%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT164+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 : n012.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 05:06:10 PM UTC 2026
% Result : Theorem 4.07s 5.57s
% Output : CNFRefutation 12.77s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1069)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,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',conj_0) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> ( ! [X38] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),X42))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X38))),v_Lab____)),v_Lba____)))) )
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_folding__image__simple_Oinsert,axiom,
! [X11,X15,X28,X1,X8,X2,X18,X13] :
( c_Finite__Set_Ofolding__image__simple(X13,X18,X2,X8,X1,X28)
=> ( c_Finite__Set_Ofinite(X18,X15)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X18),X11),X15))
=> hAPP(X28,c_Set_Oinsert(X18,X11,X15)) = hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X28,X15)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
fof(fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096,axiom,
! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X4)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,X4)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X4)),v_n____))
=> ( ( hAPP(v_h____,X4) = v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,X4)),v_c____),v_e____))) )
& ( hAPP(v_h____,X4) != v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,X4)),v_e____))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J_A_061_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_092_060_094esub_062_Ad_J_096) ).
fof(fact_pigeonhole,axiom,
! [X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X13,c_Set_Oimage(X18,X13,X2,X15))),c_Finite__Set_Ocard(X18,X15)))
=> ~ c_Fun_Oinj__on(X18,X13,X2,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
fof(fact_card__def,axiom,
! [X15,X13] :
( ( c_Finite__Set_Ofinite(X13,X15)
=> c_Finite__Set_Ocard(X13,X15) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) )
& ( ~ c_Finite__Set_Ofinite(X13,X15)
=> c_Finite__Set_Ocard(X13,X15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__def) ).
fof(fact_notin__Lin__iff,axiom,
! [X10,X11,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),c_Arrow__Order__Mirabelle_OLin))
=> ( X11 != X10
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11),X10)),X9))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X10),X11)),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X22,X23,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),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)),X9))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X22),X23)),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_PiE,axiom,
! [X11,X14,X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X18)),X2),c_FuncSet_OPi(X13,X18,X15,X14)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X11)),hAPP(X14,X11)))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_subset__insert,axiom,
! [X14,X15,X11,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),c_Set_Oinsert(X13,X11,X14)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X40))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X40),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X41))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X41),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X13,X18] :
( class_Orderings_Oord(X18)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,X18)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,X18),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,X18),X1),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_add__leE,axiom,
! [X43,X49,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X49)),X43))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X43)) ) ),
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,
! [X35,X20] :
( ~ hBOOL(hAPP(X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X20,X35))
=> ? [X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X53),X35))
& ! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X53))
=> ~ hBOOL(hAPP(X20,X4)) )
& hBOOL(hAPP(X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),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,X14,X23,X13] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X13),X23),X14))
=> X23 = X22 )
=> hBOOL(hAPP(hAPP(c_member(X13),X23),c_Set_Oinsert(X13,X22,X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_insert__ident,axiom,
! [X14,X15,X11,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X14))
=> ( c_Set_Oinsert(X13,X11,X15) = c_Set_Oinsert(X13,X11,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_not__less__eq__eq,axiom,
! [X35,X45] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35)),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X35,X45] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,X45))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_xt1_I9_J,axiom,
! [X32,X31,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),X32))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X10),X11))
| X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_order__less__asym,axiom,
! [X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X31,X32,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),X32)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_card_Oinsert,axiom,
! [X11,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X13,X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oinsert) ).
fof(fact_less__le__not__le,axiom,
! [X10,X11,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X10),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_card__insert__if,axiom,
! [X11,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)) = c_Finite__Set_Ocard(X13,X15) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X13,X15)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__if) ).
fof(fact_less__SucE,axiom,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X43)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
=> X44 = X43 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_less__antisym,axiom,
! [X44,X43] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X44)))
=> X44 = X43 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X45,X35] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X45))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,X45)))
<=> X35 = X45 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_leD,axiom,
! [X29,X30,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_card__insert__disjoint,axiom,
! [X11,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X13,X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_le__SucE,axiom,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),hAPP(c_Nat_OSuc,X43)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
=> X44 = hAPP(c_Nat_OSuc,X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X43] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X43)),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
<=> X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_not__one__less__zero,axiom,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Oone__class_Oone(X13)),c_Groups_Ozero__class_Ozero(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X30,X29,X13] :
( class_Rings_Olinordered__idom(X13)
=> ( X29 != X30
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__cases,axiom,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ( X29 != X30
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( X29 != X30
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X11,X10,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X10),X11))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_not__leE,axiom,
! [X29,X30,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__one__le__zero,axiom,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Oone__class_Oone(X13)),c_Groups_Ozero__class_Ozero(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X30,X29] :
( X29 != X30
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_equalityE,axiom,
! [X13,X14,X15] :
( X15 = X14
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_order__less__irrefl,axiom,
! [X29,X13] :
( class_Orderings_Opreorder(X13)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_linorder__le__cases,axiom,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_not__less0,axiom,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),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,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),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,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__not__refl,axiom,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_less__irrefl__nat,axiom,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(help_c__fequal__1,axiom,
! [X10,X11] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X11),X10))
| X11 = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_card__infinite,axiom,
! [X15,X13] :
( ~ c_Finite__Set_Ofinite(X13,X15)
=> c_Finite__Set_Ocard(X13,X15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
fof(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096,axiom,
? [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
& ! [X38] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),X42))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X38))),v_Lab____)),v_Lba____)))) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096) ).
fof(fact_PiProf,axiom,
! [X35] : hBOOL(hAPP(hAPP(c_member(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____)),X35))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiProf) ).
fof(fact_n_I2_J,axiom,
! [X38] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X38))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I2_J) ).
fof(fact_pred__subset__eq2,axiom,
! [X16,X17,X18,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X13,tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X13,c_COMBC(X18,tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_prod(X13,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),X13,c_COMBB(tc_prod(X13,X18),tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool),X18,c_member(tc_prod(X13,X18)))),c_Product__Type_OPair(X13,X18)))),X17)),hAPP(hAPP(c_COMBC(X13,tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X13,c_COMBC(X18,tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_prod(X13,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),X13,c_COMBB(tc_prod(X13,X18),tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool),X18,c_member(tc_prod(X13,X18)))),c_Product__Type_OPair(X13,X18)))),X16)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),X17),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact__C2_C,axiom,
! [X24,X20,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))),X20),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(X20,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,X20)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,X20,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))),X20),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(X20,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,X20)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,X20,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))),X20),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(X20,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,X20)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_max__extp__max__ext__eq,axiom,
! [X59,X11,X17,X13] :
( c_Wellfounded_Omax__extp(X13,hAPP(hAPP(c_COMBC(X13,tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X13,c_COMBC(X13,tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_prod(X13,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_HOL_Obool)),X13,c_COMBB(tc_prod(X13,X13),tc_fun(tc_fun(tc_prod(X13,X13),tc_HOL_Obool),tc_HOL_Obool),X13,c_member(tc_prod(X13,X13)))),c_Product__Type_OPair(X13,X13)))),X17),X11,X59)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X11),X59)),c_Wellfounded_Omax__ext(X13,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X16,X17,X18,X13] :
( hAPP(hAPP(c_COMBC(X13,tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X13,c_COMBC(X18,tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_prod(X13,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),X13,c_COMBB(tc_prod(X13,X18),tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool),X18,c_member(tc_prod(X13,X18)))),c_Product__Type_OPair(X13,X18)))),X17) = hAPP(hAPP(c_COMBC(X13,tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X13,c_COMBC(X18,tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X18,tc_prod(X13,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool)),X13,c_COMBB(tc_prod(X13,X18),tc_fun(tc_fun(tc_prod(X13,X18),tc_HOL_Obool),tc_HOL_Obool),X18,c_member(tc_prod(X13,X18)))),c_Product__Type_OPair(X13,X18)))),X16)
<=> X17 = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_Pi__mono,axiom,
! [X39,X14,X18,X15,X13] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),hAPP(X14,X3)),hAPP(X39,X3))) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X13,X18),tc_HOL_Obool),c_FuncSet_OPi(X13,X18,X15,X14)),c_FuncSet_OPi(X13,X18,X15,X39))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_Pi__I,axiom,
! [X14,X2,X18,X15,X13] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X15))
=> hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X3)),hAPP(X14,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X18)),X2),c_FuncSet_OPi(X13,X18,X15,X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_IIA__def,axiom,
! [X28] :
( c_Arrow__Order__Mirabelle_OIIA(X28)
<=> ! [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))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(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))
=> ! [X6,X7] :
( ! [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),X6),X7)),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),X6),X7)),hAPP(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),X6),X7)),hAPP(X28,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),X6),X7)),hAPP(X28,X5))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact__C4_C,axiom,
! [X24,X20,X12,X22,X23] :
( X23 != X22
=> ( X22 != X12
=> ( X23 != X12
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X20),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(X20,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),X12)),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,X20)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X12)),hAPP(v_F,X24))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C4_C) ).
fof(fact_dictatorI,axiom,
! [X37,X28] :
( 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))),X28),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))
=> ! [X6,X7] :
( X6 != 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),X6),X7)),hAPP(X3,X37)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),hAPP(X28,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X28,X37) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_in__lex__prod,axiom,
! [X27,X21,X25,X26,X22,X23,X18,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X13,X18),tc_prod(X13,X18))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X13,X18),tc_prod(X13,X18)),hAPP(hAPP(c_Product__Type_OPair(X13,X18),X23),X22)),hAPP(hAPP(c_Product__Type_OPair(X13,X18),X26),X25))),c_Wellfounded_Olex__prod(X13,X18,X21,X27)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X23),X26)),X21))
| ( X23 = X26
& hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X18)),hAPP(hAPP(c_Product__Type_OPair(X18,X18),X22),X25)),X27)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact__C3_C,axiom,
! [X24,X20,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))),X20),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(X20,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,X20)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096,axiom,
! [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))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(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))
=> ! [X6,X7] :
( ! [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),X6),X7)),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),X6),X7)),hAPP(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),X6),X7)),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),X6),X7)),hAPP(v_F,X5))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096) ).
fof(fact_folding__image__simple_Oeq__fold__g,axiom,
! [X15,X28,X1,X8,X2,X18,X13] :
( c_Finite__Set_Ofolding__image__simple(X13,X18,X2,X8,X1,X28)
=> ( c_Finite__Set_Ofinite(X18,X15)
=> hAPP(X28,X15) = c_Finite__Set_Ofold__image(X13,X18,X2,X1,X8,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
fof(fact_subset__image__iff,axiom,
! [X15,X2,X18,X14,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),c_Set_Oimage(X18,X13,X2,X15)))
<=> ? [X70] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),X70),X15))
& X14 = c_Set_Oimage(X18,X13,X2,X70) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_same__fstI,axiom,
! [X13,X17,X10,X19,X18,X11,X20] :
( hBOOL(hAPP(X20,X11))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X18)),hAPP(hAPP(c_Product__Type_OPair(X18,X18),X19),X10)),hAPP(X17,X11)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X13,X18),tc_prod(X13,X18))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X13,X18),tc_prod(X13,X18)),hAPP(hAPP(c_Product__Type_OPair(X13,X18),X11),X19)),hAPP(hAPP(c_Product__Type_OPair(X13,X18),X11),X10))),c_Recdef_Osame__fst(X13,X18,X20,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X13,X18] :
( class_Orderings_Oord(X18)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,X18),X2),X1))
<=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,hAPP(X2,X3)),hAPP(X1,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
! [X14,X15,X28,X1,X8,X2,X18,X13] :
( c_Finite__Set_Ofolding__image__simple__idem(X13,X18,X2,X8,X1,X28)
=> ( c_Finite__Set_Ofinite(X18,X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),X14),X15))
=> hAPP(hAPP(X2,hAPP(X28,X14)),hAPP(X28,X15)) = hAPP(X28,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [X11,X15,X28,X1,X8,X2,X18,X13] :
( c_Finite__Set_Ofolding__image__simple__idem(X13,X18,X2,X8,X1,X28)
=> ( c_Finite__Set_Ofinite(X18,X15)
=> ( hBOOL(hAPP(hAPP(c_member(X18),X11),X15))
=> hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X28,X15)) = hAPP(X28,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
! [X11,X15,X28,X1,X8,X2,X18,X13] :
( c_Finite__Set_Ofolding__image__simple__idem(X13,X18,X2,X8,X1,X28)
=> ( c_Finite__Set_Ofinite(X18,X15)
=> hAPP(X28,c_Set_Oinsert(X18,X11,X15)) = hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X28,X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [X11,X28,X1,X8,X2,X18,X13] :
( c_Finite__Set_Ofolding__image__simple__idem(X13,X18,X2,X8,X1,X28)
=> hAPP(hAPP(X2,X11),X11) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_card__bij__eq,axiom,
! [X1,X14,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X13,X18,X2,X15)),X14))
=> ( c_Fun_Oinj__on(X18,X13,X1,X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),c_Set_Oimage(X18,X13,X1,X14)),X15))
=> ( c_Finite__Set_Ofinite(X13,X15)
=> ( c_Finite__Set_Ofinite(X18,X14)
=> c_Finite__Set_Ocard(X13,X15) = c_Finite__Set_Ocard(X18,X14) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(fact_unanimity__def,axiom,
! [X28] :
( c_Arrow__Order__Mirabelle_Ounanimity(X28)
<=> ! [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))
=> ! [X6,X7] :
( ! [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),X6),X7)),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),X6),X7)),hAPP(X28,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_card__bij,axiom,
! [X1,X14,X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X18)),X2),c_FuncSet_OPi(X13,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X13),X14))))
=> ( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X18,X13)),X1),c_FuncSet_OPi(X18,X13,X14,hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X18),X15))))
=> ( c_Fun_Oinj__on(X18,X13,X1,X14)
=> ( c_Finite__Set_Ofinite(X13,X15)
=> ( c_Finite__Set_Ofinite(X18,X14)
=> c_Finite__Set_Ocard(X13,X15) = c_Finite__Set_Ocard(X18,X14) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij) ).
fof(fact_pred__subset__eq,axiom,
! [X16,X17,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X17)),hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X16)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X17),X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_inj__on__iff__card__le,axiom,
! [X14,X18,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( c_Finite__Set_Ofinite(X18,X14)
=> ( ? [X75] :
( c_Fun_Oinj__on(X13,X18,X75,X15)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X13,X18,X75,X15)),X14)) )
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X18,X14))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_in__above,axiom,
! [X10,X11,X9,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)),X9),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),X11),X10)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X9),X23),X22)))
<=> ( X11 != X10
& ( X11 = 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),X10)),X9)) )
& ( X11 != X22
=> ( ( X10 = X22
=> ( X11 = 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),X11),X23)),X9)) ) )
& ( X10 != 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),X11),X10)),X9)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_in__below,axiom,
! [X10,X11,X9,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)),X9),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),X11),X10)),c_Arrow__Order__Mirabelle_Obelow(X9,X23,X22)))
<=> ( X11 != X10
& ( X10 = 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),X11),X22)),X9)) )
& ( X10 != X23
=> ( ( X11 = X23
=> ( X10 = 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),X10)),X9)) ) )
& ( X11 != 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),X11),X10)),X9)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_card_Oeq__fold__g,axiom,
! [X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> c_Finite__Set_Ocard(X13,X15) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
fof(fact_inv__into__into,axiom,
! [X15,X2,X18,X11,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X11),c_Set_Oimage(X18,X13,X2,X15)))
=> hBOOL(hAPP(hAPP(c_member(X18),hAPP(c_Hilbert__Choice_Oinv__into(X18,X13,X15,X2),X11)),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__into) ).
fof(fact_inj__image__subset__iff,axiom,
! [X14,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X13,X18,X2,X15)),c_Set_Oimage(X13,X18,X2,X14)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_in__finite__psubset,axiom,
! [X14,X15,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X13,tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X15),X14)),c_Wellfounded_Ofinite__psubset(X13)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
& c_Finite__Set_Ofinite(X13,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_funcset__image,axiom,
! [X14,X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X18)),X2),c_FuncSet_OPi(X13,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X13),X14))))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X13,X18,X2,X15)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__image) ).
fof(fact_inv__into__injective,axiom,
! [X10,X11,X2,X15,X18,X13] :
( hAPP(c_Hilbert__Choice_Oinv__into(X13,X18,X15,X2),X11) = hAPP(c_Hilbert__Choice_Oinv__into(X13,X18,X15,X2),X10)
=> ( hBOOL(hAPP(hAPP(c_member(X18),X11),c_Set_Oimage(X13,X18,X2,X15)))
=> ( hBOOL(hAPP(hAPP(c_member(X18),X10),c_Set_Oimage(X13,X18,X2,X15)))
=> X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__injective) ).
fof(fact_Ints__odd__less__0,axiom,
! [X23,X13] :
( class_Rings_Olinordered__idom(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X23),c_Int_Oring__1__class_OInts(X13)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Oone__class_Oone(X13)),X23)),X23)),c_Groups_Ozero__class_Ozero(X13)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X23),c_Groups_Ozero__class_Ozero(X13))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_range__ex1__eq,axiom,
! [X22,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X18),X22),c_Set_Oimage(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))))
<=> ? [X3] :
( X22 = hAPP(X2,X3)
& ! [X67] :
( X22 = hAPP(X2,X67)
=> X67 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_card__image__le,axiom,
! [X2,X18,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X18,c_Set_Oimage(X13,X18,X2,X15))),c_Finite__Set_Ocard(X13,X15))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
fof(fact_inj__on__strict__subset,axiom,
! [X15,X14,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X14)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18,tc_HOL_Obool)),c_Set_Oimage(X13,X18,X2,X15)),c_Set_Oimage(X13,X18,X2,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_endo__inj__surj,axiom,
! [X2,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),c_Set_Oimage(X13,X13,X2,X15)),X15))
=> ( c_Fun_Oinj__on(X13,X13,X2,X15)
=> c_Set_Oimage(X13,X13,X2,X15) = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_card__inj__on__le,axiom,
! [X14,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X13,X18,X2,X15)),X14))
=> ( c_Finite__Set_Ofinite(X18,X14)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X18,X14))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_image__iff,axiom,
! [X15,X2,X18,X8,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X8),c_Set_Oimage(X18,X13,X2,X15)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X18),X3),X15))
& X8 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_card__inj,axiom,
! [X14,X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X18)),X2),c_FuncSet_OPi(X13,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X13),X14))))
=> ( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( c_Finite__Set_Ofinite(X18,X14)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X18,X14))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj) ).
fof(fact_Pi__anti__mono,axiom,
! [X14,X18,X15,X46,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X46),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X13,X18),tc_HOL_Obool),c_FuncSet_OPi(X13,X18,X15,X14)),c_FuncSet_OPi(X13,X18,X46,X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_finite__range__imageI,axiom,
! [X2,X36,X1,X18,X13] :
( c_Finite__Set_Ofinite(X13,c_Set_Oimage(X18,X13,X1,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))))
=> c_Finite__Set_Ofinite(X36,c_Set_Oimage(X18,X36,hAPP(c_COMBB(X13,X36,X18,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_const__Lin__Prof,axiom,
! [X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),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),X9)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_funcset__mem,axiom,
! [X11,X14,X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X18)),X2),c_FuncSet_OPi(X13,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X13),X14))))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X11)),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_image__mono,axiom,
! [X2,X18,X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),c_Set_Oimage(X13,X18,X2,X15)),c_Set_Oimage(X13,X18,X2,X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_mlex__leq,axiom,
! [X17,X13,X10,X11,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X11)),hAPP(X2,X10)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X11),X10)),X17))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X11),X10)),c_Wellfounded_Omlex__prod(X13,X2,X17))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_in__rel__def,axiom,
! [X10,X11,X17,X18,X13] :
( c_FunDef_Oin__rel(X13,X18,X17,X11,X10)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X18)),hAPP(hAPP(c_Product__Type_OPair(X13,X18),X11),X10)),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_f__inv__into__f,axiom,
! [X15,X2,X18,X10,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X10),c_Set_Oimage(X18,X13,X2,X15)))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X18,X13,X15,X2),X10)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_surj__iff__all,axiom,
! [X2,X13,X18] :
( c_Set_Oimage(X18,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))
<=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X18,X13,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X2),X3)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [X21,X13] :
( c_Nitpick_Orefl_H(X13,X21)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X3),X3)),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_inj__on__inv__into,axiom,
! [X15,X2,X18,X14,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),c_Set_Oimage(X18,X13,X2,X15)))
=> c_Fun_Oinj__on(X13,X18,c_Hilbert__Choice_Oinv__into(X18,X13,X15,X2),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
fof(fact_in__mkbot,axiom,
! [X8,X9,X10,X11] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11),X10)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X9),X8)))
<=> ( X10 != X8
& ( X11 = X8
=> X11 != X10 )
& ( X11 != 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),X11),X10)),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X8,X9,X10,X11] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11),X10)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X9),X8)))
<=> ( X11 != X8
& ( X10 = X8
=> X11 != X10 )
& ( X10 != 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),X11),X10)),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(help_c__COMBS__1,axiom,
! [X17,X57,X20,X13,X36,X18] : hAPP(c_COMBS(X18,X36,X13,X20,X57),X17) = hAPP(hAPP(X20,X17),hAPP(X57,X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_Pi__mem,axiom,
! [X11,X14,X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X18)),X2),c_FuncSet_OPi(X13,X18,X15,X14)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X11)),hAPP(X14,X11))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_inj__image__mem__iff,axiom,
! [X15,X23,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X23)),c_Set_Oimage(X13,X18,X2,X15)))
<=> hBOOL(hAPP(hAPP(c_member(X13),X23),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_image__surj__f__inv__f,axiom,
! [X15,X2,X13,X18] :
( c_Set_Oimage(X18,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))
=> c_Set_Oimage(X18,X13,X2,c_Set_Oimage(X13,X18,c_Hilbert__Choice_Oinv__into(X18,X13,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X2),X15)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
fof(fact_image__inv__into__cancel,axiom,
! [X68,X46,X15,X2,X13,X18] :
( c_Set_Oimage(X18,X13,X2,X15) = X46
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X68),X46))
=> c_Set_Oimage(X18,X13,X2,c_Set_Oimage(X13,X18,c_Hilbert__Choice_Oinv__into(X18,X13,X15,X2),X68)) = X68 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_inj__on__def,axiom,
! [X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X15))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X13),X5),X15))
=> ( hAPP(X2,X3) = hAPP(X2,X5)
=> X3 = X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_above__Lin,axiom,
! [X9,X10,X11] :
( X11 != X10
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),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,X9),X11),X10)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_range__composition,axiom,
! [X1,X2,X36,X13,X18] : c_Set_Oimage(X18,X13,hAPP(c_COMBB(X36,X13,X18,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Set_Oimage(X36,X13,X2,c_Set_Oimage(X18,X36,X1,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
fof(fact_finite__surj__inj,axiom,
! [X2,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),c_Set_Oimage(X13,X13,X2,X15)))
=> c_Fun_Oinj__on(X13,X13,X2,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_dictator__def,axiom,
! [X37,X28] :
( c_Arrow__Order__Mirabelle_Odictator(X28,X37)
<=> ! [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(X28,X3) = hAPP(X3,X37) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_inj__fun,axiom,
! [X36,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X13,tc_fun(X36,X18),hAPP(c_COMBB(X18,tc_fun(X36,X18),X13,c_COMBK(X18,X36)),X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
fof(fact_funcset__id,axiom,
! [X15,X13] : hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X13)),c_COMBI(X13)),c_FuncSet_OPi(X13,X13,X15,hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X13),X15)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_image__image,axiom,
! [X15,X1,X36,X2,X13,X18] : c_Set_Oimage(X18,X13,X2,c_Set_Oimage(X36,X18,X1,X15)) = c_Set_Oimage(X36,X13,hAPP(c_COMBB(X18,X13,X36,X2),X1),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_below__Lin,axiom,
! [X9,X10,X11] :
( X11 != X10
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),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(X9,X11,X10)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_in__measure,axiom,
! [X2,X10,X11,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X11),X10)),c_Wellfounded_Omeasure(X13,X2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X11)),hAPP(X2,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_inv__into__image__cancel,axiom,
! [X16,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X16),X15))
=> c_Set_Oimage(X18,X13,c_Hilbert__Choice_Oinv__into(X13,X18,X15,X2),c_Set_Oimage(X13,X18,X2,X16)) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
fof(fact_finite__surj,axiom,
! [X2,X14,X18,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18,tc_HOL_Obool),X14),c_Set_Oimage(X13,X18,X2,X15)))
=> c_Finite__Set_Ofinite(X18,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(fact_mkbot__Lin,axiom,
! [X11,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),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,X9),X11)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_mktop__Lin,axiom,
! [X11,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),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,X9),X11)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_image__inv__f__f,axiom,
! [X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> c_Set_Oimage(X18,X13,c_Hilbert__Choice_Oinv__into(X13,X18,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),c_Set_Oimage(X13,X18,X2,X15)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
fof(fact_inv__image__comp,axiom,
! [X73,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> c_Set_Oimage(X18,X13,c_Hilbert__Choice_Oinv__into(X13,X18,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),c_Set_Oimage(X13,X18,X2,X73)) = X73 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__image__comp) ).
