename_variables,[],[i_0_1119]) ).
cnf(i_0_2517,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X2)),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2330,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_2452,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_2494,i_0_2500,i_0_2493,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_2377,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_2438,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_2342,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_2370,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_2431,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973,i_0_1975,i_0_1981,i_0_1499,i_0_1119,i_0_1560]) ).
cnf(i_0_2518,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rename_variables,[],[i_0_1560]) ).
cnf(i_0_2519,plain,
c_Finite__Set_Ofinite(X1,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,X1,hAPP(c_COMBB(tc_Arrow__Order__Mirabelle_Oindi,X1,tc_Arrow__Order__Mirabelle_Oindi,X2),c_COMBI(tc_Arrow__Order__Mirabelle_Oindi)),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2330,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_2452,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_2494,i_0_2500,i_0_2493,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_2377,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_2438,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_2342,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_2370,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_2431,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973,i_0_1975,i_0_1981,i_0_1499,i_0_1119,i_0_1560,i_0_1202]) ).
cnf(i_0_2520,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_1202]) ).
cnf(i_0_2521,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),esk36_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi))) != esk36_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi),
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2330,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_2452,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_2494,i_0_2500,i_0_2493,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_2377,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_2438,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_2342,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_2370,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_2431,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973,i_0_1975,i_0_1981,i_0_1499,i_0_1119,i_0_1560,i_0_1202,i_0_1243]) ).
cnf(i_0_2522,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),esk36_3(X3,X2,X1))) != esk36_3(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1243]) ).
cnf(i_0_2523,plain,
$false,
inference(scs_inference,[],[i_0_2012,i_0_2005,i_0_1991,i_0_2215,i_0_2218,i_0_2330,i_0_1992,i_0_2489,i_0_2023,i_0_2104,i_0_2329,i_0_1371,i_0_1611,i_0_2221,i_0_2230,i_0_2339,i_0_2354,i_0_2390,i_0_2448,i_0_2452,i_0_1809,i_0_2404,i_0_2444,i_0_2471,i_0_2477,i_0_2481,i_0_2494,i_0_2500,i_0_2493,i_0_1810,i_0_2229,i_0_2410,i_0_2441,i_0_2467,i_0_1817,i_0_2294,i_0_2345,i_0_2348,i_0_2394,i_0_2396,i_0_2398,i_0_2400,i_0_2468,i_0_1625,i_0_1803,i_0_2121,i_0_2377,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