fof(fact_surj__f__inv__f,axiom,
! [X10,X2,X13,X18] :
( c_Set_Oimage(X18,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X18,X13,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X2),X10)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
fof(fact_mlex__less,axiom,
! [X17,X13,X10,X11,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X11)),hAPP(X2,X10)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X11),X10)),c_Wellfounded_Omlex__prod(X13,X2,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_subset__card__intvl__is__intvl,axiom,
! [X48,X15] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X15),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X48,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),c_Finite__Set_Ocard(tc_Nat_Onat,X15)))))
=> X15 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X48,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),c_Finite__Set_Ocard(tc_Nat_Onat,X15))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
fof(fact_atLeastLessThan__subset__iff,axiom,
! [X79,X12,X22,X23,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X13,X23,X22)),c_SetInterval_Oord__class_OatLeastLessThan(X13,X12,X79)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X22),X23))
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X12),X23))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X22),X79)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_surj__imp__inj__inv,axiom,
! [X2,X13,X18] :
( c_Set_Oimage(X18,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))
=> c_Fun_Oinj__on(X13,X18,c_Hilbert__Choice_Oinv__into(X18,X13,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
fof(fact_rangeI,axiom,
! [X18,X11,X2,X13] : hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X11)),c_Set_Oimage(X18,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_inj__imp__surj__inv,axiom,
! [X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> c_Set_Oimage(X18,X13,c_Hilbert__Choice_Oinv__into(X13,X18,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
fof(fact_imageI,axiom,
! [X2,X18,X15,X11,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X11)),c_Set_Oimage(X13,X18,X2,X15))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
fof(fact_range__eqI,axiom,
! [X18,X13,X11,X2,X22] :
( X22 = hAPP(X2,X11)
=> hBOOL(hAPP(hAPP(c_member(X13),X22),c_Set_Oimage(X18,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_image__eqI,axiom,
! [X13,X15,X18,X11,X2,X22] :
( X22 = hAPP(X2,X11)
=> ( hBOOL(hAPP(hAPP(c_member(X18),X11),X15))
=> hBOOL(hAPP(hAPP(c_member(X13),X22),c_Set_Oimage(X18,X13,X2,X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X18,X2,X22,X15,X11,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( X22 = hAPP(X2,X11)
=> hBOOL(hAPP(hAPP(c_member(X18),X22),c_Set_Oimage(X13,X18,X2,X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__image__eq__iff,axiom,
! [X14,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( c_Set_Oimage(X13,X18,X2,X15) = c_Set_Oimage(X13,X18,X2,X14)
<=> X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_add__less__cancel__right,axiom,
! [X22,X12,X23,X13] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X22),X12)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X23),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X31,X33,X32,X13] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X33)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X22,X23,X12,X13] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X22)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X23),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X31,X32,X33,X13] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X31)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_finite__imageD,axiom,
! [X15,X2,X18,X13] :
( c_Finite__Set_Ofinite(X13,c_Set_Oimage(X18,X13,X2,X15))
=> ( c_Fun_Oinj__on(X18,X13,X2,X15)
=> c_Finite__Set_Ofinite(X18,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_psubset__trans,axiom,
! [X39,X14,X15,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X14),X39))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_add__le__imp__le__right,axiom,
! [X31,X33,X32,X13] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X33)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X22,X12,X23,X13] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X12)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X22),X12)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X23),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X31,X32,X33,X13] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X31)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X22,X23,X12,X13] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X23)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X23),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_insert__subset,axiom,
! [X14,X15,X11,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),c_Set_Oinsert(X13,X11,X15)),X14))
<=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X14))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_inv__f__f,axiom,
! [X11,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> hAPP(c_Hilbert__Choice_Oinv__into(X13,X18,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),hAPP(X2,X11)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__f) ).
fof(fact_inv__f__eq,axiom,
! [X10,X11,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( hAPP(X2,X11) = X10
=> hAPP(c_Hilbert__Choice_Oinv__into(X13,X18,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),X10) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__f__eq) ).
fof(fact_pred__equals__eq,axiom,
! [X16,X17,X13] :
( hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X17) = hAPP(hAPP(c_COMBC(X13,tc_fun(X13,tc_HOL_Obool),tc_HOL_Obool),c_member(X13)),X16)
<=> X17 = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X35,X45,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X35)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_inv__into__f__f,axiom,
! [X11,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> hAPP(c_Hilbert__Choice_Oinv__into(X13,X18,X15,X2),hAPP(X2,X11)) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
fof(fact_inv__into__f__eq,axiom,
! [X10,X11,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( hAPP(X2,X11) = X10
=> hAPP(c_Hilbert__Choice_Oinv__into(X13,X18,X15,X2),X10) = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [X2,X18,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( c_Finite__Set_Ocard(X18,c_Set_Oimage(X13,X18,X2,X15)) = c_Finite__Set_Ocard(X13,X15)
=> c_Fun_Oinj__on(X13,X18,X2,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X18,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( c_Fun_Oinj__on(X13,X18,X2,X15)
<=> c_Finite__Set_Ocard(X18,c_Set_Oimage(X13,X18,X2,X15)) = c_Finite__Set_Ocard(X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_insert__mono,axiom,
! [X23,X58,X39,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X39),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),c_Set_Oinsert(X13,X23,X39)),c_Set_Oinsert(X13,X23,X58))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(help_c__COMBB__1,axiom,
! [X17,X57,X20,X36,X13,X18] : hAPP(hAPP(c_COMBB(X18,X13,X36,X20),X57),X17) = hAPP(X20,hAPP(X57,X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__strict__mono,axiom,
! [X56,X33,X31,X32,X13] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X33),X56))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X56))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_image__add__atLeastLessThan,axiom,
! [X78,X37,X48] : 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)),X48),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X37,X78)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X48),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X78),X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X35,X45,X48] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X45)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X35)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_add__le__less__mono,axiom,
! [X56,X33,X31,X32,X13] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),X31))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X33),X56))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X56))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X56,X33,X31,X32,X13] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X33),X56))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X56))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_subset__psubset__trans,axiom,
! [X39,X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X14),X39))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X39,X14,X15,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),X39))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [X35,X45] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X45)),X35))
<=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_insert__image,axiom,
! [X2,X18,X15,X11,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Set_Oinsert(X18,hAPP(X2,X11),c_Set_Oimage(X13,X18,X2,X15)) = c_Set_Oimage(X13,X18,X2,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__image) ).
fof(fact_card__psubset,axiom,
! [X15,X14,X13] :
( c_Finite__Set_Ofinite(X13,X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X13,X14)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(fact_add__mono,axiom,
! [X56,X33,X31,X32,X13] :
( class_Groups_Oordered__ab__semigroup__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),X31))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X33),X56))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X56))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X23,X13] :
( class_Groups_Olinordered__ab__group__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X23)),c_Groups_Ozero__class_Ozero(X13)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X23),c_Groups_Ozero__class_Ozero(X13))) ) ),
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,X13] :
( class_Rings_Olinordered__idom(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X23)),c_Groups_Ozero__class_Ozero(X13)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X23),c_Groups_Ozero__class_Ozero(X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_add__less__mono,axiom,
! [X52,X49,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),X49),X52))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X49)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X52))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_image__insert,axiom,
! [X14,X23,X2,X13,X18] : c_Set_Oimage(X18,X13,X2,c_Set_Oinsert(X18,X23,X14)) = c_Set_Oinsert(X13,hAPP(X2,X23),c_Set_Oimage(X18,X13,X2,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__insert) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [X2,X13] :
( c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( c_Set_Oimage(X13,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))
=> c_Fun_Oinj__on(X13,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_subset__inj__on,axiom,
! [X15,X14,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> c_Fun_Oinj__on(X13,X18,X2,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_card__image,axiom,
! [X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> c_Finite__Set_Ocard(X18,c_Set_Oimage(X13,X18,X2,X15)) = c_Finite__Set_Ocard(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_add__neg__neg,axiom,
! [X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),c_Groups_Ozero__class_Ozero(X13)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),c_Groups_Ozero__class_Ozero(X13)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31)),c_Groups_Ozero__class_Ozero(X13))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_Ints__add,axiom,
! [X22,X23,X13] :
( class_Rings_Oring__1(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X23),c_Int_Oring__1__class_OInts(X13)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X22),c_Int_Oring__1__class_OInts(X13)))
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X22)),c_Int_Oring__1__class_OInts(X13))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__add) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X13] :
( c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X13,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> c_Set_Oimage(X13,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_add__strict__right__mono,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X31))) ) ),
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,X13] :
( class_Groups_Olinordered__ab__group__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X23)),c_Groups_Ozero__class_Ozero(X13)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X23),c_Groups_Ozero__class_Ozero(X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_add__nonpos__neg,axiom,
! [X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),c_Groups_Ozero__class_Ozero(X13)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),c_Groups_Ozero__class_Ozero(X13)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31)),c_Groups_Ozero__class_Ozero(X13))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),c_Groups_Ozero__class_Ozero(X13)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),c_Groups_Ozero__class_Ozero(X13)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31)),c_Groups_Ozero__class_Ozero(X13))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__le__mono,axiom,
! [X52,X49,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,X49),X52))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X51),X49)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X52))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_finite__Plus__iff,axiom,
! [X14,X15,X18,X13] :
( c_Finite__Set_Ofinite(tc_sum(X13,X18),c_Sum__Type_OPlus(X13,X18,X15,X14))
<=> ( c_Finite__Set_Ofinite(X13,X15)
& c_Finite__Set_Ofinite(X18,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X14,X15,X18,X13] :
( c_Finite__Set_Ofinite(tc_sum(X13,X18),c_Sum__Type_OPlus(X13,X18,X15,X14))
=> c_Finite__Set_Ofinite(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [X14,X15,X18,X13] :
( c_Finite__Set_Ofinite(tc_sum(X13,X18),c_Sum__Type_OPlus(X13,X18,X15,X14))
=> c_Finite__Set_Ofinite(X18,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_add__right__mono,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Oordered__ab__semigroup__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),X31))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X33))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Oordered__ab__semigroup__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),X31))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X31))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__lessD1,axiom,
! [X49,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)),X49))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X51),X49)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),c_Groups_Ozero__class_Ozero(X13)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),c_Groups_Ozero__class_Ozero(X13)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31)),c_Groups_Ozero__class_Ozero(X13))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_predicate2D,axiom,
! [X10,X11,X57,X20,X18,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_fun(X18,tc_HOL_Obool)),X20),X57))
=> ( hBOOL(hAPP(hAPP(X20,X11),X10))
=> hBOOL(hAPP(hAPP(X57,X11),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X57,X18,X13,X10,X11,X20] :
( hBOOL(hAPP(hAPP(X20,X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_fun(X18,tc_HOL_Obool)),X20),X57))
=> hBOOL(hAPP(hAPP(X57,X11),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_add__less__mono1,axiom,
! [X49,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),X49)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X49))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_inj__on__iff,axiom,
! [X10,X11,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X10),X15))
=> ( hAPP(X2,X11) = hAPP(X2,X10)
<=> X11 = X10 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__on__contraD,axiom,
! [X10,X11,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( X11 != X10
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X10),X15))
=> hAPP(X2,X11) != hAPP(X2,X10) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_inj__onD,axiom,
! [X10,X11,X15,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,X15)
=> ( hAPP(X2,X11) = hAPP(X2,X10)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X10),X15))
=> X11 = X10 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_add__leD1,axiom,
! [X43,X49,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X49)),X43))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X43,X49,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X49)),X43))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__pos__pos,axiom,
! [X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),X32))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),X31))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__le__mono1,axiom,
! [X49,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),X49)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X50),X49))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_psubsetD,axiom,
! [X12,X14,X15,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X12),X15))
=> hBOOL(hAPP(hAPP(c_member(X13),X12),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_psubset__card__mono,axiom,
! [X15,X14,X13] :
( c_Finite__Set_Ofinite(X13,X14)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X13,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_inj__on__add__nat,axiom,
! [X47,X48] : 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)),X48),X47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X56,X33,X31,X32,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X56)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_subset__trans,axiom,
! [X39,X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),X39))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X39)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_add__nonneg__pos,axiom,
! [X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X32))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),X31))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),X32))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X31))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_card__Plus__conv__if,axiom,
! [X14,X18,X15,X13] :
( ( ( c_Finite__Set_Ofinite(X13,X15)
& c_Finite__Set_Ofinite(X18,X14) )
=> c_Finite__Set_Ocard(tc_sum(X13,X18),c_Sum__Type_OPlus(X13,X18,X15,X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X18,X14)) )
& ( ~ ( c_Finite__Set_Ofinite(X13,X15)
& c_Finite__Set_Ofinite(X18,X14) )
=> c_Finite__Set_Ocard(tc_sum(X13,X18),c_Sum__Type_OPlus(X13,X18,X15,X14)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_card__Plus,axiom,
! [X14,X18,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( c_Finite__Set_Ofinite(X18,X14)
=> c_Finite__Set_Ocard(tc_sum(X13,X18),c_Sum__Type_OPlus(X13,X18,X15,X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X18,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_pos__add__strict,axiom,
! [X33,X31,X32,X13] :
( class_Rings_Olinordered__semidom(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),X32))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_card__insert__le,axiom,
! [X11,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__insert__le) ).
fof(fact_Ints__odd__nonzero,axiom,
! [X23,X13] :
( class_Int_Oring__char__0(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X23),c_Int_Oring__1__class_OInts(X13)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Oone__class_Oone(X13)),X23)),X23) != c_Groups_Ozero__class_Ozero(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X23,X13] :
( class_Groups_Olinordered__ab__group__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X23)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_add__gr__0,axiom,
! [X35,X45] :
( 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),X45),X35)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X45))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_card__seteq,axiom,
! [X15,X14,X13] :
( c_Finite__Set_Ofinite(X13,X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X13,X14)),c_Finite__Set_Ocard(X13,X15)))
=> X15 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_subset__insertI2,axiom,
! [X22,X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),c_Set_Oinsert(X13,X22,X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_add__strict__increasing2,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X32))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),X32))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),X33))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X32))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X31))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_psubset__imp__subset,axiom,
! [X14,X15,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
| X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__eq,axiom,
! [X14,X15,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),X15),X14))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
& X15 != X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_insert__iff,axiom,
! [X15,X22,X23,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X23),c_Set_Oinsert(X13,X22,X15)))
<=> ( X23 = X22
| hBOOL(hAPP(hAPP(c_member(X13),X23),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X15,X22,X23,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X23),c_Set_Oinsert(X13,X22,X15)))
=> ( X23 != X22
=> hBOOL(hAPP(hAPP(c_member(X13),X23),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X23,X13] :
( class_Groups_Olinordered__ab__group__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X23)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X23)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_Pi__UNIV,axiom,
! [X15,X18,X13] : c_FuncSet_OPi(X13,X18,X15,hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X13),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X13,X18),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
fof(fact_add__increasing,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X32))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),X33))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X32,X31,X33,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X33))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),X32))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_finite__Plus,axiom,
! [X14,X18,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( c_Finite__Set_Ofinite(X18,X14)
=> c_Finite__Set_Ofinite(tc_sum(X13,X18),c_Sum__Type_OPlus(X13,X18,X15,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(help_c__COMBC__1,axiom,
! [X17,X57,X20,X13,X36,X18] : hAPP(hAPP(hAPP(c_COMBC(X18,X36,X13),X20),X57),X17) = hAPP(hAPP(X20,X17),X57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_set__eq__subset,axiom,
! [X13,X14,X15] :
( X15 = X14
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),X15))
=> X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_set__rev__mp,axiom,
! [X14,X15,X11,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> hBOOL(hAPP(hAPP(c_member(X13),X11),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_in__mono,axiom,
! [X11,X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> hBOOL(hAPP(hAPP(c_member(X13),X11),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_set__mp,axiom,
! [X11,X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> hBOOL(hAPP(hAPP(c_member(X13),X11),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_subsetD,axiom,
! [X12,X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X12),X15))
=> hBOOL(hAPP(hAPP(c_member(X13),X12),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_le__funE,axiom,
! [X11,X1,X2,X13,X18] :
( class_Orderings_Oord(X18)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,X18),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,hAPP(X2,X11)),hAPP(X1,X11))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_le__funD,axiom,
! [X11,X1,X2,X13,X18] :
( class_Orderings_Oord(X18)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,X18),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X18,hAPP(X2,X11)),hAPP(X1,X11))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_finite__imageI,axiom,
! [X66,X18,X28,X13] :
( c_Finite__Set_Ofinite(X13,X28)
=> c_Finite__Set_Ofinite(X18,c_Set_Oimage(X13,X18,X66,X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_card__mono,axiom,
! [X15,X14,X13] :
( c_Finite__Set_Ofinite(X13,X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X13,X15)),c_Finite__Set_Ocard(X13,X14))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X33,X31,X32,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_inj__eq,axiom,
! [X10,X11,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( hAPP(X2,X11) = hAPP(X2,X10)
<=> X11 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [X10,X11,X2,X18,X13] :
( c_Fun_Oinj__on(X13,X18,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( hAPP(X2,X11) = hAPP(X2,X10)
=> X11 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
fof(fact_atLeastLessThan__eq__iff,axiom,
! [X79,X12,X22,X23,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X23),X22))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X12),X79))
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X13,X23,X22) = c_SetInterval_Oord__class_OatLeastLessThan(X13,X12,X79)
<=> ( X23 = X12
& X22 = X79 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [X79,X12,X22,X23,X13] :
( class_Orderings_Olinorder(X13)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X13,X23,X22) = c_SetInterval_Oord__class_OatLeastLessThan(X13,X12,X79)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X23),X22))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X12),X79))
=> X23 = X12 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__inj_I2_J,axiom,
! [X79,X12,X22,X23,X13] :
( class_Orderings_Olinorder(X13)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X13,X23,X22) = c_SetInterval_Oord__class_OatLeastLessThan(X13,X12,X79)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X23),X22))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X12),X79))
=> X22 = X79 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_less__add__Suc1,axiom,
! [X44,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),X44)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X44,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),X44),X51)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_insertI2,axiom,
! [X22,X14,X23,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X23),X14))
=> hBOOL(hAPP(hAPP(c_member(X13),X23),c_Set_Oinsert(X13,X22,X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_less__trans__Suc,axiom,
! [X49,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),X49))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X51)),X49)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [X13] :
( c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,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(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,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,
~ ! [X74] :
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X74,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,X74,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__SucD,axiom,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),hAPP(c_Nat_OSuc,X43)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__less__eq,axiom,
! [X35,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X45)),hAPP(c_Nat_OSuc,X35)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [X18,X13] :
( c_Finite__Set_Ofinite(tc_fun(X13,X18),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X13,X18),tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X18,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_order__less__trans,axiom,
! [X34,X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X34,X29,X30,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X34),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X34),X29)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_image__Suc__atLeastLessThan,axiom,
! [X78,X37] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X37,X78)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X37),hAPP(c_Nat_OSuc,X78)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X10,X11,X13] :
( class_Groups_Oordered__comm__monoid__add(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),X10))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X11),X10) = c_Groups_Ozero__class_Ozero(X13)
<=> ( X11 = c_Groups_Ozero__class_Ozero(X13)
& X10 = c_Groups_Ozero__class_Ozero(X13) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [X18,X13] : c_Sum__Type_OPlus(X13,X18,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X13,X18),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X34,X30,X29] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X34))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X44,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),X44))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X30,X34,X29] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X34))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X44,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),X44),X50))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X35,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X35)))
<=> ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X64] :
( X45 = hAPP(c_Nat_OSuc,X64)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),X35)) ) ) ),
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,
! [X33,X31,X32,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X33)) ),
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,
! [X33,X31,X32,X13] :
( class_Groups_Oab__semigroup__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X33)) ),
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,
! [X56,X33,X32,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X56)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_insert__code,axiom,
! [X11,X15,X10,X13] :
( hBOOL(hAPP(c_Set_Oinsert(X13,X10,X15),X11))
<=> ( X10 = X11
| hBOOL(hAPP(X15,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_zero__less__two,axiom,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Oone__class_Oone(X13)),c_Groups_Oone__class_Oone(X13)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_Suc__le__mono,axiom,
! [X45,X35] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35)),hAPP(c_Nat_OSuc,X45)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_order__le__less__trans,axiom,
! [X34,X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X34,X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I8_J,axiom,
! [X34,X29,X30,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X34),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X34),X29)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X34,X29,X30,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X34),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X34),X29)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X18,X13] :
( c_Finite__Set_Ofinite(tc_sum(X13,X18),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X13,X18),tc_HOL_Obool)))
<=> ( c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
& c_Finite__Set_Ofinite(X18,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X18,X13] :
( c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( c_Finite__Set_Ofinite(X18,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(tc_prod(X13,X18),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X13,X18),tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_less__add__eq__less,axiom,
! [X43,X44,X52,X49] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X49),X52))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X52) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X49),X43)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_subset__insertI,axiom,
! [X23,X14,X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),c_Set_Oinsert(X13,X23,X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_Suc__lessD,axiom,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X43))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__mono,axiom,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),hAPP(c_Nat_OSuc,X43))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X34,X30,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X34))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add1,axiom,
! [X44,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),X44))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X30,X34,X29] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X34))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_trans__le__add2,axiom,
! [X44,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),X44),X50))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X18,X13] :
( c_Finite__Set_Ofinite(tc_fun(X13,X18),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X13,X18),tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(X18,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_nat__add__assoc,axiom,
! [X49,X43,X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),X49) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X49)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_less__eq__Suc__le,axiom,
! [X45,X35] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X45))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35)),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X35,X45] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X45)),X35))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44)),X43))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_predicate1D,axiom,
! [X11,X57,X20,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X20),X57))
=> ( hBOOL(hAPP(X20,X11))
=> hBOOL(hAPP(X57,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X57,X13,X11,X20] :
( hBOOL(hAPP(X20,X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X20),X57))
=> hBOOL(hAPP(X57,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_order__trans,axiom,
! [X34,X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X34,X29,X30,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X34),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X34),X29)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_Suc__lessI,axiom,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
=> ( hAPP(c_Nat_OSuc,X44) != X43
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X43)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__add__one,axiom,
! [X32,X13] :
( class_Rings_Olinordered__semidom(X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),c_Groups_Oone__class_Oone(X13)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_le__less__Suc__eq,axiom,
! [X35,X45] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,X45)))
<=> X35 = X45 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__leD,axiom,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44)),X43))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X47] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X47)
<=> ? [X38] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X47))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_insert__commute,axiom,
! [X15,X10,X11,X13] : c_Set_Oinsert(X13,X11,c_Set_Oinsert(X13,X10,X15)) = c_Set_Oinsert(X13,X10,c_Set_Oinsert(X13,X11,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_insertI1,axiom,
! [X14,X23,X13] : hBOOL(hAPP(hAPP(c_member(X13),X23),c_Set_Oinsert(X13,X23,X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_less__Suc__eq,axiom,
! [X35,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X35)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35))
| X45 = X35 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__leI,axiom,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44)),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X56,X33,X32,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X56)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_le__trans,axiom,
! [X49,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),X49))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51),X49)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_finite__subset,axiom,
! [X14,X15,X13] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ( c_Finite__Set_Ofinite(X13,X14)
=> c_Finite__Set_Ofinite(X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [X15,X14,X13] :
( c_Finite__Set_Ofinite(X13,X14)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> c_Finite__Set_Ofinite(X13,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_less__iff__Suc__add,axiom,
! [X35,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35))
<=> ? [X53] : X35 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X53)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__Suc__eq__le,axiom,
! [X35,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,X35)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X47] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X47)
<=> ? [X38] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X47))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_less__SucI,axiom,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X43))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [X23,X13] :
( class_Int_Oring__char__0(X13)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X23),c_Int_Oring__1__class_OInts(X13)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X23) = c_Groups_Ozero__class_Ozero(X13)
<=> X23 = c_Groups_Ozero__class_Ozero(X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_nat__case__Suc,axiom,
! [X63,X71,X72,X13] : c_Nat_Onat_Onat__case(X13,X72,X71,hAPP(c_Nat_OSuc,X63)) = hAPP(X71,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_le__Suc__eq,axiom,
! [X35,X45] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),hAPP(c_Nat_OSuc,X35)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35))
| X45 = hAPP(c_Nat_OSuc,X35) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_subset__UNIV,axiom,
! [X15,X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_nat__less__cases,axiom,
! [X20,X35,X45] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35))
=> hBOOL(hAPP(hAPP(X20,X35),X45)) )
=> ( ( X45 = X35
=> hBOOL(hAPP(hAPP(X20,X35),X45)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X45))
=> hBOOL(hAPP(hAPP(X20,X35),X45)) )
=> hBOOL(hAPP(hAPP(X20,X35),X45)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_nat__add__left__commute,axiom,
! [X34,X30,X29] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X34)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29),X34)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_xt1_I5_J,axiom,
! [X29,X30,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
=> X29 = X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X30,X29,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29))
=> X29 = X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X11,X10,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X10),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
<=> X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X10,X11,X13] :
( class_Orderings_Oorder(X13)
=> ( X11 = X10
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X10),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_card__ge__0__finite,axiom,
! [X15,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X13,X15)))
=> c_Finite__Set_Ofinite(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_le__imp__less__Suc,axiom,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X43))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X15,X13] :
( c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X13,X15) = c_Finite__Set_Ocard(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> X15 = c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_order__le__less,axiom,
! [X10,X11,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
| X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X10,X11,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
& X11 != X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__less__imp__le,axiom,
! [X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_le__add1,axiom,
! [X44,X43] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X44))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X44,X43] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_image__ident,axiom,
! [X69,X13] : c_Set_Oimage(X13,X13,c_COMBI(X13),X69) = X69,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_inj__on__id2,axiom,
! [X15,X13] : c_Fun_Oinj__on(X13,X13,c_COMBI(X13),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(fact_nat__case__0,axiom,
! [X71,X72,X13] : c_Nat_Onat_Onat__case(X13,X72,X71,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X72,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
fof(fact_xt1_I11_J,axiom,
! [X32,X31,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),X32))
=> ( X32 != X31
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X31,X32,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),X31))
=> ( X32 != X31
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X30,X29,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
| X29 = X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X31,X32,X13] :
( class_Orderings_Oorder(X13)
=> ( X32 != X31
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X32),X31))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_xt1_I12_J,axiom,
! [X31,X32,X13] :
( class_Orderings_Oorder(X13)
=> ( X32 != X31
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X31),X32))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),X32)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_less__Suc0,axiom,
! [X35] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_inj__Suc,axiom,
! [X47] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_le__antisym,axiom,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43),X44))
=> X44 = X43 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_eq__mem,axiom,
! [X10,X11,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X11),hAPP(c_fequal,X10)))
<=> X11 = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__SucI,axiom,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),hAPP(c_Nat_OSuc,X43))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_nat__less__le,axiom,
! [X35,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35))
& X45 != X35 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X35,X45] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35))
| X45 = X35 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_less__imp__le__nat,axiom,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X43,X44] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
| X44 = X43 )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X30,X29] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X29),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_insert__absorb,axiom,
! [X15,X23,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X23),X15))
=> c_Set_Oinsert(X13,X23,X15) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_linorder__neq__iff,axiom,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( X11 != X10
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X10),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
| X29 = X30
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_finite__option__UNIV,axiom,
! [X13] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X13),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X13),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_le__neq__implies__less,axiom,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
=> ( X44 != X43
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_insert__absorb2,axiom,
! [X15,X11,X13] : c_Set_Oinsert(X13,X11,c_Set_Oinsert(X13,X11,X15)) = c_Set_Oinsert(X13,X11,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [X11,X13] : hBOOL(hAPP(hAPP(c_member(X13),X11),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_UNIV__I,axiom,
! [X11,X13] : hBOOL(hAPP(hAPP(c_member(X13),X11),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_finite__insert,axiom,
! [X15,X23,X13] :
( c_Finite__Set_Ofinite(X13,c_Set_Oinsert(X13,X23,X15))
<=> c_Finite__Set_Ofinite(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__insert) ).
fof(fact_mem__def,axiom,
! [X15,X11,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
<=> hBOOL(hAPP(X15,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_linorder__le__less__linear,axiom,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_add__Suc,axiom,
! [X43,X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X43) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_le__iff__add,axiom,
! [X35,X45] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35))
<=> ? [X53] : X35 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_nat__neq__iff,axiom,
! [X35,X45] :
( X45 != X35
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X45)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_gr0__conv__Suc,axiom,
! [X35] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
<=> ? [X38] : X35 = hAPP(c_Nat_OSuc,X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X30,X29,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> X30 != X29 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X30,X29,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> X29 != X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X30,X29,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> X29 != X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_equalityD1,axiom,
! [X13,X14,X15] :
( X15 = X14
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X13,X14,X15] :
( X15 = X14
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_subset__refl,axiom,
! [X15,X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_neq0__conv,axiom,
! [X35] :
( X35 != 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)),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_add__right__cancel,axiom,
! [X12,X23,X22,X13] :
( class_Groups_Ocancel__semigroup__add(X13)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X22),X23) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X12),X23)
<=> X22 = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__right__imp__eq,axiom,
! [X33,X32,X31,X13] :
( class_Groups_Ocancel__semigroup__add(X13)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X31),X32) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X32)
=> X31 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Ocancel__ab__semigroup__add(X13)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)
=> X31 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X12,X22,X23,X13] :
( class_Groups_Ocancel__semigroup__add(X13)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X12)
<=> X22 = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [X33,X31,X32,X13] :
( class_Groups_Ocancel__semigroup__add(X13)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33)
=> X31 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_linorder__linear,axiom,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_add__Suc__right,axiom,
! [X43,X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X43)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_add__Suc__shift,axiom,
! [X43,X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X43) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_nat_Osize_I4_J,axiom,
! [X65] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X65)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X65)),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,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
=> X43 != 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,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zero__less__Suc,axiom,
! [X43] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X43))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_less__not__refl2,axiom,
! [X44,X43] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X44))
=> X44 != X43 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [X54,X55] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X54))
=> X55 != X54 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_zero__less__one,axiom,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),c_Groups_Oone__class_Oone(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_Ints__0,axiom,
! [X13] :
( class_Rings_Oring__1(X13)
=> hBOOL(hAPP(hAPP(c_member(X13),c_Groups_Ozero__class_Ozero(X13)),c_Int_Oring__1__class_OInts(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(fact_Ints__1,axiom,
! [X13] :
( class_Rings_Oring__1(X13)
=> hBOOL(hAPP(hAPP(c_member(X13),c_Groups_Oone__class_Oone(X13)),c_Int_Oring__1__class_OInts(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(fact_nat__add__right__cancel,axiom,
! [X35,X48,X45] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X48) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X35),X48)
<=> X45 = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X35,X45,X48] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X45) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X48),X35)
<=> X45 = X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_finite_OinsertI,axiom,
! [X23,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> c_Finite__Set_Ofinite(X13,c_Set_Oinsert(X13,X23,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_lessI,axiom,
! [X43] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X43))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_top1I,axiom,
! [X11,X13] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_le__0__eq,axiom,
! [X35] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X35),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X35 = 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,
! [X35,X45] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X35) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X45 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X35 = 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,
! [X35,X45] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X35)
<=> ( ( X45 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X35 = 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,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Ozero__class_Ozero(X13)),c_Groups_Oone__class_Oone(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_finite__atLeastLessThan,axiom,
! [X76,X77] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X77,X76)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(fact_nat_Osize_I2_J,axiom,
! [X65] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X65)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X65)),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,
! [X33,X32,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X33),X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_gr0I,axiom,
! [X43] :
( X43 != 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)),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_top__greatest,axiom,
! [X29,X13] :
( class_Orderings_Otop(X13)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),c_Orderings_Otop__class_Otop(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_double__eq__0__iff,axiom,
! [X23,X13] :
( class_Groups_Olinordered__ab__group__add(X13)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X23) = c_Groups_Ozero__class_Ozero(X13)
<=> X23 = c_Groups_Ozero__class_Ozero(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X23,X13] :
( class_Groups_Olinordered__ab__group__add(X13)
=> ( c_Groups_Ozero__class_Ozero(X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X23),X23)
<=> X23 = c_Groups_Ozero__class_Ozero(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__iff,axiom,
! [X23,X22,X13] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X13)
=> ( X22 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X22),X23)
<=> X23 = c_Groups_Ozero__class_Ozero(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_order__eq__refl,axiom,
! [X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( X29 = X30
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(help_c__COMBK__1,axiom,
! [X83,X82,X18,X13] : hAPP(hAPP(c_COMBK(X13,X18),X82),X83) = X82,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_nat__add__commute,axiom,
! [X43,X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_order__refl,axiom,
! [X29,X13] :
( class_Orderings_Opreorder(X13)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X29)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X43] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X43] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_top__apply,axiom,
! [X11,X18,X13] :
( class_Orderings_Otop(X13)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X18,X13)),X11) = c_Orderings_Otop__class_Otop(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_add__is__0,axiom,
! [X35,X45] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X35) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X45 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X35 = 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,
! [X43,X44] :
( X44 = X43
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(help_c__fequal__2,axiom,
! [X10,X11] :
( X11 != X10
| hBOOL(hAPP(hAPP(c_fequal,X11),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_add__eq__self__zero,axiom,
! [X43,X44] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43) = X44
=> X43 = 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,
! [X43] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X43),X43)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_finite__UNIV,axiom,
! [X13] :
( class_Finite__Set_Ofinite(X13)
=> c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,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,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Ozero__class_Ozero(X13)),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,X13] :
( class_Groups_Omonoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Ozero__class_Ozero(X13)),X32) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X32,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Ozero__class_Ozero(X13)),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,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),c_Groups_Ozero__class_Ozero(X13)) = 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,X13] :
( class_Groups_Omonoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),c_Groups_Ozero__class_Ozero(X13)) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X32,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X32),c_Groups_Ozero__class_Ozero(X13)) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X43] : hAPP(c_Nat_OSuc,X43) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_Suc__eq__plus1,axiom,
! [X43] : hAPP(c_Nat_OSuc,X43) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),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,
! [X43] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X43) = X43,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X35] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X44,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [X81,X80] :
( ( class_Finite__Set_Ofinite(X80)
& class_Finite__Set_Ofinite(X81) )
=> class_Finite__Set_Ofinite(tc_sum(X80,X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [X81,X80] :
( ( class_Finite__Set_Ofinite(X80)
& class_Finite__Set_Ofinite(X81) )
=> class_Finite__Set_Ofinite(tc_fun(X80,X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X81,X80] :
( ( class_Finite__Set_Ofinite(X80)
& class_Finite__Set_Ofinite(X81) )
=> class_Finite__Set_Ofinite(tc_prod(X80,X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(fact_nat_Oinject,axiom,
! [X62,X63] :
( hAPP(c_Nat_OSuc,X63) = hAPP(c_Nat_OSuc,X62)
<=> X63 = X62 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__inject,axiom,
! [X30,X29] :
( hAPP(c_Nat_OSuc,X29) = hAPP(c_Nat_OSuc,X30)
=> X29 = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X80,X81] :
( class_Orderings_Oord(X81)
=> class_Orderings_Oord(tc_fun(X80,X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X80,X81] :
( class_Orderings_Oorder(X81)
=> class_Orderings_Oorder(tc_fun(X80,X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X80,X81] :
( class_Orderings_Opreorder(X81)
=> class_Orderings_Opreorder(tc_fun(X80,X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Otop,axiom,
! [X80,X81] :
( class_Orderings_Otop(X81)
=> class_Orderings_Otop(tc_fun(X80,X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(fact_Suc__neq__Zero,axiom,
! [X44] : hAPP(c_Nat_OSuc,X44) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X61] : hAPP(c_Nat_OSuc,X61) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__not__Zero,axiom,
! [X44] : hAPP(c_Nat_OSuc,X44) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_Zero__neq__Suc,axiom,
! [X44] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__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__not__Suc,axiom,
! [X44] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_finite,axiom,
! [X15,X13] :
( class_Finite__Set_Ofinite(X13)
=> c_Finite__Set_Ofinite(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_finite__code,axiom,
! [X15,X13] :
( class_Finite__Set_Ofinite(X13)
=> c_Finite__Set_Ofinite(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_Suc__n__not__n,axiom,
! [X43] : hAPP(c_Nat_OSuc,X43) != X43,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X43] : X43 != hAPP(c_Nat_OSuc,X43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(help_c__COMBI__1,axiom,
! [X82,X13] : hAPP(c_COMBI(X13),X82) = X82,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_one__neq__zero,axiom,
! [X13] :
( class_Rings_Ozero__neq__one(X13)
=> c_Groups_Oone__class_Oone(X13) != c_Groups_Ozero__class_Ozero(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_zero__neq__one,axiom,
! [X13] :
( class_Rings_Ozero__neq__one(X13)
=> c_Groups_Ozero__class_Ozero(X13) != c_Groups_Oone__class_Oone(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [X81] :
( class_Finite__Set_Ofinite(X81)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X81)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(fact_nat__size,axiom,
! [X43] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X43) = X43,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096) ).
fof(fact_n_I3_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n_I3_J) ).
fof(fact_assms_I1_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),v_h____),v_n____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096) ).
fof(fact__096P_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
fof(fact_Prof__def,axiom,
c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Prof__def) ).
fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
fof(fact__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__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_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__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_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__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__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_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_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_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_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_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(fact__096a_A_126_061_Ab_096,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
fof(fact__096c_A_126_061_Ad_096,axiom,
v_c____ != v_d____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_126_061_Ad_096) ).
fof(i_0_519,negated_conjecture,
~ ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,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(assume_negation,[status(cth)],[conj_0]) ).
fof(i_0_520,plain,
~ ! [X42] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> ( ! [X38] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38),X42))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X38))),v_Lab____)),v_Lba____)))) )
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ),
inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(i_0_521,plain,
! [X11,X15,X28,X1,X8,X2,X18,X13] :
( c_Finite__Set_Ofolding__image__simple(X13,X18,X2,X8,X1,X28)
=> ( c_Finite__Set_Ofinite(X18,X15)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X18),X11),X15))
=> hAPP(X28,c_Set_Oinsert(X18,X11,X15)) = hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X28,X15)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(i_0_522,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_523,plain,
! [X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X13,c_Set_Oimage(X18,X13,X2,X15))),c_Finite__Set_Ocard(X18,X15)))
=> ~ c_Fun_Oinj__on(X18,X13,X2,X15) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).
fof(i_0_524,plain,
! [X15,X13] :
( ( c_Finite__Set_Ofinite(X13,X15)
=> c_Finite__Set_Ocard(X13,X15) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) )
& ( ~ c_Finite__Set_Ofinite(X13,X15)
=> c_Finite__Set_Ocard(X13,X15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_card__def]) ).
fof(i_0_525,plain,
! [X10,X11,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),c_Arrow__Order__Mirabelle_OLin))
=> ( X11 != X10
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X11),X10)),X9))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X10),X11)),X9)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_526,plain,
! [X22,X23,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X9),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)),X9))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X22),X23)),X9)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_527,plain,
! [X11,X14,X15,X2,X18,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X18)),X2),c_FuncSet_OPi(X13,X18,X15,X14)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X18),hAPP(X2,X11)),hAPP(X14,X11)))
=> ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_528,plain,
! [X14,X15,X11,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),c_Set_Oinsert(X13,X11,X14)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14)) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_529,plain,
~ ! [X40] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X40))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X40),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_530,plain,
~ ! [X41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X41))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X41),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_531,plain,
! [X1,X2,X13,X18] :
( class_Orderings_Oord(X18)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,X18)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,X18),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,X18),X1),X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_532,plain,
! [X43,X49,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X49)),X43))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X49),X43)) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_533,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_534,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_535,plain,
! [X35,X20] :
( ~ hBOOL(hAPP(X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X20,X35))
=> ? [X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X53),X35))
& ! [X4] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4),X53))
=> ~ hBOOL(hAPP(X20,X4)) )
& hBOOL(hAPP(X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_536,plain,
! [X22,X14,X23,X13] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X13),X23),X14))
=> X23 = X22 )
=> hBOOL(hAPP(hAPP(c_member(X13),X23),c_Set_Oinsert(X13,X22,X14))) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_537,plain,
! [X14,X15,X11,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X14))
=> ( c_Set_Oinsert(X13,X11,X15) = c_Set_Oinsert(X13,X11,X14)
<=> X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_538,plain,
! [X35,X45] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X45),X35))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X35)),X45)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_539,plain,
! [X35,X45] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X35))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,X45))) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_540,plain,
! [X32,X31,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),X32))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31)) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_541,plain,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X10),X11))
| X11 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_542,plain,
! [X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_543,plain,
! [X31,X32,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X32),X31))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X31),X32)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_544,plain,
! [X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_545,plain,
! [X30,X29,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_546,plain,
! [X11,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X13,X15)) ) ),
inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).
fof(i_0_547,plain,
! [X10,X11,X13] :
( class_Orderings_Opreorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X10),X11)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_548,plain,
! [X11,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( ( hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)) = c_Finite__Set_Ocard(X13,X15) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X13,X15)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).
fof(i_0_549,plain,
! [X43,X44] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X43)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
=> X44 = X43 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_550,plain,
! [X44,X43] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X44))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_OSuc,X44)))
=> X44 = X43 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_551,plain,
! [X45,X35] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),X45))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X35),hAPP(c_Nat_OSuc,X45)))
<=> X35 = X45 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_552,plain,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> X11 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_553,plain,
! [X29,X30,X13] :
( class_Orderings_Olinorder(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_554,plain,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_555,plain,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_556,plain,
! [X11,X15,X13] :
( c_Finite__Set_Ofinite(X13,X15)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X11),X15))
=> c_Finite__Set_Ocard(X13,c_Set_Oinsert(X13,X11,X15)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X13,X15)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).
fof(i_0_557,plain,
! [X43,X44] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),hAPP(c_Nat_OSuc,X43)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X44),X43))
=> X44 = hAPP(c_Nat_OSuc,X43) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_558,plain,
! [X43] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X43)),X43)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_559,plain,
! [X10,X11,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X11),X10))
<=> X11 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_560,plain,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Oone__class_Oone(X13)),c_Groups_Ozero__class_Ozero(X13))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_561,plain,
! [X30,X29,X13] :
( class_Rings_Olinordered__idom(X13)
=> ( X29 != X30
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_562,plain,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> ( X29 != X30
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_563,plain,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( X29 != X30
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X30),X29)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_564,plain,
! [X11,X10,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X10),X11))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X11),X10))
<=> X11 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_565,plain,
! [X29,X30,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_566,plain,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_567,plain,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,c_Groups_Oone__class_Oone(X13)),c_Groups_Ozero__class_Ozero(X13))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_568,plain,
! [X30,X29] :
( X29 != X30
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X29)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_569,plain,
! [X13,X14,X15] :
( X15 = X14
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X15),X14))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X14),X15)) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_570,plain,
! [X29,X13] :
( class_Orderings_Opreorder(X13)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X29),X29)) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_571,plain,
! [X30,X29,X13] :
( class_Orderings_Olinorder(X13)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X29),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,X30),X29)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_572,plain,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_573,plain,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_574,plain,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_575,plain,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X43)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_576,plain,
! [X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X43)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_577,plain,
! [X10,X11] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X11),X10))
| X11 = X10 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_578,plain,
! [X15,X13] :
( ~ c_Finite__Set_Ofinite(X13,X15)
=> c_Finite__Set_Ocard(X13,X15) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
fof(i_0_579,negated_conjecture,
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,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,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(fof_nnf,[status(thm)],[i_0_519]) ).
fof(i_0_580,plain,
! [X2307] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk29_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,X2307),esk29_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____)),X2307))),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),esk29_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_581,plain,
! [X2126] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk27_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,X2126),esk27_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____)),X2126))),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),esk27_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_582,plain,
! [X1914] : hBOOL(hAPP(hAPP(c_member(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____)),X1914))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
inference(variable_rename,[status(thm)],[fact_PiProf]) ).
fof(i_0_583,plain,
! [X1931] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1931),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X1931))),v_Lab____)),v_Lba____)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n_I2_J])]) ).
fof(i_0_584,plain,
! [X2222,X2223,X2224,X2225] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2225,tc_fun(X2224,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2225,tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_fun(X2224,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2224,tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_fun(X2224,tc_HOL_Obool)),X2225,c_COMBC(X2224,tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2224,tc_prod(X2225,X2224)),tc_fun(X2224,tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),X2225,c_COMBB(tc_prod(X2225,X2224),tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool),X2224,c_member(tc_prod(X2225,X2224)))),c_Product__Type_OPair(X2225,X2224)))),X2223)),hAPP(hAPP(c_COMBC(X2225,tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_fun(X2224,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2224,tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_fun(X2224,tc_HOL_Obool)),X2225,c_COMBC(X2224,tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2224,tc_prod(X2225,X2224)),tc_fun(X2224,tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),X2225,c_COMBB(tc_prod(X2225,X2224),tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool),X2224,c_member(tc_prod(X2225,X2224)))),c_Product__Type_OPair(X2225,X2224)))),X2222)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),X2223),X2222)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),X2223),X2222))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2225,tc_fun(X2224,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2225,tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_fun(X2224,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2224,tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_fun(X2224,tc_HOL_Obool)),X2225,c_COMBC(X2224,tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2224,tc_prod(X2225,X2224)),tc_fun(X2224,tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),X2225,c_COMBB(tc_prod(X2225,X2224),tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool),X2224,c_member(tc_prod(X2225,X2224)))),c_Product__Type_OPair(X2225,X2224)))),X2223)),hAPP(hAPP(c_COMBC(X2225,tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_fun(X2224,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2224,tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_fun(X2224,tc_HOL_Obool)),X2225,c_COMBC(X2224,tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2224,tc_prod(X2225,X2224)),tc_fun(X2224,tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool)),X2225,c_COMBB(tc_prod(X2225,X2224),tc_fun(tc_fun(tc_prod(X2225,X2224),tc_HOL_Obool),tc_HOL_Obool),X2224,c_member(tc_prod(X2225,X2224)))),c_Product__Type_OPair(X2225,X2224)))),X2222))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_585,plain,
! [X1736,X1737,X1738,X1739,X1740,X1741] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1741),X1740)),hAPP(v_F,X1737)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1739),X1738)),hAPP(v_F,X1736)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1741),X1740)),hAPP(X1737,esk8_6(X1736,X1737,X1738,X1739,X1740,X1741))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1739),X1738)),hAPP(X1736,esk8_6(X1736,X1737,X1738,X1739,X1740,X1741))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1736),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))),X1737),c_Arrow__Order__Mirabelle_OProf))
| X1740 = X1739
| X1741 = X1738
| X1739 = X1738
| X1741 = X1740 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1739),X1738)),hAPP(v_F,X1736)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1741),X1740)),hAPP(v_F,X1737)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1741),X1740)),hAPP(X1737,esk8_6(X1736,X1737,X1738,X1739,X1740,X1741))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1739),X1738)),hAPP(X1736,esk8_6(X1736,X1737,X1738,X1739,X1740,X1741))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1736),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))),X1737),c_Arrow__Order__Mirabelle_OProf))
| X1740 = X1739
| X1741 = X1738
| X1739 = X1738
| X1741 = X1740 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1741),X1740)),hAPP(v_F,X1737)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1739),X1738)),hAPP(v_F,X1736)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1741),X1740)),hAPP(X1737,esk8_6(X1736,X1737,X1738,X1739,X1740,X1741))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1739),X1738)),hAPP(X1736,esk8_6(X1736,X1737,X1738,X1739,X1740,X1741))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1736),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))),X1737),c_Arrow__Order__Mirabelle_OProf))
| X1740 = X1739
| X1741 = X1738
| X1739 = X1738
| X1741 = X1740 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1739),X1738)),hAPP(v_F,X1736)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1741),X1740)),hAPP(v_F,X1737)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1741),X1740)),hAPP(X1737,esk8_6(X1736,X1737,X1738,X1739,X1740,X1741))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1739),X1738)),hAPP(X1736,esk8_6(X1736,X1737,X1738,X1739,X1740,X1741))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1736),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))),X1737),c_Arrow__Order__Mirabelle_OProf))
| X1740 = X1739
| X1741 = X1738
| X1739 = X1738
| X1741 = X1740 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).
fof(i_0_586,plain,
! [X1729,X1730,X1731,X1732,X1733,X1734] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(X1730,esk7_6(X1729,X1730,X1731,X1732,X1733,X1734))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1732),X1731)),hAPP(X1729,esk7_6(X1729,X1730,X1731,X1732,X1733,X1734))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(v_F,X1730)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1732),X1731)),hAPP(v_F,X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1729),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))),X1730),c_Arrow__Order__Mirabelle_OProf))
| X1733 = X1732
| X1734 = X1731
| X1732 = X1731
| X1734 = X1733 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(X1730,esk7_6(X1729,X1730,X1731,X1732,X1733,X1734))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1732),X1731)),hAPP(X1729,esk7_6(X1729,X1730,X1731,X1732,X1733,X1734))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(v_F,X1730)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1732),X1731)),hAPP(v_F,X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1729),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))),X1730),c_Arrow__Order__Mirabelle_OProf))
| X1733 = X1732
| X1734 = X1731
| X1732 = X1731
| X1734 = X1733 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).
fof(i_0_587,plain,
! [X1716,X1717,X1718,X1719,X1720,X1721] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1721),X1720)),hAPP(v_F,X1717)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1718)),hAPP(v_F,X1716)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1721),X1720)),hAPP(X1717,esk5_6(X1716,X1717,X1718,X1719,X1720,X1721))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1718)),hAPP(X1716,esk5_6(X1716,X1717,X1718,X1719,X1720,X1721))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1716),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))),X1717),c_Arrow__Order__Mirabelle_OProf))
| X1719 = X1718
| X1721 = X1720 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1718)),hAPP(v_F,X1716)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1721),X1720)),hAPP(v_F,X1717)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1721),X1720)),hAPP(X1717,esk5_6(X1716,X1717,X1718,X1719,X1720,X1721))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1718)),hAPP(X1716,esk5_6(X1716,X1717,X1718,X1719,X1720,X1721))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1716),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))),X1717),c_Arrow__Order__Mirabelle_OProf))
| X1719 = X1718
| X1721 = X1720 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1721),X1720)),hAPP(v_F,X1717)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1718)),hAPP(v_F,X1716)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1721),X1720)),hAPP(X1717,esk5_6(X1716,X1717,X1718,X1719,X1720,X1721))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1718)),hAPP(X1716,esk5_6(X1716,X1717,X1718,X1719,X1720,X1721))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1716),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))),X1717),c_Arrow__Order__Mirabelle_OProf))
| X1719 = X1718
| X1721 = X1720 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1718)),hAPP(v_F,X1716)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1721),X1720)),hAPP(v_F,X1717)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1721),X1720)),hAPP(X1717,esk5_6(X1716,X1717,X1718,X1719,X1720,X1721))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1718)),hAPP(X1716,esk5_6(X1716,X1717,X1718,X1719,X1720,X1721))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1716),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))),X1717),c_Arrow__Order__Mirabelle_OProf))
| X1719 = X1718
| X1721 = X1720 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pairwise__neutrality])])])]) ).
fof(i_0_588,plain,
! [X2639,X2640,X2641,X2642] :
( ( ~ c_Wellfounded_Omax__extp(X2642,hAPP(hAPP(c_COMBC(X2642,tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_fun(X2642,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2642,tc_fun(tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_fun(X2642,tc_HOL_Obool)),X2642,c_COMBC(X2642,tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2642,tc_prod(X2642,X2642)),tc_fun(X2642,tc_fun(tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_HOL_Obool)),X2642,c_COMBB(tc_prod(X2642,X2642),tc_fun(tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_HOL_Obool),X2642,c_member(tc_prod(X2642,X2642)))),c_Product__Type_OPair(X2642,X2642)))),X2641),X2640,X2639)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2642,tc_HOL_Obool),tc_fun(X2642,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2642,tc_HOL_Obool),tc_fun(X2642,tc_HOL_Obool)),X2640),X2639)),c_Wellfounded_Omax__ext(X2642,X2641))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2642,tc_HOL_Obool),tc_fun(X2642,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2642,tc_HOL_Obool),tc_fun(X2642,tc_HOL_Obool)),X2640),X2639)),c_Wellfounded_Omax__ext(X2642,X2641)))
| c_Wellfounded_Omax__extp(X2642,hAPP(hAPP(c_COMBC(X2642,tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_fun(X2642,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2642,tc_fun(tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_fun(X2642,tc_HOL_Obool)),X2642,c_COMBC(X2642,tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2642,tc_prod(X2642,X2642)),tc_fun(X2642,tc_fun(tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_HOL_Obool)),X2642,c_COMBB(tc_prod(X2642,X2642),tc_fun(tc_fun(tc_prod(X2642,X2642),tc_HOL_Obool),tc_HOL_Obool),X2642,c_member(tc_prod(X2642,X2642)))),c_Product__Type_OPair(X2642,X2642)))),X2641),X2640,X2639) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])]) ).