1826,i_0_1827,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_1839,i_0_1840,i_0_1841,i_0_1842,i_0_1843,i_0_1844,i_0_1845,i_0_1846,i_0_1848,i_0_1354,i_0_1610,i_0_1811,i_0_1789,i_0_2438,i_0_1738,i_0_1405,i_0_2239,i_0_1757,i_0_1786,i_0_1782,i_0_1550,i_0_1509,i_0_2055,i_0_2233,i_0_2333,i_0_2338,i_0_2361,i_0_1771,i_0_2144,i_0_1705,i_0_2476,i_0_1725,i_0_2124,i_0_2127,i_0_2425,i_0_2475,i_0_1699,i_0_1685,i_0_2097,i_0_2109,i_0_2210,i_0_2342,i_0_1716,i_0_2114,i_0_2257,i_0_2374,i_0_2416,i_0_2419,i_0_2422,i_0_1586,i_0_2234,i_0_2370,i_0_1654,i_0_2321,i_0_2373,i_0_1761,i_0_1597,i_0_2165,i_0_2168,i_0_2185,i_0_2203,i_0_2367,i_0_2381,i_0_2462,i_0_1295,i_0_2325,i_0_2380,i_0_2391,i_0_1608,i_0_2147,i_0_2150,i_0_2162,i_0_2171,i_0_2174,i_0_2431,i_0_1609,i_0_2322,i_0_2434,i_0_1557,i_0_1556,i_0_1555,i_0_1271,i_0_1412,i_0_2084,i_0_2200,i_0_2254,i_0_2268,i_0_1413,i_0_2058,i_0_1468,i_0_1469,i_0_1370,i_0_1372,i_0_1435,i_0_1436,i_0_1307,i_0_1232,i_0_1335,i_0_1491,i_0_1493,i_0_1514,i_0_1522,i_0_1571,i_0_1580,i_0_1637,i_0_1658,i_0_1702,i_0_1703,i_0_1709,i_0_1710,i_0_1722,i_0_1731,i_0_1794,i_0_1850,i_0_1147,i_0_1149,i_0_1170,i_0_1195,i_0_1218,i_0_1237,i_0_1240,i_0_1244,i_0_1263,i_0_1274,i_0_1277,i_0_1278,i_0_1285,i_0_1286,i_0_1292,i_0_1293,i_0_1297,i_0_1331,i_0_1346,i_0_1347,i_0_1382,i_0_1384,i_0_1398,i_0_1399,i_0_1423,i_0_1472,i_0_1480,i_0_1511,i_0_1512,i_0_1516,i_0_1518,i_0_1526,i_0_1540,i_0_1542,i_0_1572,i_0_1599,i_0_1602,i_0_1629,i_0_1631,i_0_1638,i_0_1666,i_0_1669,i_0_1704,i_0_1711,i_0_1719,i_0_1745,i_0_1768,i_0_1808,i_0_1989,i_0_1852,i_0_1916,i_0_1246,i_0_1247,i_0_1251,i_0_1273,i_0_1309,i_0_1324,i_0_1450,i_0_1454,i_0_1462,i_0_1508,i_0_1528,i_0_1532,i_0_1533,i_0_1537,i_0_1553,i_0_1554,i_0_1563,i_0_1569,i_0_1570,i_0_1605,i_0_1607,i_0_1649,i_0_1668,i_0_1672,i_0_1674,i_0_1675,i_0_1676,i_0_1689,i_0_1754,i_0_1755,i_0_1756,i_0_1986,i_0_1988,i_0_1851,i_0_1925,i_0_1927,i_0_1929,i_0_1930,i_0_1931,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_1941,i_0_1944,i_0_1945,i_0_1946,i_0_1947,i_0_1948,i_0_1957,i_0_1968,i_0_1116,i_0_1190,i_0_1224,i_0_1229,i_0_1250,i_0_1257,i_0_1268,i_0_1275,i_0_1276,i_0_1280,i_0_1306,i_0_1317,i_0_1327,i_0_1360,i_0_1457,i_0_1459,i_0_1545,i_0_1562,i_0_1565,i_0_1587,i_0_1594,i_0_1603,i_0_1663,i_0_1693,i_0_1748,i_0_1987,i_0_1918,i_0_1919,i_0_1920,i_0_1921,i_0_1923,i_0_1924,i_0_1233,i_0_1242,i_0_1328,i_0_1425,i_0_1484,i_0_1485,i_0_1502,i_0_1503,i_0_1504,i_0_1505,i_0_1593,i_0_1657,i_0_1977,i_0_1982,i_0_1181,i_0_1239,i_0_1320,i_0_1439,i_0_1440,i_0_1529,i_0_1530,i_0_1188,i_0_1204,i_0_1465,i_0_1466,i_0_1487,i_0_1488,i_0_1187,i_0_1203,i_0_1973,i_0_1975,i_0_1981,i_0_1499,i_0_1119,i_0_1560,i_0_1202,i_0_1243,i_0_1458]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT166+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
% 0.15/0.34 % Computer : n010.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:04:06 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 4.17/5.75 % Version : CSE_E---1.7
% 4.17/5.75 % Problem : theBenchmark.p
% 4.17/5.75 % SZS status Theorem for theBenchmark.p
% 4.17/5.75 % SZS output start CNFRefutation
% See solution above
% 10.47/12.04 % Total time : 5.395s
%------------------------------------------------------------------------------