fof(i_0_589,plain,
! [X1655,X1656,X1657,X1658] :
( ( hAPP(hAPP(c_COMBC(X1658,tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_fun(X1657,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1657,tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_fun(X1657,tc_HOL_Obool)),X1658,c_COMBC(X1657,tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1657,tc_prod(X1658,X1657)),tc_fun(X1657,tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),X1658,c_COMBB(tc_prod(X1658,X1657),tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool),X1657,c_member(tc_prod(X1658,X1657)))),c_Product__Type_OPair(X1658,X1657)))),X1656) != hAPP(hAPP(c_COMBC(X1658,tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_fun(X1657,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1657,tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_fun(X1657,tc_HOL_Obool)),X1658,c_COMBC(X1657,tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1657,tc_prod(X1658,X1657)),tc_fun(X1657,tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),X1658,c_COMBB(tc_prod(X1658,X1657),tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool),X1657,c_member(tc_prod(X1658,X1657)))),c_Product__Type_OPair(X1658,X1657)))),X1655)
| X1656 = X1655 )
& ( X1656 != X1655
| hAPP(hAPP(c_COMBC(X1658,tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_fun(X1657,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1657,tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_fun(X1657,tc_HOL_Obool)),X1658,c_COMBC(X1657,tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1657,tc_prod(X1658,X1657)),tc_fun(X1657,tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),X1658,c_COMBB(tc_prod(X1658,X1657),tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool),X1657,c_member(tc_prod(X1658,X1657)))),c_Product__Type_OPair(X1658,X1657)))),X1656) = hAPP(hAPP(c_COMBC(X1658,tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_fun(X1657,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1657,tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_fun(X1657,tc_HOL_Obool)),X1658,c_COMBC(X1657,tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1657,tc_prod(X1658,X1657)),tc_fun(X1657,tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool)),X1658,c_COMBB(tc_prod(X1658,X1657),tc_fun(tc_fun(tc_prod(X1658,X1657),tc_HOL_Obool),tc_HOL_Obool),X1657,c_member(tc_prod(X1658,X1657)))),c_Product__Type_OPair(X1658,X1657)))),X1655) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_590,plain,
! [X2453,X2454,X2455,X2456,X2457] :
( ( hBOOL(hAPP(hAPP(c_member(X2457),esk30_5(X2453,X2454,X2455,X2456,X2457)),X2456))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2457,X2455),tc_HOL_Obool),c_FuncSet_OPi(X2457,X2455,X2456,X2454)),c_FuncSet_OPi(X2457,X2455,X2456,X2453))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2455,tc_HOL_Obool),hAPP(X2454,esk30_5(X2453,X2454,X2455,X2456,X2457))),hAPP(X2453,esk30_5(X2453,X2454,X2455,X2456,X2457))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2457,X2455),tc_HOL_Obool),c_FuncSet_OPi(X2457,X2455,X2456,X2454)),c_FuncSet_OPi(X2457,X2455,X2456,X2453))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_591,plain,
! [X2459,X2460,X2461,X2462,X2463] :
( ( hBOOL(hAPP(hAPP(c_member(X2463),esk31_5(X2459,X2460,X2461,X2462,X2463)),X2462))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2463,X2461)),X2460),c_FuncSet_OPi(X2463,X2461,X2462,X2459))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2461),hAPP(X2460,esk31_5(X2459,X2460,X2461,X2462,X2463))),hAPP(X2459,esk31_5(X2459,X2460,X2461,X2462,X2463))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2463,X2461)),X2460),c_FuncSet_OPi(X2463,X2461,X2462,X2459))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_592,plain,
! [X1754,X1755,X1756,X1757,X1758,X1760,X1765,X1766] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X1758)),hAPP(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),X1757),X1758)),hAPP(X1754,X1756)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X1758)),hAPP(X1755,esk9_5(X1754,X1755,X1756,X1757,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),X1757),X1758)),hAPP(X1756,esk9_5(X1754,X1755,X1756,X1757,X1758))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1756),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))),X1755),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1754) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X1758)),hAPP(X1754,X1756)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X1758)),hAPP(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),X1757),X1758)),hAPP(X1755,esk9_5(X1754,X1755,X1756,X1757,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),X1757),X1758)),hAPP(X1756,esk9_5(X1754,X1755,X1756,X1757,X1758))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1756),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))),X1755),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1754) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X1758)),hAPP(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),X1757),X1758)),hAPP(X1754,X1756)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X1758)),hAPP(X1755,esk9_5(X1754,X1755,X1756,X1757,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),X1757),X1758)),hAPP(X1756,esk9_5(X1754,X1755,X1756,X1757,X1758))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1756),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))),X1755),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1754) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X1758)),hAPP(X1754,X1756)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X1758)),hAPP(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),X1757),X1758)),hAPP(X1755,esk9_5(X1754,X1755,X1756,X1757,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),X1757),X1758)),hAPP(X1756,esk9_5(X1754,X1755,X1756,X1757,X1758))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1756),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))),X1755),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X1754) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk10_1(X1760)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1760) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk11_1(X1760)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(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),esk12_1(X1760)),esk13_1(X1760))),hAPP(esk10_1(X1760),X1765)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1760)),esk13_1(X1760))),hAPP(esk11_1(X1760),X1765)))
| c_Arrow__Order__Mirabelle_OIIA(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),esk12_1(X1760)),esk13_1(X1760))),hAPP(esk11_1(X1760),X1766)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1760)),esk13_1(X1760))),hAPP(esk10_1(X1760),X1766)))
| c_Arrow__Order__Mirabelle_OIIA(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),esk12_1(X1760)),esk13_1(X1760))),hAPP(X1760,esk10_1(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),esk12_1(X1760)),esk13_1(X1760))),hAPP(X1760,esk11_1(X1760))))
| c_Arrow__Order__Mirabelle_OIIA(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),esk12_1(X1760)),esk13_1(X1760))),hAPP(X1760,esk10_1(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),esk12_1(X1760)),esk13_1(X1760))),hAPP(X1760,esk11_1(X1760))))
| c_Arrow__Order__Mirabelle_OIIA(X1760) ) ),
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_593,plain,
! [X1723,X1724,X1725,X1726,X1727] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(v_F,X1724)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1726),X1725)),hAPP(v_F,X1723)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(X1724,esk6_5(X1723,X1724,X1725,X1726,X1727))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1726),X1725)),hAPP(X1723,esk6_5(X1723,X1724,X1725,X1726,X1727))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1723),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1724),c_Arrow__Order__Mirabelle_OProf))
| X1727 = X1725
| X1726 = X1725
| X1727 = X1726 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1726),X1725)),hAPP(v_F,X1723)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(v_F,X1724)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(X1724,esk6_5(X1723,X1724,X1725,X1726,X1727))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1726),X1725)),hAPP(X1723,esk6_5(X1723,X1724,X1725,X1726,X1727))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1723),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1724),c_Arrow__Order__Mirabelle_OProf))
| X1727 = X1725
| X1726 = X1725
| X1727 = X1726 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(v_F,X1724)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1726),X1725)),hAPP(v_F,X1723)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(X1724,esk6_5(X1723,X1724,X1725,X1726,X1727))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1726),X1725)),hAPP(X1723,esk6_5(X1723,X1724,X1725,X1726,X1727))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1723),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1724),c_Arrow__Order__Mirabelle_OProf))
| X1727 = X1725
| X1726 = X1725
| X1727 = X1726 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1726),X1725)),hAPP(v_F,X1723)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(v_F,X1724)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(X1724,esk6_5(X1723,X1724,X1725,X1726,X1727))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1726),X1725)),hAPP(X1723,esk6_5(X1723,X1724,X1725,X1726,X1727))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1723),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1724),c_Arrow__Order__Mirabelle_OProf))
| X1727 = X1725
| X1726 = X1725
| X1727 = X1726 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C4_C])])])]) ).
fof(i_0_594,plain,
! [X1926,X1927] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk18_2(X1926,X1927)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X1927,X1926)
| ~ 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))),X1927),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( esk19_2(X1926,X1927) != esk20_2(X1926,X1927)
| c_Arrow__Order__Mirabelle_Odictator(X1927,X1926)
| ~ 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))),X1927),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk19_2(X1926,X1927)),esk20_2(X1926,X1927))),hAPP(esk18_2(X1926,X1927),X1926)))
| c_Arrow__Order__Mirabelle_Odictator(X1927,X1926)
| ~ 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))),X1927),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk19_2(X1926,X1927)),esk20_2(X1926,X1927))),hAPP(X1927,esk18_2(X1926,X1927))))
| c_Arrow__Order__Mirabelle_Odictator(X1927,X1926)
| ~ 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))),X1927),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_595,plain,
! [X1743,X1744,X1745,X1746,X1747,X1748,X1749,X1750] :
( ( X1748 = X1746
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1750,X1750)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1750),X1748),X1746)),X1744))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1750,X1749),tc_prod(X1750,X1749))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1750,X1749),tc_prod(X1750,X1749)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1749),X1748),X1747)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1749),X1746),X1745))),c_Wellfounded_Olex__prod(X1750,X1749,X1744,X1743))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1749,X1749)),hAPP(hAPP(c_Product__Type_OPair(X1749,X1749),X1747),X1745)),X1743))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1750,X1750)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1750),X1748),X1746)),X1744))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1750,X1749),tc_prod(X1750,X1749))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1750,X1749),tc_prod(X1750,X1749)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1749),X1748),X1747)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1749),X1746),X1745))),c_Wellfounded_Olex__prod(X1750,X1749,X1744,X1743))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1750,X1750)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1750),X1748),X1746)),X1744))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1750,X1749),tc_prod(X1750,X1749))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1750,X1749),tc_prod(X1750,X1749)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1749),X1748),X1747)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1749),X1746),X1745))),c_Wellfounded_Olex__prod(X1750,X1749,X1744,X1743))) )
& ( X1748 != X1746
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1749,X1749)),hAPP(hAPP(c_Product__Type_OPair(X1749,X1749),X1747),X1745)),X1743))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1750,X1749),tc_prod(X1750,X1749))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1750,X1749),tc_prod(X1750,X1749)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1749),X1748),X1747)),hAPP(hAPP(c_Product__Type_OPair(X1750,X1749),X1746),X1745))),c_Wellfounded_Olex__prod(X1750,X1749,X1744,X1743))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_596,plain,
! [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,X1712)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1713),X1714)),hAPP(v_F,X1711)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X1712,esk4_4(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),X1713),X1714)),hAPP(X1711,esk4_4(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))),X1711),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))),X1712),c_Arrow__Order__Mirabelle_OProf))
| 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),X1713),X1714)),hAPP(v_F,X1711)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,X1712)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X1712,esk4_4(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),X1713),X1714)),hAPP(X1711,esk4_4(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))),X1711),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))),X1712),c_Arrow__Order__Mirabelle_OProf))
| 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,X1712)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1713),X1714)),hAPP(v_F,X1711)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X1712,esk4_4(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),X1713),X1714)),hAPP(X1711,esk4_4(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))),X1711),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))),X1712),c_Arrow__Order__Mirabelle_OProf))
| 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),X1713),X1714)),hAPP(v_F,X1711)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,X1712)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(X1712,esk4_4(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),X1713),X1714)),hAPP(X1711,esk4_4(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))),X1711),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))),X1712),c_Arrow__Order__Mirabelle_OProf))
| X1714 = X1713 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C3_C])])])]) ).
fof(i_0_597,plain,
! [X1638,X1639,X1640,X1641] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(v_F,X1638)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(v_F,X1639)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(X1638,esk2_4(X1638,X1639,X1640,X1641))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(X1639,esk2_4(X1638,X1639,X1640,X1641))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1639),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))),X1638),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),X1640),X1641)),hAPP(v_F,X1639)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(v_F,X1638)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(X1638,esk2_4(X1638,X1639,X1640,X1641))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(X1639,esk2_4(X1638,X1639,X1640,X1641))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1639),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))),X1638),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),X1640),X1641)),hAPP(v_F,X1638)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(v_F,X1639)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(X1638,esk2_4(X1638,X1639,X1640,X1641))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(X1639,esk2_4(X1638,X1639,X1640,X1641))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1639),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))),X1638),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),X1640),X1641)),hAPP(v_F,X1639)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(v_F,X1638)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(X1638,esk2_4(X1638,X1639,X1640,X1641))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1640),X1641)),hAPP(X1639,esk2_4(X1638,X1639,X1640,X1641))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1639),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))),X1638),c_Arrow__Order__Mirabelle_OProf)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096])])])])]) ).
fof(i_0_598,plain,
! [X2904,X2905,X2906,X2907,X2908,X2909,X2910] :
( ~ c_Finite__Set_Ofolding__image__simple(X2910,X2909,X2908,X2907,X2906,X2905)
| ~ c_Finite__Set_Ofinite(X2909,X2904)
| hAPP(X2905,X2904) = c_Finite__Set_Ofold__image(X2910,X2909,X2908,X2906,X2907,X2904) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).
fof(i_0_599,plain,
! [X3086,X3087,X3088,X3089,X3090,X3092,X3093,X3094,X3095,X3096,X3097] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3088,tc_HOL_Obool),esk40_5(X3086,X3087,X3088,X3089,X3090)),X3086))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3090,tc_HOL_Obool),X3089),c_Set_Oimage(X3088,X3090,X3087,X3086))) )
& ( X3089 = c_Set_Oimage(X3088,X3090,X3087,esk40_5(X3086,X3087,X3088,X3089,X3090))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3090,tc_HOL_Obool),X3089),c_Set_Oimage(X3088,X3090,X3087,X3086))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3094,tc_HOL_Obool),X3097),X3092))
| X3095 != c_Set_Oimage(X3094,X3096,X3093,X3097)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3096,tc_HOL_Obool),X3095),c_Set_Oimage(X3094,X3096,X3093,X3092))) ) ),
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_600,plain,
! [X1664,X1665,X1666,X1667,X1668,X1669,X1670] :
( ~ hBOOL(hAPP(X1670,X1669))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1668,X1668)),hAPP(hAPP(c_Product__Type_OPair(X1668,X1668),X1667),X1666)),hAPP(X1665,X1669)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1664,X1668),tc_prod(X1664,X1668))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1664,X1668),tc_prod(X1664,X1668)),hAPP(hAPP(c_Product__Type_OPair(X1664,X1668),X1669),X1667)),hAPP(hAPP(c_Product__Type_OPair(X1664,X1668),X1669),X1666))),c_Recdef_Osame__fst(X1664,X1668,X1670,X1665))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_601,plain,
! [X1966,X1967,X1968,X1969,X1970] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1968,X1969),X1967),X1966))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1969,hAPP(X1967,X1970)),hAPP(X1966,X1970)))
| ~ class_Orderings_Oord(X1969) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1969,hAPP(X1967,esk21_4(X1966,X1967,X1968,X1969))),hAPP(X1966,esk21_4(X1966,X1967,X1968,X1969))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1968,X1969),X1967),X1966))
| ~ class_Orderings_Oord(X1969) ) ),
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_602,plain,
! [X2513,X2514,X2515,X2516,X2517,X2518,X2519,X2520] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2520,X2519,X2518,X2517,X2516,X2515)
| ~ c_Finite__Set_Ofinite(X2519,X2514)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2519,tc_HOL_Obool),X2513),X2514))
| hAPP(hAPP(X2518,hAPP(X2515,X2513)),hAPP(X2515,X2514)) = hAPP(X2515,X2514) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_603,plain,
! [X2631,X2632,X2633,X2634,X2635,X2636,X2637,X2638] :
( ~ c_Finite__Set_Ofolding__image__simple(X2638,X2637,X2636,X2635,X2634,X2633)
| ~ c_Finite__Set_Ofinite(X2637,X2632)
| hBOOL(hAPP(hAPP(c_member(X2637),X2631),X2632))
| hAPP(X2633,c_Set_Oinsert(X2637,X2631,X2632)) = hAPP(hAPP(X2636,hAPP(X2634,X2631)),hAPP(X2633,X2632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_521])]) ).
fof(i_0_604,plain,
! [X2617,X2618,X2619,X2620,X2621,X2622,X2623,X2624] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2624,X2623,X2622,X2621,X2620,X2619)
| ~ c_Finite__Set_Ofinite(X2623,X2618)
| ~ hBOOL(hAPP(hAPP(c_member(X2623),X2617),X2618))
| hAPP(hAPP(X2622,hAPP(X2620,X2617)),hAPP(X2619,X2618)) = hAPP(X2619,X2618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_605,plain,
! [X2535,X2536,X2537,X2538,X2539,X2540,X2541,X2542] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2542,X2541,X2540,X2539,X2538,X2537)
| ~ c_Finite__Set_Ofinite(X2541,X2536)
| hAPP(X2537,c_Set_Oinsert(X2541,X2535,X2536)) = hAPP(hAPP(X2540,hAPP(X2538,X2535)),hAPP(X2537,X2536)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).
fof(i_0_606,plain,
! [X2543,X2544,X2545,X2546,X2547,X2548,X2549] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2549,X2548,X2547,X2546,X2545,X2544)
| hAPP(hAPP(X2547,X2543),X2543) = X2543 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).
fof(i_0_607,plain,
! [X3143,X3144,X3145,X3146,X3147,X3148] :
( ~ c_Fun_Oinj__on(X3148,X3147,X3146,X3145)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3147,tc_HOL_Obool),c_Set_Oimage(X3148,X3147,X3146,X3145)),X3144))
| ~ c_Fun_Oinj__on(X3147,X3148,X3143,X3144)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3148,tc_HOL_Obool),c_Set_Oimage(X3147,X3148,X3143,X3144)),X3145))
| ~ c_Finite__Set_Ofinite(X3148,X3145)
| ~ c_Finite__Set_Ofinite(X3147,X3144)
| c_Finite__Set_Ocard(X3148,X3145) = c_Finite__Set_Ocard(X3147,X3144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).
fof(i_0_608,plain,
! [X1767,X1768,X1769,X1770,X1772,X1776] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X1767)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1768),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),X1769),X1770)),hAPP(X1768,esk14_4(X1767,X1768,X1769,X1770))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1769),X1770)),hAPP(X1767,X1768))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk15_1(X1772)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(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),esk16_1(X1772)),esk17_1(X1772))),hAPP(esk15_1(X1772),X1776)))
| c_Arrow__Order__Mirabelle_Ounanimity(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),esk16_1(X1772)),esk17_1(X1772))),hAPP(X1772,esk15_1(X1772))))
| c_Arrow__Order__Mirabelle_Ounanimity(X1772) ) ),
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_609,plain,
! [X2465,X2466,X2467,X2468,X2469,X2470] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2470,X2469)),X2468),c_FuncSet_OPi(X2470,X2469,X2467,hAPP(c_COMBK(tc_fun(X2469,tc_HOL_Obool),X2470),X2466))))
| ~ c_Fun_Oinj__on(X2470,X2469,X2468,X2467)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2469,X2470)),X2465),c_FuncSet_OPi(X2469,X2470,X2466,hAPP(c_COMBK(tc_fun(X2470,tc_HOL_Obool),X2469),X2467))))
| ~ c_Fun_Oinj__on(X2469,X2470,X2465,X2466)
| ~ c_Finite__Set_Ofinite(X2470,X2467)
| ~ c_Finite__Set_Ofinite(X2469,X2466)
| c_Finite__Set_Ocard(X2470,X2467) = c_Finite__Set_Ocard(X2469,X2466) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij])]) ).
fof(i_0_610,plain,
! [X2278,X2279,X2280] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2280,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2280,tc_fun(X2280,tc_HOL_Obool),tc_HOL_Obool),c_member(X2280)),X2279)),hAPP(hAPP(c_COMBC(X2280,tc_fun(X2280,tc_HOL_Obool),tc_HOL_Obool),c_member(X2280)),X2278)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2280,tc_HOL_Obool),X2279),X2278)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2280,tc_HOL_Obool),X2279),X2278))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2280,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2280,tc_fun(X2280,tc_HOL_Obool),tc_HOL_Obool),c_member(X2280)),X2279)),hAPP(hAPP(c_COMBC(X2280,tc_fun(X2280,tc_HOL_Obool),tc_HOL_Obool),c_member(X2280)),X2278))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_611,plain,
! [X1637] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( hAPP(v_h____,X1637) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( hAPP(v_h____,X1637) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( hAPP(v_h____,X1637) != v_n____
| hAPP(v_h____,X1637) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| hAPP(v_h____,X1637) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( hAPP(v_h____,X1637) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X1637)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( hAPP(v_h____,X1637) != v_n____
| hAPP(v_h____,X1637) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| hAPP(v_h____,X1637) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( hAPP(v_h____,X1637) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),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____,X1637)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637)),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____,X1637)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X1637))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_522])])]) ).
fof(i_0_612,plain,
! [X3110,X3111,X3112,X3113] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X3113,c_Set_Oimage(X3112,X3113,X3111,X3110))),c_Finite__Set_Ocard(X3112,X3110)))
| ~ c_Fun_Oinj__on(X3112,X3113,X3111,X3110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])]) ).
fof(i_0_613,plain,
! [X3155,X3156,X3157,X3158,X3159] :
( ( ~ c_Fun_Oinj__on(X3158,X3156,X3159,X3157)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3156,tc_HOL_Obool),c_Set_Oimage(X3158,X3156,X3159,X3157)),X3155))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3158,X3157)),c_Finite__Set_Ocard(X3156,X3155)))
| ~ c_Finite__Set_Ofinite(X3156,X3155)
| ~ c_Finite__Set_Ofinite(X3158,X3157) )
& ( c_Fun_Oinj__on(X3158,X3156,esk42_4(X3155,X3156,X3157,X3158),X3157)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3158,X3157)),c_Finite__Set_Ocard(X3156,X3155)))
| ~ c_Finite__Set_Ofinite(X3156,X3155)
| ~ c_Finite__Set_Ofinite(X3158,X3157) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3156,tc_HOL_Obool),c_Set_Oimage(X3158,X3156,esk42_4(X3155,X3156,X3157,X3158),X3157)),X3155))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3158,X3157)),c_Finite__Set_Ocard(X3156,X3155)))
| ~ c_Finite__Set_Ofinite(X3156,X3155)
| ~ c_Finite__Set_Ofinite(X3158,X3157) ) ),
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_614,plain,
! [X1861,X1862,X1863,X1864,X1865] :
( ( X1862 != X1861
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1862 != X1864
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1865),X1861)),X1863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1861 != X1864
| X1862 = X1865
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1865)),X1863))
| X1862 = X1864
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1861 = X1864
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),X1863))
| X1862 = X1864
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1862 != X1864
| X1862 = X1864
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1861 != X1864
| X1861 = X1864
| X1862 = X1864
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),X1863))
| X1861 = X1864
| X1862 = X1864
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1861 != X1864
| X1862 != X1865
| X1862 = X1864
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),X1863))
| X1862 != X1865
| X1862 = X1864
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1861 != X1864
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1865)),X1863))
| X1862 = X1864
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),X1863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1865)),X1863))
| X1862 = X1864
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1862 != X1864
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1865),X1861)),X1863))
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1861 != X1864
| X1861 = X1864
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1865),X1861)),X1863))
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),X1863))
| X1861 = X1864
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1865),X1861)),X1863))
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1861 != X1864
| X1862 != X1865
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1865),X1861)),X1863))
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),X1863))
| X1862 != X1865
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1865),X1861)),X1863))
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( X1861 != X1864
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1865)),X1863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1865),X1861)),X1863))
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),X1863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1865)),X1863))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1865),X1861)),X1863))
| X1862 = X1861
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1862),X1861)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1863),X1865),X1864)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1863),c_Arrow__Order__Mirabelle_OLin))
| X1865 = X1864 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_615,plain,
! [X1887,X1888,X1889,X1890,X1891] :
( ( X1888 != X1887
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1887 != X1891
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1890)),X1889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1888 != X1891
| X1887 = X1890
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1890),X1887)),X1889))
| X1887 = X1891
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1888 = X1891
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),X1889))
| X1887 = X1891
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1887 != X1891
| X1887 = X1891
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1888 != X1891
| X1888 = X1891
| X1887 = X1891
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),X1889))
| X1888 = X1891
| X1887 = X1891
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1888 != X1891
| X1887 != X1890
| X1887 = X1891
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),X1889))
| X1887 != X1890
| X1887 = X1891
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1888 != X1891
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1890),X1887)),X1889))
| X1887 = X1891
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),X1889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1890),X1887)),X1889))
| X1887 = X1891
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1887 != X1891
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1890)),X1889))
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1888 != X1891
| X1888 = X1891
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1890)),X1889))
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),X1889))
| X1888 = X1891
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1890)),X1889))
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1888 != X1891
| X1887 != X1890
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1890)),X1889))
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),X1889))
| X1887 != X1890
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1890)),X1889))
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( X1888 != X1891
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1890),X1887)),X1889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1890)),X1889))
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),X1889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1890),X1887)),X1889))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1890)),X1889))
| X1888 = X1887
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),c_Arrow__Order__Mirabelle_Obelow(X1889,X1891,X1890)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1889),c_Arrow__Order__Mirabelle_OLin))
| X1891 = X1890 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_616,plain,
! [X2911,X2912] :
( ( ~ c_Finite__Set_Ofinite(X2912,X2911)
| c_Finite__Set_Ocard(X2912,X2911) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2912,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2912),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2911) )
& ( c_Finite__Set_Ofinite(X2912,X2911)
| c_Finite__Set_Ocard(X2912,X2911) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])]) ).
fof(i_0_617,plain,
! [X2902,X2903] :
( ~ c_Finite__Set_Ofinite(X2903,X2902)
| c_Finite__Set_Ocard(X2903,X2902) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2903,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2903),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2902) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).
fof(i_0_618,plain,
! [X3002,X3003,X3004,X3005,X3006] :
( ~ hBOOL(hAPP(hAPP(c_member(X3006),X3005),c_Set_Oimage(X3004,X3006,X3003,X3002)))
| hBOOL(hAPP(hAPP(c_member(X3004),hAPP(c_Hilbert__Choice_Oinv__into(X3004,X3006,X3002,X3003),X3005)),X3002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).
fof(i_0_619,plain,
! [X2948,X2949,X2950,X2951,X2952] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2951,tc_HOL_Obool),c_Set_Oimage(X2952,X2951,X2950,X2949)),c_Set_Oimage(X2952,X2951,X2950,X2948)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2952,tc_HOL_Obool),X2949),X2948))
| ~ c_Fun_Oinj__on(X2952,X2951,X2950,c_Orderings_Otop__class_Otop(tc_fun(X2952,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2952,tc_HOL_Obool),X2949),X2948))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2951,tc_HOL_Obool),c_Set_Oimage(X2952,X2951,X2950,X2949)),c_Set_Oimage(X2952,X2951,X2950,X2948)))
| ~ c_Fun_Oinj__on(X2952,X2951,X2950,c_Orderings_Otop__class_Otop(tc_fun(X2952,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_620,plain,
! [X2503,X2504,X2505] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2505,tc_HOL_Obool)),X2504),X2503))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2505,tc_HOL_Obool),tc_fun(X2505,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2505,tc_HOL_Obool),tc_fun(X2505,tc_HOL_Obool)),X2504),X2503)),c_Wellfounded_Ofinite__psubset(X2505))) )
& ( c_Finite__Set_Ofinite(X2505,X2503)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2505,tc_HOL_Obool),tc_fun(X2505,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2505,tc_HOL_Obool),tc_fun(X2505,tc_HOL_Obool)),X2504),X2503)),c_Wellfounded_Ofinite__psubset(X2505))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2505,tc_HOL_Obool)),X2504),X2503))
| ~ c_Finite__Set_Ofinite(X2505,X2503)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2505,tc_HOL_Obool),tc_fun(X2505,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2505,tc_HOL_Obool),tc_fun(X2505,tc_HOL_Obool)),X2504),X2503)),c_Wellfounded_Ofinite__psubset(X2505))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).
fof(i_0_621,plain,
! [X3138,X3139,X3140,X3141,X3142] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3142,X3141)),X3140),c_FuncSet_OPi(X3142,X3141,X3139,hAPP(c_COMBK(tc_fun(X3141,tc_HOL_Obool),X3142),X3138))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3141,tc_HOL_Obool),c_Set_Oimage(X3142,X3141,X3140,X3139)),X3138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_622,plain,
! [X3007,X3008,X3009,X3010,X3011,X3012] :
( hAPP(c_Hilbert__Choice_Oinv__into(X3012,X3011,X3010,X3009),X3008) != hAPP(c_Hilbert__Choice_Oinv__into(X3012,X3011,X3010,X3009),X3007)
| ~ hBOOL(hAPP(hAPP(c_member(X3011),X3008),c_Set_Oimage(X3012,X3011,X3009,X3010)))
| ~ hBOOL(hAPP(hAPP(c_member(X3011),X3007),c_Set_Oimage(X3012,X3011,X3009,X3010)))
| X3008 = X3007 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).
fof(i_0_623,plain,
! [X2855,X2856] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2856),c_Groups_Oone__class_Oone(X2856)),X2855)),X2855)),c_Groups_Ozero__class_Ozero(X2856)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2856),X2855),c_Groups_Ozero__class_Ozero(X2856)))
| ~ hBOOL(hAPP(hAPP(c_member(X2856),X2855),c_Int_Oring__1__class_OInts(X2856)))
| ~ class_Rings_Olinordered__idom(X2856) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2856),X2855),c_Groups_Ozero__class_Ozero(X2856)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2856),c_Groups_Oone__class_Oone(X2856)),X2855)),X2855)),c_Groups_Ozero__class_Ozero(X2856)))
| ~ hBOOL(hAPP(hAPP(c_member(X2856),X2855),c_Int_Oring__1__class_OInts(X2856)))
| ~ class_Rings_Olinordered__idom(X2856) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).
fof(i_0_624,plain,
! [X2925,X2926,X2927,X2928,X2930,X2931] :
( ( X2925 = hAPP(X2926,esk36_4(X2925,X2926,X2927,X2928))
| ~ hBOOL(hAPP(hAPP(c_member(X2927),X2925),c_Set_Oimage(X2928,X2927,X2926,c_Orderings_Otop__class_Otop(tc_fun(X2928,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2928,X2927,X2926,c_Orderings_Otop__class_Otop(tc_fun(X2928,tc_HOL_Obool))) )
& ( X2925 != hAPP(X2926,X2930)
| X2930 = esk36_4(X2925,X2926,X2927,X2928)
| ~ hBOOL(hAPP(hAPP(c_member(X2927),X2925),c_Set_Oimage(X2928,X2927,X2926,c_Orderings_Otop__class_Otop(tc_fun(X2928,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2928,X2927,X2926,c_Orderings_Otop__class_Otop(tc_fun(X2928,tc_HOL_Obool))) )
& ( X2925 = hAPP(X2926,esk37_5(X2925,X2926,X2927,X2928,X2931))
| X2925 != hAPP(X2926,X2931)
| hBOOL(hAPP(hAPP(c_member(X2927),X2925),c_Set_Oimage(X2928,X2927,X2926,c_Orderings_Otop__class_Otop(tc_fun(X2928,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2928,X2927,X2926,c_Orderings_Otop__class_Otop(tc_fun(X2928,tc_HOL_Obool))) )
& ( esk37_5(X2925,X2926,X2927,X2928,X2931) != X2931
| X2925 != hAPP(X2926,X2931)
| hBOOL(hAPP(hAPP(c_member(X2927),X2925),c_Set_Oimage(X2928,X2927,X2926,c_Orderings_Otop__class_Otop(tc_fun(X2928,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2928,X2927,X2926,c_Orderings_Otop__class_Otop(tc_fun(X2928,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_625,plain,
! [X2953,X2954,X2955,X2956] :
( ~ c_Finite__Set_Ofinite(X2956,X2955)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2954,c_Set_Oimage(X2956,X2954,X2953,X2955))),c_Finite__Set_Ocard(X2956,X2955))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_626,plain,
! [X3035,X3036,X3037,X3038,X3039] :
( ~ c_Fun_Oinj__on(X3039,X3038,X3037,X3036)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3039,tc_HOL_Obool)),X3035),X3036))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3038,tc_HOL_Obool)),c_Set_Oimage(X3039,X3038,X3037,X3035)),c_Set_Oimage(X3039,X3038,X3037,X3036))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_627,plain,
! [X2938,X2939,X2940] :
( ~ c_Finite__Set_Ofinite(X2940,X2939)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2940,tc_HOL_Obool),c_Set_Oimage(X2940,X2940,X2938,X2939)),X2939))
| ~ c_Fun_Oinj__on(X2940,X2940,X2938,X2939)
| c_Set_Oimage(X2940,X2940,X2938,X2939) = X2939 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_628,plain,
! [X3149,X3150,X3151,X3152,X3153] :
( ~ c_Fun_Oinj__on(X3153,X3152,X3151,X3150)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3152,tc_HOL_Obool),c_Set_Oimage(X3153,X3152,X3151,X3150)),X3149))
| ~ c_Finite__Set_Ofinite(X3152,X3149)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3153,X3150)),c_Finite__Set_Ocard(X3152,X3149))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).
fof(i_0_629,plain,
! [X3040,X3041,X3042,X3043,X3044,X3046,X3047,X3048,X3049,X3050,X3051] :
( ( hBOOL(hAPP(hAPP(c_member(X3042),esk39_4(X3040,X3041,X3042,X3043)),X3040))
| ~ hBOOL(hAPP(hAPP(c_member(X3044),X3043),c_Set_Oimage(X3042,X3044,X3041,X3040))) )
& ( X3043 = hAPP(X3041,esk39_4(X3040,X3041,X3042,X3043))
| ~ hBOOL(hAPP(hAPP(c_member(X3044),X3043),c_Set_Oimage(X3042,X3044,X3041,X3040))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3048),X3050),X3046))
| X3049 != hAPP(X3047,X3050)
| hBOOL(hAPP(hAPP(c_member(X3051),X3049),c_Set_Oimage(X3048,X3051,X3047,X3046))) ) ),
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_630,plain,
! [X1786,X1787,X1788] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1786)),X1788))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1786),X1787)),X1788))
| X1787 = X1786
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1788),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),X1786),X1787)),X1788))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1787),X1786)),X1788))
| X1787 = X1786
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1788),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])])]) ).
fof(i_0_631,plain,
! [X1789,X1790,X1791] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1791),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),X1790),X1789)),X1791))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1789),X1790)),X1791)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_526])]) ).
fof(i_0_632,plain,
! [X2448,X2449,X2450,X2451,X2452] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2452,X2451)),X2450),c_FuncSet_OPi(X2452,X2451,X2449,hAPP(c_COMBK(tc_fun(X2451,tc_HOL_Obool),X2452),X2448))))
| ~ c_Fun_Oinj__on(X2452,X2451,X2450,X2449)
| ~ c_Finite__Set_Ofinite(X2451,X2448)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2452,X2449)),c_Finite__Set_Ocard(X2451,X2448))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj])]) ).
fof(i_0_633,plain,
! [X2139,X2140,X2141,X2142,X2143] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2143,tc_HOL_Obool),X2142),X2141))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2143,X2140),tc_HOL_Obool),c_FuncSet_OPi(X2143,X2140,X2141,X2139)),c_FuncSet_OPi(X2143,X2140,X2142,X2139))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_634,plain,
! [X3105,X3106,X3107,X3108,X3109] :
( ~ c_Finite__Set_Ofinite(X3109,c_Set_Oimage(X3108,X3109,X3107,c_Orderings_Otop__class_Otop(tc_fun(X3108,tc_HOL_Obool))))
| c_Finite__Set_Ofinite(X3106,c_Set_Oimage(X3108,X3106,hAPP(c_COMBB(X3109,X3106,X3108,X3105),X3107),c_Orderings_Otop__class_Otop(tc_fun(X3108,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).
fof(i_0_635,plain,
! [X1860] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1860),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),X1860)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_636,plain,
! [X1872,X1873,X1874,X1875,X1876,X1877] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1877,X1876)),X1875),c_FuncSet_OPi(X1877,X1876,X1874,hAPP(c_COMBK(tc_fun(X1876,tc_HOL_Obool),X1877),X1873))))
| ~ hBOOL(hAPP(hAPP(c_member(X1877),X1872),X1874))
| hBOOL(hAPP(hAPP(c_member(X1876),hAPP(X1875,X1872)),X1873)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_637,plain,
! [X3081,X3082,X3083,X3084,X3085] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3085,tc_HOL_Obool),X3084),X3083))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3082,tc_HOL_Obool),c_Set_Oimage(X3085,X3082,X3081,X3084)),c_Set_Oimage(X3085,X3082,X3081,X3083))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_638,plain,
! [X2110,X2111,X2112,X2113,X2114] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2114,X2113)),hAPP(X2114,X2112)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2111,X2111)),hAPP(hAPP(c_Product__Type_OPair(X2111,X2111),X2113),X2112)),X2110))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2111,X2111)),hAPP(hAPP(c_Product__Type_OPair(X2111,X2111),X2113),X2112)),c_Wellfounded_Omlex__prod(X2111,X2114,X2110))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_639,plain,
! [X1659,X1660,X1661,X1662,X1663] :
( ( ~ c_FunDef_Oin__rel(X1663,X1662,X1661,X1660,X1659)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1663,X1662)),hAPP(hAPP(c_Product__Type_OPair(X1663,X1662),X1660),X1659)),X1661)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1663,X1662)),hAPP(hAPP(c_Product__Type_OPair(X1663,X1662),X1660),X1659)),X1661))
| c_FunDef_Oin__rel(X1663,X1662,X1661,X1660,X1659) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_640,plain,
! [X2997,X2998,X2999,X3000,X3001] :
( ~ hBOOL(hAPP(hAPP(c_member(X3001),X3000),c_Set_Oimage(X2999,X3001,X2998,X2997)))
| hAPP(X2998,hAPP(c_Hilbert__Choice_Oinv__into(X2999,X3001,X2997,X2998),X3000)) = X3000 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).
fof(i_0_641,plain,
! [X3019,X3020,X3021,X3022,X3023,X3024,X3025] :
( ( c_Set_Oimage(X3021,X3020,X3019,c_Orderings_Otop__class_Otop(tc_fun(X3021,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3020,tc_HOL_Obool))
| hAPP(X3019,hAPP(c_Hilbert__Choice_Oinv__into(X3021,X3020,c_Orderings_Otop__class_Otop(tc_fun(X3021,tc_HOL_Obool)),X3019),X3022)) = X3022 )
& ( hAPP(X3023,hAPP(c_Hilbert__Choice_Oinv__into(X3025,X3024,c_Orderings_Otop__class_Otop(tc_fun(X3025,tc_HOL_Obool)),X3023),esk38_3(X3023,X3024,X3025))) != esk38_3(X3023,X3024,X3025)
| c_Set_Oimage(X3025,X3024,X3023,c_Orderings_Otop__class_Otop(tc_fun(X3025,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3024,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_642,plain,
! [X1678,X1679,X1680,X1681,X1682] :
( ( ~ c_Nitpick_Orefl_H(X1679,X1678)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1679,X1679)),hAPP(hAPP(c_Product__Type_OPair(X1679,X1679),X1680),X1680)),X1678)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1682,X1682)),hAPP(hAPP(c_Product__Type_OPair(X1682,X1682),esk3_2(X1681,X1682)),esk3_2(X1681,X1682))),X1681))
| c_Nitpick_Orefl_H(X1682,X1681) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def])])])])]) ).
fof(i_0_643,plain,
! [X3119,X3120,X3121,X3122,X3123] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3123,tc_HOL_Obool),X3122),c_Set_Oimage(X3121,X3123,X3120,X3119)))
| c_Fun_Oinj__on(X3123,X3121,c_Hilbert__Choice_Oinv__into(X3121,X3123,X3119,X3120),X3122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).
fof(i_0_644,plain,
! [X1643,X1644,X1645,X1646] :
( ( X1645 != X1643
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1644),X1643))) )
& ( X1646 != X1643
| X1646 != X1645
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1644),X1643))) )
& ( X1646 = X1643
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),X1644))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1644),X1643))) )
& ( X1646 != X1643
| X1646 = X1643
| X1645 = X1643
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1644),X1643))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),X1644))
| X1646 = X1643
| X1645 = X1643
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1644),X1643))) )
& ( X1646 != X1643
| X1646 = X1645
| X1645 = X1643
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1644),X1643))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),X1644))
| X1646 = X1645
| X1645 = X1643
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1646),X1645)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1644),X1643))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_645,plain,
! [X1647,X1648,X1649,X1650] :
( ( X1650 != X1647
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1648),X1647))) )
& ( X1649 != X1647
| X1650 != X1649
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1648),X1647))) )
& ( X1649 = X1647
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),X1648))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1648),X1647))) )
& ( X1649 != X1647
| X1649 = X1647
| X1650 = X1647
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1648),X1647))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),X1648))
| X1649 = X1647
| X1650 = X1647
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1648),X1647))) )
& ( X1649 != X1647
| X1650 = X1649
| X1650 = X1647
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1648),X1647))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),X1648))
| X1650 = X1649
| X1650 = X1647
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1650),X1649)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1648),X1647))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_646,plain,
! [X3235,X3236,X3237,X3238,X3239,X3240] : hAPP(c_COMBS(X3240,X3239,X3238,X3237,X3236),X3235) = hAPP(hAPP(X3237,X3235),hAPP(X3236,X3235)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_647,plain,
! [X1903,X1904,X1905,X1906,X1907,X1908] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1908,X1907)),X1906),c_FuncSet_OPi(X1908,X1907,X1905,X1904)))
| ~ hBOOL(hAPP(hAPP(c_member(X1908),X1903),X1905))
| hBOOL(hAPP(hAPP(c_member(X1907),hAPP(X1906,X1903)),hAPP(X1904,X1903))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_648,plain,
! [X1866,X1867,X1868,X1869,X1870,X1871] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1871,X1870)),X1869),c_FuncSet_OPi(X1871,X1870,X1868,X1867)))
| hBOOL(hAPP(hAPP(c_member(X1870),hAPP(X1869,X1866)),hAPP(X1867,X1866)))
| ~ hBOOL(hAPP(hAPP(c_member(X1871),X1866),X1868)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])]) ).
fof(i_0_649,plain,
! [X2933,X2934,X2935,X2936,X2937] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2936),hAPP(X2935,X2934)),c_Set_Oimage(X2937,X2936,X2935,X2933)))
| hBOOL(hAPP(hAPP(c_member(X2937),X2934),X2933))
| ~ c_Fun_Oinj__on(X2937,X2936,X2935,c_Orderings_Otop__class_Otop(tc_fun(X2937,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2937),X2934),X2933))
| hBOOL(hAPP(hAPP(c_member(X2936),hAPP(X2935,X2934)),c_Set_Oimage(X2937,X2936,X2935,X2933)))
| ~ c_Fun_Oinj__on(X2937,X2936,X2935,c_Orderings_Otop__class_Otop(tc_fun(X2937,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_650,plain,
! [X3031,X3032,X3033,X3034] :
( c_Set_Oimage(X3034,X3033,X3032,c_Orderings_Otop__class_Otop(tc_fun(X3034,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3033,tc_HOL_Obool))
| c_Set_Oimage(X3034,X3033,X3032,c_Set_Oimage(X3033,X3034,c_Hilbert__Choice_Oinv__into(X3034,X3033,c_Orderings_Otop__class_Otop(tc_fun(X3034,tc_HOL_Obool)),X3032),X3031)) = X3031 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).
fof(i_0_651,plain,
! [X3013,X3014,X3015,X3016,X3017,X3018] :
( c_Set_Oimage(X3018,X3017,X3016,X3015) != X3014
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3017,tc_HOL_Obool),X3013),X3014))
| c_Set_Oimage(X3018,X3017,X3016,c_Set_Oimage(X3017,X3018,c_Hilbert__Choice_Oinv__into(X3018,X3017,X3015,X3016),X3013)) = X3013 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).
fof(i_0_652,plain,
! [X2098,X2099,X2100,X2101,X2102,X2103,X2104,X2105,X2106,X2107] :
( ( ~ c_Fun_Oinj__on(X2101,X2100,X2099,X2098)
| ~ hBOOL(hAPP(hAPP(c_member(X2101),X2102),X2098))
| ~ hBOOL(hAPP(hAPP(c_member(X2101),X2103),X2098))
| hAPP(X2099,X2102) != hAPP(X2099,X2103)
| X2102 = X2103 )
& ( hBOOL(hAPP(hAPP(c_member(X2107),esk22_4(X2104,X2105,X2106,X2107)),X2104))
| c_Fun_Oinj__on(X2107,X2106,X2105,X2104) )
& ( hBOOL(hAPP(hAPP(c_member(X2107),esk23_4(X2104,X2105,X2106,X2107)),X2104))
| c_Fun_Oinj__on(X2107,X2106,X2105,X2104) )
& ( hAPP(X2105,esk22_4(X2104,X2105,X2106,X2107)) = hAPP(X2105,esk23_4(X2104,X2105,X2106,X2107))
| c_Fun_Oinj__on(X2107,X2106,X2105,X2104) )
& ( esk22_4(X2104,X2105,X2106,X2107) != esk23_4(X2104,X2105,X2106,X2107)
| c_Fun_Oinj__on(X2107,X2106,X2105,X2104) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__def])])])])])]) ).
fof(i_0_653,plain,
! [X1779,X1780,X1781] :
( X1781 = X1780
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1779),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,X1779),X1781),X1780)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_654,plain,
! [X3068,X3069,X3070,X3071,X3072] : c_Set_Oimage(X3072,X3071,hAPP(c_COMBB(X3070,X3071,X3072,X3069),X3068),c_Orderings_Otop__class_Otop(tc_fun(X3072,tc_HOL_Obool))) = c_Set_Oimage(X3070,X3071,X3069,c_Set_Oimage(X3072,X3070,X3068,c_Orderings_Otop__class_Otop(tc_fun(X3072,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_range__composition]) ).
fof(i_0_655,plain,
! [X2941,X2942,X2943] :
( ~ c_Finite__Set_Ofinite(X2943,X2942)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2943,tc_HOL_Obool),X2942),c_Set_Oimage(X2943,X2943,X2941,X2942)))
| c_Fun_Oinj__on(X2943,X2943,X2941,X2942) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_656,plain,
! [X2117,X2118,X2119,X2120,X2121] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2118,X2117)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2119),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2118,X2119) = hAPP(X2119,X2117) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk24_2(X2120,X2121)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2121,X2120) )
& ( hAPP(X2121,esk24_2(X2120,X2121)) != hAPP(esk24_2(X2120,X2121),X2120)
| c_Arrow__Order__Mirabelle_Odictator(X2121,X2120) ) ),
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_657,plain,
! [X1922,X1923,X1924,X1925] :
( ~ c_Fun_Oinj__on(X1925,X1924,X1923,c_Orderings_Otop__class_Otop(tc_fun(X1925,tc_HOL_Obool)))
| c_Fun_Oinj__on(X1925,tc_fun(X1922,X1924),hAPP(c_COMBB(X1924,tc_fun(X1922,X1924),X1925,c_COMBK(X1924,X1922)),X1923),c_Orderings_Otop__class_Otop(tc_fun(X1925,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).
fof(i_0_658,plain,
! [X1912,X1913] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1913,X1913)),c_COMBI(X1913)),c_FuncSet_OPi(X1913,X1913,X1912,hAPP(c_COMBK(tc_fun(X1913,tc_HOL_Obool),X1913),X1912)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_659,plain,
! [X3073,X3074,X3075,X3076,X3077,X3078] : c_Set_Oimage(X3078,X3077,X3076,c_Set_Oimage(X3075,X3078,X3074,X3073)) = c_Set_Oimage(X3075,X3077,hAPP(c_COMBB(X3078,X3077,X3075,X3076),X3074),X3073),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_660,plain,
! [X1919,X1920,X1921] :
( X1921 = X1920
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1919),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(X1919,X1921,X1920)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_661,plain,
! [X1674,X1675,X1676,X1677] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1677,X1677)),hAPP(hAPP(c_Product__Type_OPair(X1677,X1677),X1676),X1675)),c_Wellfounded_Omeasure(X1677,X1674)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1674,X1676)),hAPP(X1674,X1675))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1674,X1676)),hAPP(X1674,X1675)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1677,X1677)),hAPP(hAPP(c_Product__Type_OPair(X1677,X1677),X1676),X1675)),c_Wellfounded_Omeasure(X1677,X1674))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_662,plain,
! [X3114,X3115,X3116,X3117,X3118] :
( ~ c_Fun_Oinj__on(X3118,X3117,X3116,X3115)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3118,tc_HOL_Obool),X3114),X3115))
| c_Set_Oimage(X3117,X3118,c_Hilbert__Choice_Oinv__into(X3118,X3117,X3115,X3116),c_Set_Oimage(X3118,X3117,X3116,X3114)) = X3114 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).
fof(i_0_663,plain,
! [X2979,X2980,X2981,X2982,X2983] :
( ~ c_Finite__Set_Ofinite(X2983,X2982)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2981,tc_HOL_Obool),X2980),c_Set_Oimage(X2983,X2981,X2979,X2982)))
| c_Finite__Set_Ofinite(X2981,X2980) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
fof(i_0_664,plain,
! [X1782,X1783] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1783),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,X1783),X1782)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_665,plain,
! [X1784,X1785] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1785),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,X1785),X1784)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_666,plain,
! [X3131,X3132,X3133,X3134] :
( ~ c_Fun_Oinj__on(X3134,X3133,X3132,c_Orderings_Otop__class_Otop(tc_fun(X3134,tc_HOL_Obool)))
| c_Set_Oimage(X3133,X3134,c_Hilbert__Choice_Oinv__into(X3134,X3133,c_Orderings_Otop__class_Otop(tc_fun(X3134,tc_HOL_Obool)),X3132),c_Set_Oimage(X3134,X3133,X3132,X3131)) = X3131 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).
fof(i_0_667,plain,
! [X3127,X3128,X3129,X3130] :
( ~ c_Fun_Oinj__on(X3130,X3129,X3128,c_Orderings_Otop__class_Otop(tc_fun(X3130,tc_HOL_Obool)))
| c_Set_Oimage(X3129,X3130,c_Hilbert__Choice_Oinv__into(X3130,X3129,c_Orderings_Otop__class_Otop(tc_fun(X3130,tc_HOL_Obool)),X3128),c_Set_Oimage(X3130,X3129,X3128,X3127)) = X3127 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).
fof(i_0_668,plain,
! [X3027,X3028,X3029,X3030] :
( c_Set_Oimage(X3030,X3029,X3028,c_Orderings_Otop__class_Otop(tc_fun(X3030,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3029,tc_HOL_Obool))
| hAPP(X3028,hAPP(c_Hilbert__Choice_Oinv__into(X3030,X3029,c_Orderings_Otop__class_Otop(tc_fun(X3030,tc_HOL_Obool)),X3028),X3027)) = X3027 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).
fof(i_0_669,plain,
! [X1684,X1685,X1686,X1687,X1688] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1688,X1687)),hAPP(X1688,X1686)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1685,X1685)),hAPP(hAPP(c_Product__Type_OPair(X1685,X1685),X1687),X1686)),c_Wellfounded_Omlex__prod(X1685,X1688,X1684))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_670,plain,
! [X3195,X3196] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X3196),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3195,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3195),c_Finite__Set_Ocard(tc_Nat_Onat,X3196)))))
| X3196 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3195,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3195),c_Finite__Set_Ocard(tc_Nat_Onat,X3196))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).
fof(i_0_671,plain,
! [X3197,X3198,X3199,X3200,X3201] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3201,X3198),X3200))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3201,X3199),X3200))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3201,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X3201,X3200,X3199)),c_SetInterval_Oord__class_OatLeastLessThan(X3201,X3198,X3197)))
| ~ class_Orderings_Olinorder(X3201) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3201,X3199),X3197))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3201,X3199),X3200))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3201,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X3201,X3200,X3199)),c_SetInterval_Oord__class_OatLeastLessThan(X3201,X3198,X3197)))
| ~ class_Orderings_Olinorder(X3201) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).
fof(i_0_672,plain,
! [X3124,X3125,X3126] :
( c_Set_Oimage(X3126,X3125,X3124,c_Orderings_Otop__class_Otop(tc_fun(X3126,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3125,tc_HOL_Obool))
| c_Fun_Oinj__on(X3125,X3126,c_Hilbert__Choice_Oinv__into(X3126,X3125,c_Orderings_Otop__class_Otop(tc_fun(X3126,tc_HOL_Obool)),X3124),c_Orderings_Otop__class_Otop(tc_fun(X3125,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).
fof(i_0_673,plain,
! [X2970,X2971,X2972,X2973] : hBOOL(hAPP(hAPP(c_member(X2973),hAPP(X2972,X2971)),c_Set_Oimage(X2970,X2973,X2972,c_Orderings_Otop__class_Otop(tc_fun(X2970,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_674,plain,
! [X3135,X3136,X3137] :
( ~ c_Fun_Oinj__on(X3137,X3136,X3135,c_Orderings_Otop__class_Otop(tc_fun(X3137,tc_HOL_Obool)))
| c_Set_Oimage(X3136,X3137,c_Hilbert__Choice_Oinv__into(X3137,X3136,c_Orderings_Otop__class_Otop(tc_fun(X3137,tc_HOL_Obool)),X3135),c_Orderings_Otop__class_Otop(tc_fun(X3136,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3137,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).
fof(i_0_675,plain,
! [X3052,X3053,X3054,X3055,X3056] :
( ~ hBOOL(hAPP(hAPP(c_member(X3056),X3055),X3054))
| hBOOL(hAPP(hAPP(c_member(X3053),hAPP(X3052,X3055)),c_Set_Oimage(X3056,X3053,X3052,X3054))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_676,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_677,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_678,plain,
! [X2974,X2975,X2976,X2977,X2978] :
( X2978 != hAPP(X2977,X2976)
| hBOOL(hAPP(hAPP(c_member(X2975),X2978),c_Set_Oimage(X2974,X2975,X2977,c_Orderings_Otop__class_Otop(tc_fun(X2974,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_679,plain,
! [X2915,X2916,X2917,X2918,X2919,X2920] :
( X2920 != hAPP(X2919,X2918)
| ~ hBOOL(hAPP(hAPP(c_member(X2917),X2918),X2916))
| hBOOL(hAPP(hAPP(c_member(X2915),X2920),c_Set_Oimage(X2917,X2915,X2919,X2916))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_680,plain,
! [X3057,X3058,X3059,X3060,X3061,X3062] :
( ~ hBOOL(hAPP(hAPP(c_member(X3062),X3061),X3060))
| X3059 != hAPP(X3058,X3061)
| hBOOL(hAPP(hAPP(c_member(X3057),X3059),c_Set_Oimage(X3062,X3057,X3058,X3060))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_681,plain,
! [X2988,X2989,X2990,X2991,X2992] :
( ( c_Set_Oimage(X2992,X2991,X2990,X2989) != c_Set_Oimage(X2992,X2991,X2990,X2988)
| X2989 = X2988
| ~ c_Fun_Oinj__on(X2992,X2991,X2990,c_Orderings_Otop__class_Otop(tc_fun(X2992,tc_HOL_Obool))) )
& ( X2989 != X2988
| c_Set_Oimage(X2992,X2991,X2990,X2989) = c_Set_Oimage(X2992,X2991,X2990,X2988)
| ~ c_Fun_Oinj__on(X2992,X2991,X2990,c_Orderings_Otop__class_Otop(tc_fun(X2992,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_682,plain,
! [X2427,X2428,X2429,X2430] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2430),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2430),X2429),X2428)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2430),X2427),X2428)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2430),X2429),X2427))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2430) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2430),X2429),X2427))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2430),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2430),X2429),X2428)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2430),X2427),X2428)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2430) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_683,plain,
! [X2324,X2325,X2326,X2327] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2327)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2327),X2326),X2325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2327),X2324),X2325)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2327),X2326),X2324)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_684,plain,
! [X2431,X2432,X2433,X2434] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2434),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2434),X2433),X2432)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2434),X2433),X2431)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2434),X2432),X2431))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2434) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2434),X2432),X2431))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2434),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2434),X2433),X2432)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2434),X2433),X2431)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2434) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_685,plain,
! [X2320,X2321,X2322,X2323] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2323)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2323),X2322),X2321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2323),X2322),X2320)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2323),X2321),X2320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_686,plain,
! [X2984,X2985,X2986,X2987] :
( ~ c_Finite__Set_Ofinite(X2987,c_Set_Oimage(X2986,X2987,X2985,X2984))
| ~ c_Fun_Oinj__on(X2986,X2987,X2985,X2984)
| c_Finite__Set_Ofinite(X2986,X2984) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_687,plain,
! [X1962,X1963,X1964,X1965] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1965,tc_HOL_Obool)),X1964),X1963))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1965,tc_HOL_Obool)),X1963),X1962))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1965,tc_HOL_Obool)),X1964),X1962)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_688,plain,
! [X2419,X2420,X2421,X2422] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2422)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2422,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2422),X2421),X2420)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2422),X2419),X2420)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2422,X2421),X2419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_689,plain,
! [X2398,X2399,X2400,X2401] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2401,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2401),X2400),X2399)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2401),X2398),X2399)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2401,X2400),X2398))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2401) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2401,X2400),X2398))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2401,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2401),X2400),X2399)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2401),X2398),X2399)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2401) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_690,plain,
! [X2423,X2424,X2425,X2426] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2426)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2426,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2426),X2425),X2424)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2426),X2425),X2423)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2426,X2424),X2423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_691,plain,
! [X2402,X2403,X2404,X2405] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2405,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2405),X2404),X2403)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2405),X2404),X2402)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2405,X2403),X2402))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2405) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2405,X2403),X2402))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2405,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2405),X2404),X2403)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2405),X2404),X2402)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2405) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_692,plain,
! [X2610,X2611,X2612,X2613] :
( ( hBOOL(hAPP(hAPP(c_member(X2613),X2612),X2610))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2613,tc_HOL_Obool),c_Set_Oinsert(X2613,X2612,X2611)),X2610)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2613,tc_HOL_Obool),X2611),X2610))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2613,tc_HOL_Obool),c_Set_Oinsert(X2613,X2612,X2611)),X2610)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2613),X2612),X2610))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2613,tc_HOL_Obool),X2611),X2610))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2613,tc_HOL_Obool),c_Set_Oinsert(X2613,X2612,X2611)),X2610)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_693,plain,
! [X1883,X1884,X1885,X1886] :
( ~ c_Fun_Oinj__on(X1886,X1885,X1884,c_Orderings_Otop__class_Otop(tc_fun(X1886,tc_HOL_Obool)))
| hAPP(c_Hilbert__Choice_Oinv__into(X1886,X1885,c_Orderings_Otop__class_Otop(tc_fun(X1886,tc_HOL_Obool)),X1884),hAPP(X1884,X1883)) = X1883 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).
fof(i_0_694,plain,
! [X1878,X1879,X1880,X1881,X1882] :
( ~ c_Fun_Oinj__on(X1882,X1881,X1880,c_Orderings_Otop__class_Otop(tc_fun(X1882,tc_HOL_Obool)))
| hAPP(X1880,X1879) != X1878
| hAPP(c_Hilbert__Choice_Oinv__into(X1882,X1881,c_Orderings_Otop__class_Otop(tc_fun(X1882,tc_HOL_Obool)),X1880),X1878) = X1879 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).
fof(i_0_695,plain,
! [X1671,X1672,X1673] :
( ( hAPP(hAPP(c_COMBC(X1673,tc_fun(X1673,tc_HOL_Obool),tc_HOL_Obool),c_member(X1673)),X1672) != hAPP(hAPP(c_COMBC(X1673,tc_fun(X1673,tc_HOL_Obool),tc_HOL_Obool),c_member(X1673)),X1671)
| X1672 = X1671 )
& ( X1672 != X1671
| hAPP(hAPP(c_COMBC(X1673,tc_fun(X1673,tc_HOL_Obool),tc_HOL_Obool),c_member(X1673)),X1672) = hAPP(hAPP(c_COMBC(X1673,tc_fun(X1673,tc_HOL_Obool),tc_HOL_Obool),c_member(X1673)),X1671) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_696,plain,
! [X2166,X2167,X2168] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2168),X2167)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2168),X2166)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2167),X2166)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2167),X2166))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2168),X2167)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2168),X2166))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_697,plain,
! [X1898,X1899,X1900,X1901,X1902] :
( ~ c_Fun_Oinj__on(X1902,X1901,X1900,X1899)
| ~ hBOOL(hAPP(hAPP(c_member(X1902),X1898),X1899))
| hAPP(c_Hilbert__Choice_Oinv__into(X1902,X1901,X1899,X1900),hAPP(X1900,X1898)) = X1898 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).
fof(i_0_698,plain,
! [X1892,X1893,X1894,X1895,X1896,X1897] :
( ~ c_Fun_Oinj__on(X1897,X1896,X1895,X1894)
| ~ hBOOL(hAPP(hAPP(c_member(X1897),X1893),X1894))
| hAPP(X1895,X1893) != X1892
| hAPP(c_Hilbert__Choice_Oinv__into(X1897,X1896,X1894,X1895),X1892) = X1893 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).
fof(i_0_699,plain,
! [X2957,X2958,X2959,X2960] :
( ~ c_Finite__Set_Ofinite(X2960,X2959)
| c_Finite__Set_Ocard(X2958,c_Set_Oimage(X2960,X2958,X2957,X2959)) != c_Finite__Set_Ocard(X2960,X2959)
| c_Fun_Oinj__on(X2960,X2958,X2957,X2959) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_700,plain,
! [X2961,X2962,X2963,X2964] :
( ( ~ c_Fun_Oinj__on(X2964,X2962,X2961,X2963)
| c_Finite__Set_Ocard(X2962,c_Set_Oimage(X2964,X2962,X2961,X2963)) = c_Finite__Set_Ocard(X2964,X2963)
| ~ c_Finite__Set_Ofinite(X2964,X2963) )
& ( c_Finite__Set_Ocard(X2962,c_Set_Oimage(X2964,X2962,X2961,X2963)) != c_Finite__Set_Ocard(X2964,X2963)
| c_Fun_Oinj__on(X2964,X2962,X2961,X2963)
| ~ c_Finite__Set_Ofinite(X2964,X2963) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).
fof(i_0_701,plain,
! [X2557,X2558,X2559,X2560] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2560,tc_HOL_Obool),X2559),X2558))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2560,tc_HOL_Obool),c_Set_Oinsert(X2560,X2557,X2559)),c_Set_Oinsert(X2560,X2557,X2558))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(i_0_702,plain,
! [X3223,X3224,X3225,X3226,X3227,X3228] : hAPP(hAPP(c_COMBB(X3228,X3227,X3226,X3225),X3224),X3223) = hAPP(X3225,hAPP(X3224,X3223)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_703,plain,
! [X2443,X2444,X2445,X2446,X2447] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2447)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2447),X2446),X2445))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2447),X2444),X2443))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2447),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2447),X2446),X2444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2447),X2445),X2443))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_704,plain,
! [X3165,X3166,X3167] : 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)),X3167),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3166,X3165)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3166),X3167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3165),X3167)),
inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).
fof(i_0_705,plain,
! [X2195,X2196,X2197] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2197),X2196)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2197),X2195)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2196),X2195)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2196),X2195))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2197),X2196)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2197),X2195))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_706,plain,
! [X2310,X2311,X2312,X2313,X2314] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2314)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2314,X2313),X2312))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2314),X2311),X2310))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2314),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2314),X2313),X2311)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2314),X2312),X2310))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_707,plain,
! [X2315,X2316,X2317,X2318,X2319] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2319)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2319),X2318),X2317))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2319,X2316),X2315))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2319),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2319),X2318),X2316)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2319),X2317),X2315))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_708,plain,
! [X2274,X2275,X2276,X2277] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2277,tc_HOL_Obool),X2276),X2275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2277,tc_HOL_Obool)),X2275),X2274))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2277,tc_HOL_Obool)),X2276),X2274)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_709,plain,
! [X2270,X2271,X2272,X2273] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2273,tc_HOL_Obool)),X2272),X2271))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2273,tc_HOL_Obool),X2271),X2270))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2273,tc_HOL_Obool)),X2272),X2270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_710,plain,
! [X2913,X2914] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2914)),X2913))
| hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2914),X2913)) )
& ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2914),X2913))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2914)),X2913)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_711,plain,
! [X2965,X2966,X2967,X2968,X2969] :
( ~ hBOOL(hAPP(hAPP(c_member(X2969),X2968),X2967))
| c_Set_Oinsert(X2966,hAPP(X2965,X2968),c_Set_Oimage(X2969,X2966,X2965,X2967)) = c_Set_Oimage(X2969,X2966,X2965,X2967) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
fof(i_0_712,plain,
! [X2471,X2472,X2473] :
( ~ c_Finite__Set_Ofinite(X2473,X2472)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2473,tc_HOL_Obool),X2471),X2472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2473,X2471)),c_Finite__Set_Ocard(X2473,X2472)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2473,tc_HOL_Obool)),X2471),X2472)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_713,plain,
! [X2414,X2415,X2416,X2417,X2418] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2418)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2418,X2417),X2416))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2418,X2415),X2414))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2418,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2418),X2417),X2415)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2418),X2416),X2414))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_714,plain,
! [X2704,X2705] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2705),X2704),X2704)),c_Groups_Ozero__class_Ozero(X2705)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2705),X2704),c_Groups_Ozero__class_Ozero(X2705)))
| ~ class_Groups_Olinordered__ab__group__add(X2705) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2705),X2704),c_Groups_Ozero__class_Ozero(X2705)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2705),X2704),X2704)),c_Groups_Ozero__class_Ozero(X2705)))
| ~ class_Groups_Olinordered__ab__group__add(X2705) ) ),
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_715,plain,
! [X2740,X2741] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2741),X2740),X2740)),c_Groups_Ozero__class_Ozero(X2741)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2741),X2740),c_Groups_Ozero__class_Ozero(X2741)))
| ~ class_Rings_Olinordered__idom(X2741) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2741),X2740),c_Groups_Ozero__class_Ozero(X2741)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2741),X2740),X2740)),c_Groups_Ozero__class_Ozero(X2741)))
| ~ class_Rings_Olinordered__idom(X2741) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_716,plain,
! [X2153,X2154,X2155,X2156] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2156),X2155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2154),X2153))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2156),X2154)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2155),X2153))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_717,plain,
! [X3063,X3064,X3065,X3066,X3067] : c_Set_Oimage(X3067,X3066,X3065,c_Set_Oinsert(X3067,X3064,X3063)) = c_Set_Oinsert(X3066,hAPP(X3065,X3064),c_Set_Oimage(X3067,X3066,X3065,X3063)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
fof(i_0_718,plain,
! [X2944,X2945] :
( ~ c_Finite__Set_Ofinite(X2945,c_Orderings_Otop__class_Otop(tc_fun(X2945,tc_HOL_Obool)))
| c_Set_Oimage(X2945,X2945,X2944,c_Orderings_Otop__class_Otop(tc_fun(X2945,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2945,tc_HOL_Obool))
| c_Fun_Oinj__on(X2945,X2945,X2944,c_Orderings_Otop__class_Otop(tc_fun(X2945,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_719,plain,
! [X2252,X2253,X2254,X2255,X2256] :
( ~ c_Fun_Oinj__on(X2256,X2255,X2254,X2253)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2256,tc_HOL_Obool),X2252),X2253))
| c_Fun_Oinj__on(X2256,X2255,X2254,X2252) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_720,plain,
! [X2993,X2994,X2995,X2996] :
( ~ c_Fun_Oinj__on(X2996,X2995,X2994,X2993)
| c_Finite__Set_Ocard(X2995,c_Set_Oimage(X2996,X2995,X2994,X2993)) = c_Finite__Set_Ocard(X2996,X2993) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_721,plain,
! [X2694,X2695,X2696] :
( ~ class_Groups_Oordered__comm__monoid__add(X2696)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2696),X2695),c_Groups_Ozero__class_Ozero(X2696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2696),X2694),c_Groups_Ozero__class_Ozero(X2696)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2696),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2696),X2695),X2694)),c_Groups_Ozero__class_Ozero(X2696))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_722,plain,
! [X2859,X2860,X2861] :
( ~ class_Rings_Oring__1(X2861)
| ~ hBOOL(hAPP(hAPP(c_member(X2861),X2860),c_Int_Oring__1__class_OInts(X2861)))
| ~ hBOOL(hAPP(hAPP(c_member(X2861),X2859),c_Int_Oring__1__class_OInts(X2861)))
| hBOOL(hAPP(hAPP(c_member(X2861),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2861),X2860),X2859)),c_Int_Oring__1__class_OInts(X2861))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).
fof(i_0_723,plain,
! [X2946,X2947] :
( ~ c_Finite__Set_Ofinite(X2947,c_Orderings_Otop__class_Otop(tc_fun(X2947,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X2947,X2947,X2946,c_Orderings_Otop__class_Otop(tc_fun(X2947,tc_HOL_Obool)))
| c_Set_Oimage(X2947,X2947,X2946,c_Orderings_Otop__class_Otop(tc_fun(X2947,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2947,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_724,plain,
! [X2435,X2436,X2437,X2438] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2438)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2438),X2437),X2436))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2438),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2438),X2437),X2435)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2438),X2436),X2435))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_725,plain,
! [X2439,X2440,X2441,X2442] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2442)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2442),X2441),X2440))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2442),X2439),X2441)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2442),X2439),X2440))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_726,plain,
! [X2675,X2676] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2676,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2676),X2675),X2675)),c_Groups_Ozero__class_Ozero(X2676)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2676,X2675),c_Groups_Ozero__class_Ozero(X2676)))
| ~ class_Groups_Olinordered__ab__group__add(X2676) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2676,X2675),c_Groups_Ozero__class_Ozero(X2676)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2676,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2676),X2675),X2675)),c_Groups_Ozero__class_Ozero(X2676)))
| ~ class_Groups_Olinordered__ab__group__add(X2676) ) ),
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_727,plain,
! [X2606,X2607,X2608,X2609] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2609,tc_HOL_Obool),X2607),c_Set_Oinsert(X2609,X2608,X2606)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2609,tc_HOL_Obool),X2607),X2606))
| hBOOL(hAPP(hAPP(c_member(X2609),X2608),X2607)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2609,tc_HOL_Obool),X2607),X2606))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2609,tc_HOL_Obool),X2607),c_Set_Oinsert(X2609,X2608,X2606)))
| hBOOL(hAPP(hAPP(c_member(X2609),X2608),X2607)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])]) ).
fof(i_0_728,plain,
! [X2716,X2717,X2718] :
( ~ class_Groups_Oordered__comm__monoid__add(X2718)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2718,X2717),c_Groups_Ozero__class_Ozero(X2718)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2718),X2716),c_Groups_Ozero__class_Ozero(X2718)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2718),X2717),X2716)),c_Groups_Ozero__class_Ozero(X2718))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_729,plain,
! [X2719,X2720,X2721] :
( ~ class_Groups_Oordered__comm__monoid__add(X2721)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2721),X2720),c_Groups_Ozero__class_Ozero(X2721)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2721,X2719),c_Groups_Ozero__class_Ozero(X2721)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2721),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2721),X2720),X2719)),c_Groups_Ozero__class_Ozero(X2721))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_730,plain,
! [X2182,X2183,X2184,X2185] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2185),X2184))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2183),X2182))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2185),X2183)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2184),X2182))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_731,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk25_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk25_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])])]) ).
fof(i_0_732,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk26_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk26_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])])]) ).
fof(i_0_733,plain,
! [X2602,X2603,X2604,X2605] :
( ( c_Finite__Set_Ofinite(X2605,X2603)
| ~ c_Finite__Set_Ofinite(tc_sum(X2605,X2604),c_Sum__Type_OPlus(X2605,X2604,X2603,X2602)) )
& ( c_Finite__Set_Ofinite(X2604,X2602)
| ~ c_Finite__Set_Ofinite(tc_sum(X2605,X2604),c_Sum__Type_OPlus(X2605,X2604,X2603,X2602)) )
& ( ~ c_Finite__Set_Ofinite(X2605,X2603)
| ~ c_Finite__Set_Ofinite(X2604,X2602)
| c_Finite__Set_Ofinite(tc_sum(X2605,X2604),c_Sum__Type_OPlus(X2605,X2604,X2603,X2602)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_734,plain,
! [X2594,X2595,X2596,X2597] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2597,X2596),c_Sum__Type_OPlus(X2597,X2596,X2595,X2594))
| c_Finite__Set_Ofinite(X2597,X2595) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_735,plain,
! [X2590,X2591,X2592,X2593] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2593,X2592),c_Sum__Type_OPlus(X2593,X2592,X2591,X2590))
| c_Finite__Set_Ofinite(X2592,X2590) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_736,plain,
! [X2406,X2407,X2408,X2409] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2409)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2409,X2408),X2407))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2409,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2409),X2408),X2406)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2409),X2407),X2406))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_737,plain,
! [X2410,X2411,X2412,X2413] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2413)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2413,X2412),X2411))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2413,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2413),X2410),X2412)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2413),X2410),X2411))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_738,plain,
! [X2146,X2147,X2148] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2148),X2147)),X2146))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2148),X2146)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_739,plain,
! [X2691,X2692,X2693] :
( ~ class_Groups_Oordered__comm__monoid__add(X2693)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2693,X2692),c_Groups_Ozero__class_Ozero(X2693)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2693,X2691),c_Groups_Ozero__class_Ozero(X2693)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2693,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2693),X2692),X2691)),c_Groups_Ozero__class_Ozero(X2693))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_740,plain,
! [X2257,X2258,X2259,X2260] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2259,X2260),X2258),X2257))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2259,X2260)),X2258),X2257))
| ~ class_Orderings_Oord(X2260) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2259,X2260),X2257),X2258))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2259,X2260)),X2258),X2257))
| ~ class_Orderings_Oord(X2260) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2259,X2260),X2258),X2257))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2259,X2260),X2257),X2258))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2259,X2260)),X2258),X2257))
| ~ class_Orderings_Oord(X2260) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_531])])]) ).
fof(i_0_741,plain,
! [X2354,X2355,X2356,X2357,X2358,X2359] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2359,tc_fun(X2358,tc_HOL_Obool)),X2357),X2356))
| ~ hBOOL(hAPP(hAPP(X2357,X2355),X2354))
| hBOOL(hAPP(hAPP(X2356,X2355),X2354)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_742,plain,
! [X2363,X2364,X2365,X2366,X2367,X2368] :
( ~ hBOOL(hAPP(hAPP(X2368,X2367),X2366))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2365,tc_fun(X2364,tc_HOL_Obool)),X2368),X2363))
| hBOOL(hAPP(hAPP(X2363,X2367),X2366)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_743,plain,
! [X2157,X2158,X2159] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2159),X2158))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2159),X2157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2158),X2157))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_744,plain,
! [X1948,X1949,X1950,X1951,X1952,X1953] :
( ( hAPP(X1951,X1949) != hAPP(X1951,X1948)
| X1949 = X1948
| ~ hBOOL(hAPP(hAPP(c_member(X1953),X1948),X1950))
| ~ hBOOL(hAPP(hAPP(c_member(X1953),X1949),X1950))
| ~ c_Fun_Oinj__on(X1953,X1952,X1951,X1950) )
& ( X1949 != X1948
| hAPP(X1951,X1949) = hAPP(X1951,X1948)
| ~ hBOOL(hAPP(hAPP(c_member(X1953),X1948),X1950))
| ~ hBOOL(hAPP(hAPP(c_member(X1953),X1949),X1950))
| ~ c_Fun_Oinj__on(X1953,X1952,X1951,X1950) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_745,plain,
! [X1954,X1955,X1956,X1957,X1958,X1959] :
( ~ c_Fun_Oinj__on(X1959,X1958,X1957,X1956)
| X1955 = X1954
| ~ hBOOL(hAPP(hAPP(c_member(X1959),X1955),X1956))
| ~ hBOOL(hAPP(hAPP(c_member(X1959),X1954),X1956))
| hAPP(X1957,X1955) != hAPP(X1957,X1954) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_746,plain,
! [X1942,X1943,X1944,X1945,X1946,X1947] :
( ~ c_Fun_Oinj__on(X1947,X1946,X1945,X1944)
| hAPP(X1945,X1943) != hAPP(X1945,X1942)
| ~ hBOOL(hAPP(hAPP(c_member(X1947),X1943),X1944))
| ~ hBOOL(hAPP(hAPP(c_member(X1947),X1942),X1944))
| X1943 = X1942 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_747,plain,
! [X2173,X2174,X2175] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2175),X2173))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2175),X2174)),X2173)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2174),X2173))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2175),X2174)),X2173)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_532])])]) ).
fof(i_0_748,plain,
! [X2176,X2177,X2178] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2178),X2177)),X2176))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2178),X2176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_749,plain,
! [X2179,X2180,X2181] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2181),X2180)),X2179))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2180),X2179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_750,plain,
! [X2701,X2702,X2703] :
( ~ class_Groups_Oordered__comm__monoid__add(X2703)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2703),c_Groups_Ozero__class_Ozero(X2703)),X2702))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2703),c_Groups_Ozero__class_Ozero(X2703)),X2701))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2703),c_Groups_Ozero__class_Ozero(X2703)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2703),X2702),X2701))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_751,plain,
! [X2186,X2187,X2188] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2188),X2187))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2188),X2186)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2187),X2186))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_752,plain,
! [X1915,X1916,X1917,X1918] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1918,tc_HOL_Obool)),X1917),X1916))
| ~ hBOOL(hAPP(hAPP(c_member(X1918),X1915),X1917))
| hBOOL(hAPP(hAPP(c_member(X1918),X1915),X1916)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_753,plain,
! [X2474,X2475,X2476] :
( ~ c_Finite__Set_Ofinite(X2476,X2475)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2476,tc_HOL_Obool)),X2474),X2475))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2476,X2474)),c_Finite__Set_Ocard(X2476,X2475))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_754,plain,
! [X2144,X2145] : 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)),X2145),X2144),
inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).
fof(i_0_755,plain,
! [X2871,X2872,X2873,X2874,X2875] :
( ~ class_Rings_Ocomm__semiring__1(X2875)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2875),X2874),X2873)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2875),X2872),X2871)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2875),X2874),X2872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2875),X2873),X2871)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_756,plain,
! [X2350,X2351,X2352,X2353] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2353,tc_HOL_Obool),X2352),X2351))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2353,tc_HOL_Obool),X2351),X2350))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2353,tc_HOL_Obool),X2352),X2350)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_757,plain,
! [X2730,X2731,X2732] :
( ~ class_Groups_Oordered__comm__monoid__add(X2732)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2732,c_Groups_Ozero__class_Ozero(X2732)),X2731))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2732),c_Groups_Ozero__class_Ozero(X2732)),X2730))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2732),c_Groups_Ozero__class_Ozero(X2732)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2732),X2731),X2730))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_758,plain,
! [X2733,X2734,X2735] :
( ~ class_Groups_Oordered__comm__monoid__add(X2735)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2735),c_Groups_Ozero__class_Ozero(X2735)),X2734))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2735,c_Groups_Ozero__class_Ozero(X2735)),X2733))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2735),c_Groups_Ozero__class_Ozero(X2735)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2735),X2734),X2733))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_759,plain,
! [X2171,X2172] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2172),X2171)),X2172)),
inference(variable_rename,[status(thm)],[i_0_533]) ).
fof(i_0_760,plain,
! [X2169,X2170] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2170),X2169)),X2169)),
inference(variable_rename,[status(thm)],[i_0_534]) ).
fof(i_0_761,plain,
! [X2627,X2628,X2629,X2630] :
( ( ~ c_Finite__Set_Ofinite(X2630,X2629)
| ~ c_Finite__Set_Ofinite(X2628,X2627)
| c_Finite__Set_Ocard(tc_sum(X2630,X2628),c_Sum__Type_OPlus(X2630,X2628,X2629,X2627)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2630,X2629)),c_Finite__Set_Ocard(X2628,X2627)) )
& ( c_Finite__Set_Ofinite(X2630,X2629)
| c_Finite__Set_Ocard(tc_sum(X2630,X2628),c_Sum__Type_OPlus(X2630,X2628,X2629,X2627)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X2628,X2627)
| c_Finite__Set_Ocard(tc_sum(X2630,X2628),c_Sum__Type_OPlus(X2630,X2628,X2629,X2627)) = 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_762,plain,
! [X2506,X2507,X2508,X2509] :
( ~ c_Finite__Set_Ofinite(X2509,X2508)
| ~ c_Finite__Set_Ofinite(X2507,X2506)
| c_Finite__Set_Ocard(tc_sum(X2509,X2507),c_Sum__Type_OPlus(X2509,X2507,X2508,X2506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2509,X2508)),c_Finite__Set_Ocard(X2507,X2506)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_763,plain,
! [X2697,X2698,X2699,X2700] :
( ~ class_Rings_Olinordered__semidom(X2700)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2700),c_Groups_Ozero__class_Ozero(X2700)),X2699))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2700),X2698),X2697))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2700),X2698),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2700),X2699),X2697))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_764,plain,
! [X2614,X2615,X2616] :
( ~ c_Finite__Set_Ofinite(X2616,X2615)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2616,X2615)),c_Finite__Set_Ocard(X2616,c_Set_Oinsert(X2616,X2614,X2615)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).
fof(i_0_765,plain,
! [X2865,X2866] :
( ~ class_Int_Oring__char__0(X2866)
| ~ hBOOL(hAPP(hAPP(c_member(X2866),X2865),c_Int_Oring__1__class_OInts(X2866)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2866),c_Groups_Oone__class_Oone(X2866)),X2865)),X2865) != c_Groups_Ozero__class_Ozero(X2866) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).
fof(i_0_766,plain,
! [X2706,X2707] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2707),c_Groups_Ozero__class_Ozero(X2707)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2707),X2706),X2706)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2707),c_Groups_Ozero__class_Ozero(X2707)),X2706))
| ~ class_Groups_Olinordered__ab__group__add(X2707) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2707),c_Groups_Ozero__class_Ozero(X2707)),X2706))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2707),c_Groups_Ozero__class_Ozero(X2707)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2707),X2706),X2706)))
| ~ class_Groups_Olinordered__ab__group__add(X2707) ) ),
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_767,plain,
! [X2712,X2713] :
( ( ~ 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),X2713),X2712)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2713))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2712)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2713))
| 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),X2713),X2712))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2712))
| 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),X2713),X2712))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_768,plain,
! [X2477,X2478,X2479] :
( ~ c_Finite__Set_Ofinite(X2479,X2478)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2479,tc_HOL_Obool),X2477),X2478))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2479,X2478)),c_Finite__Set_Ocard(X2479,X2477)))
| X2477 = X2478 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_769,plain,
! [X2553,X2554,X2555,X2556] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2556,tc_HOL_Obool),X2555),X2554))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2556,tc_HOL_Obool),X2555),c_Set_Oinsert(X2556,X2553,X2554))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_770,plain,
! [X2722,X2723,X2724,X2725] :
( ~ class_Groups_Oordered__comm__monoid__add(X2725)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2725,c_Groups_Ozero__class_Ozero(X2725)),X2724))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2725),X2723),X2722))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2725),X2723),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2725),X2724),X2722))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_771,plain,
! [X2726,X2727,X2728,X2729] :
( ~ class_Groups_Oordered__comm__monoid__add(X2729)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2729),c_Groups_Ozero__class_Ozero(X2729)),X2728))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2729,X2727),X2726))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2729),X2727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2729),X2728),X2726))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_772,plain,
! [X2677,X2678,X2679] :
( ~ class_Groups_Oordered__comm__monoid__add(X2679)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2679,c_Groups_Ozero__class_Ozero(X2679)),X2678))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2679,c_Groups_Ozero__class_Ozero(X2679)),X2677))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2679,c_Groups_Ozero__class_Ozero(X2679)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2679),X2678),X2677))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_773,plain,
! [X2267,X2268,X2269] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2269,tc_HOL_Obool)),X2268),X2267))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2269,tc_HOL_Obool),X2268),X2267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_774,plain,
! [X2264,X2265,X2266] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2266,tc_HOL_Obool),X2265),X2264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2266,tc_HOL_Obool)),X2265),X2264))
| X2265 = X2264 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2266,tc_HOL_Obool)),X2265),X2264))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2266,tc_HOL_Obool),X2265),X2264)) )
& ( X2265 != X2264
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2266,tc_HOL_Obool),X2265),X2264)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_775,plain,
! [X2261,X2262,X2263] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2263,tc_HOL_Obool),X2262),X2261))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2263,tc_HOL_Obool)),X2262),X2261)) )
& ( X2262 != X2261
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2263,tc_HOL_Obool)),X2262),X2261)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2263,tc_HOL_Obool),X2262),X2261))
| X2262 = X2261
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2263,tc_HOL_Obool)),X2262),X2261)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_776,plain,
! [X2564,X2565,X2566,X2567] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2567),X2566),c_Set_Oinsert(X2567,X2565,X2564)))
| X2566 = X2565
| hBOOL(hAPP(hAPP(c_member(X2567),X2566),X2564)) )
& ( X2566 != X2565
| hBOOL(hAPP(hAPP(c_member(X2567),X2566),c_Set_Oinsert(X2567,X2565,X2564))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2567),X2566),X2564))
| hBOOL(hAPP(hAPP(c_member(X2567),X2566),c_Set_Oinsert(X2567,X2565,X2564))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_777,plain,
! [X2521,X2522,X2523,X2524] :
( ~ hBOOL(hAPP(hAPP(c_member(X2524),X2523),c_Set_Oinsert(X2524,X2522,X2521)))
| X2523 = X2522
| hBOOL(hAPP(hAPP(c_member(X2524),X2523),X2521)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
fof(i_0_778,plain,
! [X2673,X2674] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2674,c_Groups_Ozero__class_Ozero(X2674)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2674),X2673),X2673)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2674,c_Groups_Ozero__class_Ozero(X2674)),X2673))
| ~ class_Groups_Olinordered__ab__group__add(X2674) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2674,c_Groups_Ozero__class_Ozero(X2674)),X2673))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2674,c_Groups_Ozero__class_Ozero(X2674)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2674),X2673),X2673)))
| ~ class_Groups_Olinordered__ab__group__add(X2674) ) ),
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_779,plain,
! [X1909,X1910,X1911] : c_FuncSet_OPi(X1911,X1910,X1909,hAPP(c_COMBK(tc_fun(X1910,tc_HOL_Obool),X1911),c_Orderings_Otop__class_Otop(tc_fun(X1910,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1911,X1910),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pi__UNIV]) ).
fof(i_0_780,plain,
! [X2683,X2684,X2685,X2686] :
( ~ class_Groups_Oordered__comm__monoid__add(X2686)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2686,c_Groups_Ozero__class_Ozero(X2686)),X2685))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2686,X2684),X2683))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2686,X2684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2686),X2685),X2683))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_781,plain,
! [X2687,X2688,X2689,X2690] :
( ~ class_Groups_Oordered__comm__monoid__add(X2690)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2690,c_Groups_Ozero__class_Ozero(X2690)),X2689))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2690,X2688),X2687))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2690,X2688),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2690),X2687),X2689))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_782,plain,
! [X2598,X2599,X2600,X2601] :
( ~ c_Finite__Set_Ofinite(X2601,X2600)
| ~ c_Finite__Set_Ofinite(X2599,X2598)
| c_Finite__Set_Ofinite(tc_sum(X2601,X2599),c_Sum__Type_OPlus(X2601,X2599,X2600,X2598)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_783,plain,
! [X3229,X3230,X3231,X3232,X3233,X3234] : hAPP(hAPP(hAPP(c_COMBC(X3234,X3233,X3232),X3231),X3230),X3229) = hAPP(hAPP(X3231,X3229),X3230),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_784,plain,
! [X2333,X2334,X2335] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2333,tc_HOL_Obool),X2335),X2334))
| X2335 != X2334 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2333,tc_HOL_Obool),X2334),X2335))
| X2335 != X2334 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2333,tc_HOL_Obool),X2335),X2334))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2333,tc_HOL_Obool),X2334),X2335))
| X2335 = X2334 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_785,plain,
! [X2328,X2329,X2330] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2330,tc_HOL_Obool),X2329),X2328))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2330,tc_HOL_Obool),X2328),X2329))
| X2329 = X2328 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_786,plain,
! [X2230,X2231,X2232,X2233] :
( ~ hBOOL(hAPP(hAPP(c_member(X2233),X2232),X2231))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2233,tc_HOL_Obool),X2231),X2230))
| hBOOL(hAPP(hAPP(c_member(X2233),X2232),X2230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_787,plain,
! [X2234,X2235,X2236,X2237] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2237,tc_HOL_Obool),X2236),X2235))
| ~ hBOOL(hAPP(hAPP(c_member(X2237),X2234),X2236))
| hBOOL(hAPP(hAPP(c_member(X2237),X2234),X2235)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_788,plain,
! [X2226,X2227,X2228,X2229] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2229,tc_HOL_Obool),X2228),X2227))
| ~ hBOOL(hAPP(hAPP(c_member(X2229),X2226),X2228))
| hBOOL(hAPP(hAPP(c_member(X2229),X2226),X2227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_789,plain,
! [X2135,X2136,X2137,X2138] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2138,tc_HOL_Obool),X2137),X2136))
| ~ hBOOL(hAPP(hAPP(c_member(X2138),X2135),X2137))
| hBOOL(hAPP(hAPP(c_member(X2138),X2135),X2136)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_790,plain,
! [X2019,X2020,X2021,X2022,X2023] :
( ~ class_Orderings_Oord(X2023)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2022,X2023),X2021),X2020))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2023,hAPP(X2021,X2019)),hAPP(X2020,X2019))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_791,plain,
! [X1981,X1982,X1983,X1984,X1985] :
( ~ class_Orderings_Oord(X1985)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1984,X1985),X1983),X1982))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1985,hAPP(X1983,X1981)),hAPP(X1982,X1981))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_792,plain,
! [X2921,X2922,X2923,X2924] :
( ~ c_Finite__Set_Ofinite(X2924,X2923)
| c_Finite__Set_Ofinite(X2922,c_Set_Oimage(X2924,X2922,X2921,X2923)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
fof(i_0_793,plain,
! [X2480,X2481,X2482] :
( ~ c_Finite__Set_Ofinite(X2482,X2481)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2482,tc_HOL_Obool),X2480),X2481))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2482,X2480)),c_Finite__Set_Ocard(X2482,X2481))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_794,plain,
! [X2876,X2877,X2878,X2879] :
( ~ class_Rings_Ocomm__semiring__1(X2879)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2879),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2879),X2878),X2877)),X2876) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2879),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2879),X2878),X2876)),X2877) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_795,plain,
! [X1932,X1933,X1934,X1935,X1936] :
( ( hAPP(X1934,X1933) != hAPP(X1934,X1932)
| X1933 = X1932
| ~ c_Fun_Oinj__on(X1936,X1935,X1934,c_Orderings_Otop__class_Otop(tc_fun(X1936,tc_HOL_Obool))) )
& ( X1933 != X1932
| hAPP(X1934,X1933) = hAPP(X1934,X1932)
| ~ c_Fun_Oinj__on(X1936,X1935,X1934,c_Orderings_Otop__class_Otop(tc_fun(X1936,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_796,plain,
! [X1937,X1938,X1939,X1940,X1941] :
( ~ c_Fun_Oinj__on(X1941,X1940,X1939,c_Orderings_Otop__class_Otop(tc_fun(X1941,tc_HOL_Obool)))
| hAPP(X1939,X1938) != hAPP(X1939,X1937)
| X1938 = X1937 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_797,plain,
! [X3180,X3181,X3182,X3183,X3184] :
( ( X3183 = X3181
| c_SetInterval_Oord__class_OatLeastLessThan(X3184,X3183,X3182) != c_SetInterval_Oord__class_OatLeastLessThan(X3184,X3181,X3180)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3184),X3181),X3180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3184),X3183),X3182))
| ~ class_Orderings_Olinorder(X3184) )
& ( X3182 = X3180
| c_SetInterval_Oord__class_OatLeastLessThan(X3184,X3183,X3182) != c_SetInterval_Oord__class_OatLeastLessThan(X3184,X3181,X3180)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3184),X3181),X3180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3184),X3183),X3182))
| ~ class_Orderings_Olinorder(X3184) )
& ( X3183 != X3181
| X3182 != X3180
| c_SetInterval_Oord__class_OatLeastLessThan(X3184,X3183,X3182) = c_SetInterval_Oord__class_OatLeastLessThan(X3184,X3181,X3180)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3184),X3181),X3180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3184),X3183),X3182))
| ~ class_Orderings_Olinorder(X3184) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).
fof(i_0_798,plain,
! [X3185,X3186,X3187,X3188,X3189] :
( ~ class_Orderings_Olinorder(X3189)
| c_SetInterval_Oord__class_OatLeastLessThan(X3189,X3188,X3187) != c_SetInterval_Oord__class_OatLeastLessThan(X3189,X3186,X3185)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3189),X3188),X3187))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3189),X3186),X3185))
| X3188 = X3186 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).
fof(i_0_799,plain,
! [X3190,X3191,X3192,X3193,X3194] :
( ~ class_Orderings_Olinorder(X3194)
| c_SetInterval_Oord__class_OatLeastLessThan(X3194,X3193,X3192) != c_SetInterval_Oord__class_OatLeastLessThan(X3194,X3191,X3190)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3194),X3193),X3192))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3194),X3191),X3190))
| X3192 = X3190 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).
fof(i_0_800,plain,
! [X2898,X2899,X2901] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk35_2(X2898,X2899)),X2898))
| ~ hBOOL(hAPP(X2899,X2898))
| hBOOL(hAPP(X2899,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2901),esk35_2(X2898,X2899)))
| ~ hBOOL(hAPP(X2899,X2901))
| ~ hBOOL(hAPP(X2899,X2898))
| hBOOL(hAPP(X2899,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X2899,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk35_2(X2898,X2899)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X2899,X2898))
| hBOOL(hAPP(X2899,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_535])])])])]) ).
fof(i_0_801,plain,
! [X2820,X2821] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2821),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2821),X2820)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_802,plain,
! [X2822,X2823] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2823),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2822),X2823)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_803,plain,
! [X2572,X2573,X2574,X2575] :
( ~ hBOOL(hAPP(hAPP(c_member(X2575),X2574),X2573))
| hBOOL(hAPP(hAPP(c_member(X2575),X2574),c_Set_Oinsert(X2575,X2572,X2573))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_804,plain,
! [X2525,X2526,X2527,X2528] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2528),X2527),X2526))
| hBOOL(hAPP(hAPP(c_member(X2528),X2527),c_Set_Oinsert(X2528,X2525,X2526))) )
& ( X2527 != X2525
| hBOOL(hAPP(hAPP(c_member(X2528),X2527),c_Set_Oinsert(X2528,X2525,X2526))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_536])])]) ).
fof(i_0_805,plain,
! [X2770,X2771,X2772] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2772),X2771))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2771),X2770))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2772)),X2770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_806,plain,
! [X2739] :
( ~ c_Finite__Set_Ofinite(X2739,c_Orderings_Otop__class_Otop(tc_fun(X2739,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(X2739,c_Orderings_Otop__class_Otop(tc_fun(X2739,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_807,plain,
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk41_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,esk41_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_808,plain,
! [X2777,X2778] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2778)),hAPP(c_Nat_OSuc,X2777)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2778),X2777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_809,plain,
! [X2760,X2761] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2761)),hAPP(c_Nat_OSuc,X2760)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2761),X2760)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2761),X2760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2761)),hAPP(c_Nat_OSuc,X2760))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_810,plain,
! [X2742,X2743] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2743,X2742),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2743,X2742),tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2742,c_Orderings_Otop__class_Otop(tc_fun(X2742,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Finite__Set_Ofinite(X2743,c_Orderings_Otop__class_Otop(tc_fun(X2743,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_811,plain,
! [X1846,X1847,X1848,X1849] :
( ~ class_Orderings_Opreorder(X1849)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1849),X1848),X1847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1849),X1847),X1846))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1849),X1848),X1846)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_812,plain,
! [X1850,X1851,X1852,X1853] :
( ~ class_Orderings_Oorder(X1853)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1853),X1852),X1851))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1853),X1850),X1852))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1853),X1850),X1851)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_813,plain,
! [X3163,X3164] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3164,X3163)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3164),hAPP(c_Nat_OSuc,X3163)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).
fof(i_0_814,plain,
! [X2680,X2681,X2682] :
( ( X2681 = c_Groups_Ozero__class_Ozero(X2682)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2682),X2681),X2680) != c_Groups_Ozero__class_Ozero(X2682)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2682,c_Groups_Ozero__class_Ozero(X2682)),X2680))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2682,c_Groups_Ozero__class_Ozero(X2682)),X2681))
| ~ class_Groups_Oordered__comm__monoid__add(X2682) )
& ( X2680 = c_Groups_Ozero__class_Ozero(X2682)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2682),X2681),X2680) != c_Groups_Ozero__class_Ozero(X2682)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2682,c_Groups_Ozero__class_Ozero(X2682)),X2680))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2682,c_Groups_Ozero__class_Ozero(X2682)),X2681))
| ~ class_Groups_Oordered__comm__monoid__add(X2682) )
& ( X2681 != c_Groups_Ozero__class_Ozero(X2682)
| X2680 != c_Groups_Ozero__class_Ozero(X2682)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2682),X2681),X2680) = c_Groups_Ozero__class_Ozero(X2682)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2682,c_Groups_Ozero__class_Ozero(X2682)),X2680))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2682,c_Groups_Ozero__class_Ozero(X2682)),X2681))
| ~ class_Groups_Oordered__comm__monoid__add(X2682) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_815,plain,
! [X2625,X2626] : c_Sum__Type_OPlus(X2626,X2625,c_Orderings_Otop__class_Otop(tc_fun(X2626,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2625,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2626,X2625),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_816,plain,
! [X2241,X2242,X2243] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2243),X2242))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2243),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2242),X2241))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_817,plain,
! [X2163,X2164,X2165] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2165),X2164))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2165),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2164),X2163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_818,plain,
! [X2238,X2239,X2240] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2240),X2239))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2240),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2238),X2239))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_819,plain,
! [X2160,X2161,X2162] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2162),X2161))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2162),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2160),X2161))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_820,plain,
! [X2810,X2811,X2813,X2814,X2815] :
( ( X2811 = hAPP(c_Nat_OSuc,esk33_2(X2810,X2811))
| X2811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2811),hAPP(c_Nat_OSuc,X2810))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_2(X2810,X2811)),X2810))
| X2811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2811),hAPP(c_Nat_OSuc,X2810))) )
& ( X2814 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2814),hAPP(c_Nat_OSuc,X2813))) )
& ( X2814 != hAPP(c_Nat_OSuc,X2815)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2815),X2813))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2814),hAPP(c_Nat_OSuc,X2813))) ) ),
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_821,plain,
! [X2880,X2881,X2882,X2883] :
( ~ class_Rings_Ocomm__semiring__1(X2883)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2883),X2882),X2881)),X2880) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2883),X2882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2883),X2881),X2880)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_822,plain,
! [X2392,X2393,X2394,X2395] :
( ~ class_Groups_Oab__semigroup__add(X2395)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2395),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2395),X2394),X2393)),X2392) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2395),X2394),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2395),X2393),X2392)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_823,plain,
! [X2884,X2885,X2886,X2887] :
( ~ class_Rings_Ocomm__semiring__1(X2887)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2887),X2886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2887),X2885),X2884)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2887),X2886),X2885)),X2884) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_824,plain,
! [X2579,X2580,X2581,X2582] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2582,X2581,X2580),X2579))
| X2581 = X2579
| hBOOL(hAPP(X2580,X2579)) )
& ( X2581 != X2579
| hBOOL(hAPP(c_Set_Oinsert(X2582,X2581,X2580),X2579)) )
& ( ~ hBOOL(hAPP(X2580,X2579))
| hBOOL(hAPP(c_Set_Oinsert(X2582,X2581,X2580),X2579)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_825,plain,
! [X2736] :
( ~ class_Rings_Olinordered__semidom(X2736)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2736),c_Groups_Ozero__class_Ozero(X2736)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2736),c_Groups_Oone__class_Oone(X2736)),c_Groups_Oone__class_Oone(X2736)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_826,plain,
! [X2790,X2791] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2791)),hAPP(c_Nat_OSuc,X2790)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2791),X2790)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2791),X2790))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2791)),hAPP(c_Nat_OSuc,X2790))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_827,plain,
! [X2086,X2087,X2088,X2089] :
( ~ class_Orderings_Opreorder(X2089)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2089,X2088),X2087))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2089),X2087),X2086))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2089),X2088),X2086)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_828,plain,
! [X2078,X2079,X2080,X2081] :
( ~ class_Orderings_Opreorder(X2081)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2081),X2080),X2079))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2081,X2079),X2078))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2081),X2080),X2078)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_829,plain,
! [X2090,X2091,X2092,X2093] :
( ~ class_Orderings_Oorder(X2093)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2093,X2092),X2091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2093),X2090),X2092))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2093),X2090),X2091)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_830,plain,
! [X2082,X2083,X2084,X2085] :
( ~ class_Orderings_Oorder(X2085)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2085),X2084),X2083))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2085,X2082),X2084))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2085),X2082),X2083)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_831,plain,
! [X2494,X2495] :
( ( c_Finite__Set_Ofinite(X2495,c_Orderings_Otop__class_Otop(tc_fun(X2495,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2495,X2494),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2495,X2494),tc_HOL_Obool))) )
& ( c_Finite__Set_Ofinite(X2494,c_Orderings_Otop__class_Otop(tc_fun(X2494,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2495,X2494),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2495,X2494),tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2495,c_Orderings_Otop__class_Otop(tc_fun(X2495,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2494,c_Orderings_Otop__class_Otop(tc_fun(X2494,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_sum(X2495,X2494),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2495,X2494),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_832,plain,
! [X2496,X2497] :
( ~ c_Finite__Set_Ofinite(X2497,c_Orderings_Otop__class_Otop(tc_fun(X2497,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2496,c_Orderings_Otop__class_Otop(tc_fun(X2496,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_prod(X2497,X2496),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2497,X2496),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_833,plain,
! [X2149,X2150,X2151,X2152] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2152),X2151))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2150),X2151) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2152),X2149)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2150),X2149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_834,plain,
! [X2550,X2551,X2552] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2552,tc_HOL_Obool),X2551),c_Set_Oinsert(X2552,X2550,X2551))),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_835,plain,
! [X2568,X2569,X2570,X2571] :
( ( c_Set_Oinsert(X2571,X2570,X2569) != c_Set_Oinsert(X2571,X2570,X2568)
| X2569 = X2568
| hBOOL(hAPP(hAPP(c_member(X2571),X2570),X2568))
| hBOOL(hAPP(hAPP(c_member(X2571),X2570),X2569)) )
& ( X2569 != X2568
| c_Set_Oinsert(X2571,X2570,X2569) = c_Set_Oinsert(X2571,X2570,X2568)
| hBOOL(hAPP(hAPP(c_member(X2571),X2570),X2568))
| hBOOL(hAPP(hAPP(c_member(X2571),X2570),X2569)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_537])])]) ).
fof(i_0_836,plain,
! [X2775,X2776] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2776)),X2775))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2776),X2775)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_837,plain,
! [X2786,X2787] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2787),X2786))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2786)),X2787)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2786)),X2787))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2787),X2786)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])]) ).
fof(i_0_838,plain,
! [X2746,X2747] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2747),X2746))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2747)),hAPP(c_Nat_OSuc,X2746))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_839,plain,
! [X2247,X2248,X2249] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2249),X2248))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2249),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2248),X2247))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_840,plain,
! [X2192,X2193,X2194] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2194),X2193))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2193),X2192))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_841,plain,
! [X2244,X2245,X2246] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2246),X2245))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2246),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2244),X2245))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_842,plain,
! [X2189,X2190,X2191] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2191),X2190))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2189),X2190))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_843,plain,
! [X2501,X2502] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2502,X2501),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2502,X2501),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2501,c_Orderings_Otop__class_Otop(tc_fun(X2501,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_844,plain,
! [X2756,X2757] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2757),X2756))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2756),hAPP(c_Nat_OSuc,X2757))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2756),hAPP(c_Nat_OSuc,X2757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2757),X2756)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])]) ).
fof(i_0_845,plain,
! [X2213,X2214,X2215] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2215),X2214)),X2213) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2215),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2214),X2213)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_846,plain,
! [X2842,X2843] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2843),X2842))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2843)),X2842)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2843)),X2842))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2843),X2842)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_847,plain,
! [X2838,X2839] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2839)),X2838))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2839),X2838)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2839),X2838))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2839)),X2838)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_848,plain,
! [X2830,X2831] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2831)),X2830))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2831),X2830)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_849,plain,
! [X2346,X2347,X2348,X2349] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2349,tc_HOL_Obool),X2348),X2347))
| ~ hBOOL(hAPP(X2348,X2346))
| hBOOL(hAPP(X2347,X2346)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_850,plain,
! [X2336,X2337,X2338,X2339] :
( ~ hBOOL(hAPP(X2339,X2338))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2337,tc_HOL_Obool),X2339),X2336))
| hBOOL(hAPP(X2336,X2338)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_851,plain,
! [X2008,X2009,X2010,X2011] :
( ~ class_Orderings_Opreorder(X2011)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2011,X2010),X2009))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2011,X2009),X2008))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2011,X2010),X2008)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_852,plain,
! [X2015,X2016,X2017,X2018] :
( ~ class_Orderings_Oorder(X2018)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2018,X2017),X2016))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2018,X2015),X2017))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2018,X2015),X2016)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_853,plain,
! [X2768,X2769] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2769),X2768))
| hAPP(c_Nat_OSuc,X2769) = X2768
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2769)),X2768)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_854,plain,
! [X1827,X1828,X1829] :
( ~ class_Orderings_Oorder(X1829)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1829),X1828),X1827))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1829),X1827),X1828)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])]) ).
fof(i_0_855,plain,
! [X1797,X1798,X1799] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1799),X1798),X1797))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1799),X1797),X1798))
| X1798 = X1797
| ~ class_Orderings_Olinorder(X1799) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1799),X1797),X1798))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1799),X1798),X1797))
| ~ class_Orderings_Olinorder(X1799) )
& ( X1798 != X1797
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1799),X1798),X1797))
| ~ class_Orderings_Olinorder(X1799) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])])]) ).
fof(i_0_856,plain,
! [X1854,X1855,X1856] :
( ~ class_Orderings_Opreorder(X1856)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1856),X1855),X1854))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1856),X1854),X1855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])]) ).
fof(i_0_857,plain,
! [X1824,X1825,X1826] :
( ~ class_Orderings_Opreorder(X1826)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1826),X1825),X1824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1826),X1824),X1825)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])]) ).
fof(i_0_858,plain,
! [X1815,X1816,X1817] :
( ~ class_Orderings_Opreorder(X1817)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1817),X1816),X1815))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1817),X1815),X1816)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])]) ).
fof(i_0_859,plain,
! [X1812,X1813,X1814] :
( ~ class_Orderings_Opreorder(X1814)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1814),X1813),X1812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1814),X1812),X1813)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])]) ).
fof(i_0_860,plain,
! [X2308,X2309] :
( ~ class_Rings_Olinordered__semidom(X2309)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2309),X2308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2309),X2308),c_Groups_Oone__class_Oone(X2309)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_861,plain,
! [X2832,X2833] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2832),hAPP(c_Nat_OSuc,X2833)))
| X2832 = X2833
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2833),X2832)) )
& ( X2832 != X2833
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2832),hAPP(c_Nat_OSuc,X2833)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2833),X2832)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_862,plain,
! [X2796,X2797] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2797)),X2796))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2797),X2796)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_863,plain,
! [X2510,X2511,X2512] :
( ~ c_Finite__Set_Ofinite(X2512,X2511)
| hBOOL(hAPP(hAPP(c_member(X2512),X2510),X2511))
| c_Finite__Set_Ocard(X2512,c_Set_Oinsert(X2512,X2510,X2511)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X2512,X2511)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])]) ).
fof(i_0_864,plain,
! [X2039,X2040,X2041] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2041,X2040),X2039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2041),X2040),X2039))
| ~ class_Orderings_Opreorder(X2041) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2041,X2039),X2040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2041),X2040),X2039))
| ~ class_Orderings_Opreorder(X2041) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2041,X2040),X2039))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2041,X2039),X2040))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2041),X2040),X2039))
| ~ class_Orderings_Opreorder(X2041) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])])]) ).
fof(i_0_865,plain,
! [X2848,X2849,X2850] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2850),X2848),X2849))
| c_Finite__Set_Ocard(X2850,c_Set_Oinsert(X2850,X2848,X2849)) = c_Finite__Set_Ocard(X2850,X2849)
| ~ c_Finite__Set_Ofinite(X2850,X2849) )
& ( hBOOL(hAPP(hAPP(c_member(X2850),X2848),X2849))
| c_Finite__Set_Ocard(X2850,c_Set_Oinsert(X2850,X2848,X2849)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2850,X2849))
| ~ c_Finite__Set_Ofinite(X2850,X2849) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])])]) ).
fof(i_0_866,plain,
! [X3168,X3170,X3171,X3172] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3168)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3170),X3168))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3170),esk43_1(X3168))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk44_2(X3171,X3172)),X3171))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3171) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk44_2(X3171,X3172)),X3172))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3171) ) ),
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_867,plain,
! [X2583,X2584,X2585,X2586] : c_Set_Oinsert(X2586,X2585,c_Set_Oinsert(X2586,X2584,X2583)) = c_Set_Oinsert(X2586,X2584,c_Set_Oinsert(X2586,X2585,X2583)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_868,plain,
! [X2561,X2562,X2563] : hBOOL(hAPP(hAPP(c_member(X2563),X2562),c_Set_Oinsert(X2563,X2562,X2561))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_869,plain,
! [X2773,X2774] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2774),hAPP(c_Nat_OSuc,X2773)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2774),X2773))
| X2774 = X2773 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])]) ).
fof(i_0_870,plain,
! [X2764,X2765] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2765),X2764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2765),hAPP(c_Nat_OSuc,X2764)))
| X2764 = X2765 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).
fof(i_0_871,plain,
! [X2762,X2763] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2763),hAPP(c_Nat_OSuc,X2762)))
| X2763 = X2762
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2763),X2762)) )
& ( X2763 != X2762
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2763),hAPP(c_Nat_OSuc,X2762)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2763),X2762)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])])]) ).
fof(i_0_872,plain,
! [X2758,X2759] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),hAPP(c_Nat_OSuc,X2758)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),X2758))
| X2759 = X2758 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),X2758))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),hAPP(c_Nat_OSuc,X2758))) )
& ( X2759 != X2758
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),hAPP(c_Nat_OSuc,X2758))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_873,plain,
! [X2834,X2835] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2835),X2834))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2835)),X2834)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_874,plain,
! [X2888,X2889,X2890,X2891] :
( ~ class_Rings_Ocomm__semiring__1(X2891)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2891),X2890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2891),X2889),X2888)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2891),X2889),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2891),X2890),X2888)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_875,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,X2300),X2299))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2301),X2299)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_876,plain,
! [X2490,X2491,X2492] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2492,tc_HOL_Obool),X2491),X2490))
| ~ c_Finite__Set_Ofinite(X2492,X2490)
| c_Finite__Set_Ofinite(X2492,X2491) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_877,plain,
! [X2487,X2488,X2489] :
( ~ c_Finite__Set_Ofinite(X2489,X2488)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2489,tc_HOL_Obool),X2487),X2488))
| c_Finite__Set_Ofinite(X2489,X2487) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_878,plain,
! [X2066,X2067,X2068] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2068),X2067),X2066))
| X2067 = X2066
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2068,X2067),X2066))
| ~ class_Orderings_Olinorder(X2068) )
& ( X2067 != X2066
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2068),X2067),X2066))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2068,X2067),X2066))
| ~ class_Orderings_Olinorder(X2068) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])])]) ).
fof(i_0_879,plain,
! [X2060,X2061,X2062] :
( ~ class_Orderings_Olinorder(X2062)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2062,X2061),X2060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2062),X2060),X2061)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])]) ).
fof(i_0_880,plain,
! [X2027,X2028,X2029] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2029),X2028),X2027))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2029,X2027),X2028))
| ~ class_Orderings_Olinorder(X2029) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2029,X2027),X2028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2029),X2028),X2027))
| ~ class_Orderings_Olinorder(X2029) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])])]) ).
fof(i_0_881,plain,
! [X2030,X2031,X2032] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2032,X2031),X2030))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2032),X2030),X2031))
| ~ class_Orderings_Olinorder(X2032) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2032),X2030),X2031))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2032,X2031),X2030))
| ~ class_Orderings_Olinorder(X2032) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])])]) ).
fof(i_0_882,plain,
! [X2824,X2825,X2827,X2828,X2829] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2825),X2824))
| X2824 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2825),esk34_2(X2824,X2825))) )
& ( X2827 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2828),X2829))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2828),X2827)) ) ),
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_883,plain,
! [X2840,X2841] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2841),hAPP(c_Nat_OSuc,X2840)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2841),X2840)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2841),X2840))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2841),hAPP(c_Nat_OSuc,X2840))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_884,plain,
! [X3174,X3176,X3177,X3178] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X3174)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3176),X3174))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3176),esk45_1(X3174))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk46_2(X3177,X3178)),X3177))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3177) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk46_2(X3177,X3178)),X3178))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X3177) ) ),
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_885,plain,
! [X2845,X2846,X2847] :
( ~ c_Finite__Set_Ofinite(X2847,X2846)
| hBOOL(hAPP(hAPP(c_member(X2847),X2845),X2846))
| c_Finite__Set_Ocard(X2847,c_Set_Oinsert(X2847,X2845,X2846)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2847,X2846)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])]) ).
fof(i_0_886,plain,
! [X2766,X2767] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2767),X2766))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2767),hAPP(c_Nat_OSuc,X2766))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_887,plain,
! [X2863,X2864] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2864),X2863),X2863) != c_Groups_Ozero__class_Ozero(X2864)
| X2863 = c_Groups_Ozero__class_Ozero(X2864)
| ~ hBOOL(hAPP(hAPP(c_member(X2864),X2863),c_Int_Oring__1__class_OInts(X2864)))
| ~ class_Int_Oring__char__0(X2864) )
& ( X2863 != c_Groups_Ozero__class_Ozero(X2864)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2864),X2863),X2863) = c_Groups_Ozero__class_Ozero(X2864)
| ~ hBOOL(hAPP(hAPP(c_member(X2864),X2863),c_Int_Oring__1__class_OInts(X2864)))
| ~ class_Int_Oring__char__0(X2864) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).
fof(i_0_888,plain,
! [X3098,X3099,X3100,X3101] : c_Nat_Onat_Onat__case(X3101,X3100,X3099,hAPP(c_Nat_OSuc,X3098)) = hAPP(X3099,X3098),
inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).
fof(i_0_889,plain,
! [X2794,X2795] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2795),hAPP(c_Nat_OSuc,X2794)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2795),X2794))
| X2795 = hAPP(c_Nat_OSuc,X2794) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])]) ).
fof(i_0_890,plain,
! [X2788,X2789] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),hAPP(c_Nat_OSuc,X2788)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),X2788))
| X2789 = hAPP(c_Nat_OSuc,X2788) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),X2788))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),hAPP(c_Nat_OSuc,X2788))) )
& ( X2789 != hAPP(c_Nat_OSuc,X2788)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),hAPP(c_Nat_OSuc,X2788))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_891,plain,
! [X2250,X2251] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2251,tc_HOL_Obool),X2250),c_Orderings_Otop__class_Otop(tc_fun(X2251,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_892,plain,
! [X2281,X2282,X2283] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2282),X2283))
| hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| X2283 = X2282
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2283),X2282)) )
& ( ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| X2283 = X2282
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2283),X2282)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2282),X2283))
| hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2283),X2282)) )
& ( ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2283),X2282)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2282),X2283))
| hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| X2283 = X2282
| ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283)) )
& ( ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| X2283 = X2282
| ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2282),X2283))
| hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283)) )
& ( ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283))
| ~ hBOOL(hAPP(hAPP(X2281,X2282),X2283)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_893,plain,
! [X2210,X2211,X2212] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2211),X2210)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2212),X2210)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_894,plain,
! [X2012,X2013,X2014] :
( ~ class_Orderings_Oorder(X2014)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2014,X2013),X2012))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2014,X2012),X2013))
| X2012 = X2013 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_895,plain,
! [X2005,X2006,X2007] :
( ~ class_Orderings_Oorder(X2007)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2007,X2006),X2005))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2007,X2005),X2006))
| X2006 = X2005 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_896,plain,
! [X1986,X1987,X1988] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1988,X1986),X1987))
| X1986 = X1987
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1988,X1987),X1986))
| ~ class_Orderings_Oorder(X1988) )
& ( X1986 != X1987
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1988,X1986),X1987))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1988,X1987),X1986))
| ~ class_Orderings_Oorder(X1988) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_897,plain,
! [X1975,X1976,X1977] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1977,X1976),X1975))
| X1976 != X1975
| ~ class_Orderings_Oorder(X1977) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1977,X1975),X1976))
| X1976 != X1975
| ~ class_Orderings_Oorder(X1977) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1977,X1976),X1975))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1977,X1975),X1976))
| X1976 = X1975
| ~ class_Orderings_Oorder(X1977) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_898,plain,
! [X2737,X2738] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2738,X2737)))
| c_Finite__Set_Ofinite(X2738,X2737) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
fof(i_0_899,plain,
! [X2785] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2785)),X2785)),
inference(variable_rename,[status(thm)],[i_0_558]) ).
fof(i_0_900,plain,
! [X2836,X2837] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2837),X2836))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2837),hAPP(c_Nat_OSuc,X2836))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_901,plain,
! [X2499,X2500] :
( ~ c_Finite__Set_Ofinite(X2500,c_Orderings_Otop__class_Otop(tc_fun(X2500,tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2500,X2499) != c_Finite__Set_Ocard(X2500,c_Orderings_Otop__class_Otop(tc_fun(X2500,tc_HOL_Obool)))
| X2499 = c_Orderings_Otop__class_Otop(tc_fun(X2500,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_902,plain,
! [X2042,X2043,X2044] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2044,X2043),X2042))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2044),X2043),X2042))
| X2043 = X2042
| ~ class_Orderings_Oorder(X2044) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2044),X2043),X2042))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2044,X2043),X2042))
| ~ class_Orderings_Oorder(X2044) )
& ( X2043 != X2042
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2044,X2043),X2042))
| ~ class_Orderings_Oorder(X2044) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_903,plain,
! [X2036,X2037,X2038] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2038,X2037),X2036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2038),X2037),X2036))
| ~ class_Orderings_Oorder(X2038) )
& ( X2037 != X2036
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2038),X2037),X2036))
| ~ class_Orderings_Oorder(X2038) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2038,X2037),X2036))
| X2037 = X2036
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2038),X2037),X2036))
| ~ class_Orderings_Oorder(X2038) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_904,plain,
! [X2063,X2064,X2065] :
( ~ class_Orderings_Opreorder(X2065)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2065),X2064),X2063))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2065,X2064),X2063)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_905,plain,
! [X2204,X2205] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2205),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2205),X2204))),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_906,plain,
! [X2206,X2207] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2207),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2206),X2207))),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_907,plain,
! [X3079,X3080] : c_Set_Oimage(X3080,X3080,c_COMBI(X3080),X3079) = X3079,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_908,plain,
! [X2115,X2116] : c_Fun_Oinj__on(X2116,X2116,c_COMBI(X2116),X2115),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_909,plain,
! [X3102,X3103,X3104] : c_Nat_Onat_Onat__case(X3104,X3103,X3102,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3103,
inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).
fof(i_0_910,plain,
! [X2075,X2076,X2077] :
( ~ class_Orderings_Oorder(X2077)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2077,X2076),X2075))
| X2075 = X2076
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2077),X2076),X2075)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_911,plain,
! [X2072,X2073,X2074] :
( ~ class_Orderings_Oorder(X2074)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2074,X2073),X2072))
| X2073 = X2072
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2074),X2073),X2072)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_912,plain,
! [X2069,X2070,X2071] :
( ~ class_Orderings_Oorder(X2071)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2071,X2070),X2069))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2071),X2070),X2069))
| X2070 = X2069 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_913,plain,
! [X2054,X2055,X2056] :
( ~ class_Orderings_Oorder(X2056)
| X2055 = X2054
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2056,X2055),X2054))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2056),X2055),X2054)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_914,plain,
! [X2051,X2052,X2053] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2053,X2052),X2051))
| X2052 = X2051
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2053),X2052),X2051))
| ~ class_Orderings_Olinorder(X2053) )
& ( X2052 != X2051
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2053,X2052),X2051))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2053),X2052),X2051))
| ~ class_Orderings_Olinorder(X2053) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])])]) ).
fof(i_0_915,plain,
! [X2057,X2058,X2059] :
( ~ class_Orderings_Oorder(X2059)
| X2058 = X2057
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2059,X2057),X2058))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2059),X2057),X2058)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_916,plain,
! [X2809] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2809),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X2809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2809),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_917,plain,
! [X2804] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2804),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_918,plain,
! [X2302,X2303] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2303),X2302))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2302),X2303))
| X2303 = X2302 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_919,plain,
! [X1705,X1706,X1707] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1707),X1706),hAPP(c_fequal,X1705)))
| X1706 = X1705 )
& ( X1706 != X1705
| hBOOL(hAPP(hAPP(c_member(X1707),X1706),hAPP(c_fequal,X1705))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_920,plain,
! [X2792,X2793] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2793),X2792))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2793),hAPP(c_Nat_OSuc,X2792))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_921,plain,
! [X2711] :
( ~ class_Rings_Olinordered__semidom(X2711)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2711),c_Groups_Oone__class_Oone(X2711)),c_Groups_Ozero__class_Ozero(X2711))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])]) ).
fof(i_0_922,plain,
! [X2304,X2305] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2305),X2304))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2305),X2304)) )
& ( X2305 != X2304
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2305),X2304)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2305),X2304))
| X2305 = X2304
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2305),X2304)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_923,plain,
! [X2133,X2134] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2134),X2133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2134),X2133))
| X2134 = X2133 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2134),X2133))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2134),X2133)) )
& ( X2134 != X2133
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2134),X2133)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_924,plain,
! [X2131,X2132] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2132),X2131))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2132),X2131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_925,plain,
! [X2127,X2128] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2128),X2127))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2128),X2127)) )
& ( X2128 != X2127
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2128),X2127)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_926,plain,
! [X2096,X2097] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2097),X2096))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2097),X2096)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_927,plain,
! [X2576,X2577,X2578] :
( ~ hBOOL(hAPP(hAPP(c_member(X2578),X2577),X2576))
| c_Set_Oinsert(X2578,X2577,X2576) = X2576 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_928,plain,
! [X1794,X1795,X1796] :
( ( X1795 = X1794
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1796),X1795),X1794))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1796),X1794),X1795))
| ~ class_Orderings_Olinorder(X1796) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1796),X1795),X1794))
| X1795 != X1794
| ~ class_Orderings_Olinorder(X1796) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1796),X1794),X1795))
| X1795 != X1794
| ~ class_Orderings_Olinorder(X1796) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_929,plain,
! [X2369,X2370,X2371] :
( ~ class_Rings_Olinordered__idom(X2371)
| X2370 = X2369
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2371),X2370),X2369))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2371),X2369),X2370)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])]) ).
fof(i_0_930,plain,
! [X1857,X1858,X1859] :
( ~ class_Orderings_Olinorder(X1859)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1859),X1858),X1857))
| X1858 = X1857
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1859),X1857),X1858)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])]) ).
fof(i_0_931,plain,
! [X1806,X1807,X1808] :
( ~ class_Orderings_Olinorder(X1808)
| X1807 = X1806
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1808),X1807),X1806))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1808),X1806),X1807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_932,plain,
! [X1803,X1804,X1805] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1805),X1803),X1804))
| X1803 = X1804
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1805),X1804),X1803))
| ~ class_Orderings_Olinorder(X1805) )
& ( X1803 != X1804
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1805),X1803),X1804))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1805),X1804),X1803))
| ~ class_Orderings_Olinorder(X1805) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])])]) ).
fof(i_0_933,plain,
! [X1800,X1801,X1802] :
( ~ class_Orderings_Olinorder(X1802)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1802),X1801),X1800))
| X1801 = X1800
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1802),X1800),X1801)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_934,plain,
! [X2493] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X2493),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2493),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2493,c_Orderings_Otop__class_Otop(tc_fun(X2493,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2493,c_Orderings_Otop__class_Otop(tc_fun(X2493,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X2493),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2493),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_935,plain,
! [X2129,X2130] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2130),X2129))
| X2130 = X2129
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2130),X2129)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_936,plain,
! [X2587,X2588,X2589] : c_Set_Oinsert(X2589,X2588,c_Set_Oinsert(X2589,X2588,X2587)) = c_Set_Oinsert(X2589,X2588,X2587),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
fof(i_0_937,plain,
! [X1777,X1778] : hBOOL(hAPP(hAPP(c_member(X1778),X1777),c_Orderings_Otop__class_Otop(tc_fun(X1778,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_938,plain,
! [X1691,X1692] : hBOOL(hAPP(hAPP(c_member(X1692),X1691),c_Orderings_Otop__class_Otop(tc_fun(X1692,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_939,plain,
! [X2532,X2533,X2534] :
( ( ~ c_Finite__Set_Ofinite(X2534,c_Set_Oinsert(X2534,X2533,X2532))
| c_Finite__Set_Ofinite(X2534,X2532) )
& ( ~ c_Finite__Set_Ofinite(X2534,X2532)
| c_Finite__Set_Ofinite(X2534,c_Set_Oinsert(X2534,X2533,X2532)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).
fof(i_0_940,plain,
! [X1708,X1709,X1710] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1710),X1709),X1708))
| hBOOL(hAPP(X1708,X1709)) )
& ( ~ hBOOL(hAPP(X1708,X1709))
| hBOOL(hAPP(hAPP(c_member(X1710),X1709),X1708)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_941,plain,
! [X2048,X2049,X2050] :
( ~ class_Orderings_Olinorder(X2050)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2050,X2049),X2048))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2050),X2048),X2049)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])]) ).
fof(i_0_942,plain,
! [X2033,X2034,X2035] :
( ~ class_Orderings_Olinorder(X2035)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2035,X2034),X2033))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2035),X2033),X2034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_943,plain,
! [X2045,X2046,X2047] :
( ~ class_Orderings_Olinorder(X2047)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2047),X2046),X2045))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2047,X2045),X2046)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])]) ).
fof(i_0_944,plain,
! [X2781,X2782] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2782)),X2781) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2782),X2781)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_945,plain,
! [X2708] :
( ~ class_Rings_Olinordered__semidom(X2708)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2708,c_Groups_Oone__class_Oone(X2708)),c_Groups_Ozero__class_Ozero(X2708))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_946,plain,
! [X2198,X2199,X2201,X2202,X2203] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2199),X2198))
| X2198 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2199),esk28_2(X2198,X2199)) )
& ( X2201 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2202),X2203)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2202),X2201)) ) ),
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_947,plain,
! [X2291,X2292] :
( ( X2292 = X2291
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2292),X2291))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2291),X2292)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2292),X2291))
| X2292 != X2291 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2291),X2292))
| X2292 != X2291 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_948,plain,
! [X2289,X2290] :
( X2290 = X2289
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2290),X2289))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2289),X2290)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_949,plain,
! [X2805,X2807,X2808] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2805))
| X2805 = hAPP(c_Nat_OSuc,esk32_1(X2805)) )
& ( X2807 != hAPP(c_Nat_OSuc,X2808)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2807)) ) ),
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_950,plain,
! [X1821,X1822,X1823] :
( ~ class_Orderings_Oorder(X1823)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1823),X1822),X1821))
| X1821 != X1822 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_951,plain,
! [X1818,X1819,X1820] :
( ~ class_Orderings_Oorder(X1820)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1820),X1819),X1818))
| X1819 != X1818 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_952,plain,
! [X1809,X1810,X1811] :
( ~ class_Orderings_Oorder(X1811)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1811),X1810),X1809))
| X1810 != X1809 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_953,plain,
! [X2360,X2361,X2362] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2360,tc_HOL_Obool),X2362),X2361))
| X2362 != X2361 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2360,tc_HOL_Obool),X2361),X2362))
| X2362 != X2361 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])])]) ).
fof(i_0_954,plain,
! [X2340,X2341,X2342] :
( X2342 != X2341
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2340,tc_HOL_Obool),X2342),X2341)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_955,plain,
! [X2343,X2344,X2345] :
( X2345 != X2344
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2343,tc_HOL_Obool),X2344),X2345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_956,plain,
! [X1792,X1793] :
( ~ class_Orderings_Opreorder(X1793)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1793),X1792),X1792)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])]) ).
fof(i_0_957,plain,
! [X2331,X2332] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2332,tc_HOL_Obool),X2331),X2331)),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_958,plain,
! [X2657] :
( ( X2657 = 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)),X2657)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2657))
| X2657 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_959,plain,
! [X2384,X2385,X2386,X2387] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2387),X2386),X2385) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2387),X2384),X2385)
| X2386 = X2384
| ~ class_Groups_Ocancel__semigroup__add(X2387) )
& ( X2386 != X2384
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2387),X2386),X2385) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2387),X2384),X2385)
| ~ class_Groups_Ocancel__semigroup__add(X2387) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_960,plain,
! [X2372,X2373,X2374,X2375] :
( ~ class_Groups_Ocancel__semigroup__add(X2375)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2375),X2374),X2373) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2375),X2372),X2373)
| X2374 = X2372 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_961,plain,
! [X2376,X2377,X2378,X2379] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X2379)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2379),X2378),X2377) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2379),X2378),X2376)
| X2377 = X2376 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_962,plain,
! [X2388,X2389,X2390,X2391] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2391),X2390),X2389) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2391),X2390),X2388)
| X2389 = X2388
| ~ class_Groups_Ocancel__semigroup__add(X2391) )
& ( X2389 != X2388
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2391),X2390),X2389) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2391),X2390),X2388)
| ~ class_Groups_Ocancel__semigroup__add(X2391) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_963,plain,
! [X2380,X2381,X2382,X2383] :
( ~ class_Groups_Ocancel__semigroup__add(X2383)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2383),X2382),X2381) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2383),X2382),X2380)
| X2381 = X2380 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_964,plain,
! [X2024,X2025,X2026] :
( ~ class_Orderings_Olinorder(X2026)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2026,X2025),X2024))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2026,X2024),X2025)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])]) ).
fof(i_0_965,plain,
! [X1972,X1973,X1974] :
( ~ class_Orderings_Olinorder(X1974)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1974,X1973),X1972))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1974,X1972),X1973)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_966,plain,
! [X2783,X2784] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2784),hAPP(c_Nat_OSuc,X2783)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2784),X2783)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_967,plain,
! [X2779,X2780] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2780)),X2779) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2780),hAPP(c_Nat_OSuc,X2779)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_968,plain,
! [X2658] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2658),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_572]) ).
fof(i_0_969,plain,
! [X2656] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2656),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_573]) ).
fof(i_0_970,plain,
! [X2643] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2643),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_574]) ).
fof(i_0_971,plain,
! [X2854] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2854)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2854)),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_972,plain,
! [X2654,X2655] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2655),X2654))
| X2654 != 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_973,plain,
! [X2295,X2296] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2296),X2295))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2295),X2296)) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_974,plain,
! [X2749] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2749))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_975,plain,
! [X2286,X2287] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2287),X2286))
| X2286 != X2287 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_976,plain,
! [X2284,X2285] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2285),X2284))
| X2285 != X2284 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_977,plain,
! [X2710] :
( ~ class_Rings_Olinordered__semidom(X2710)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2710),c_Groups_Ozero__class_Ozero(X2710)),c_Groups_Oone__class_Oone(X2710))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_978,plain,
! [X2858] :
( ~ class_Rings_Oring__1(X2858)
| hBOOL(hAPP(hAPP(c_member(X2858),c_Groups_Ozero__class_Ozero(X2858)),c_Int_Oring__1__class_OInts(X2858))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).
fof(i_0_979,plain,
! [X2862] :
( ~ class_Rings_Oring__1(X2862)
| hBOOL(hAPP(hAPP(c_member(X2862),c_Groups_Oone__class_Oone(X2862)),c_Int_Oring__1__class_OInts(X2862))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).
fof(i_0_980,plain,
! [X2293] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2293),X2293)),
inference(variable_rename,[status(thm)],[i_0_575]) ).
fof(i_0_981,plain,
! [X2288] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2288),X2288)),
inference(variable_rename,[status(thm)],[i_0_576]) ).
fof(i_0_982,plain,
! [X2219,X2220,X2221] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2221),X2220) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2219),X2220)
| X2221 = X2219 )
& ( X2221 != X2219
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2221),X2220) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2219),X2220) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_983,plain,
! [X2216,X2217,X2218] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2218),X2217) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2218),X2216)
| X2217 = X2216 )
& ( X2217 != X2216
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2218),X2217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2218),X2216) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_984,plain,
! [X2529,X2530,X2531] :
( ~ c_Finite__Set_Ofinite(X2531,X2530)
| c_Finite__Set_Ofinite(X2531,c_Set_Oinsert(X2531,X2529,X2530)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).
fof(i_0_985,plain,
! [X2748] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2748),hAPP(c_Nat_OSuc,X2748))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_986,plain,
! [X1689,X1690] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1690,tc_HOL_Obool)),X1689)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_987,plain,
! [X2645] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2645),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X2645 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2645 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2645),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_988,plain,
! [X2818,X2819] :
( ( X2819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2819 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2818) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2818 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2819 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2818) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2818 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2818) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2818 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2818 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2818) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2819 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2818 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2818) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2819 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2818 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2818) = 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_989,plain,
! [X2816,X2817] :
( ( X2817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2817 = 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),X2817),X2816) )
& ( X2816 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2817 = 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),X2817),X2816) )
& ( X2817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2816 = 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),X2817),X2816) )
& ( X2816 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2816 = 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),X2817),X2816) )
& ( X2817 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2816 != 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),X2817),X2816) )
& ( X2817 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2816 != 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),X2817),X2816) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_990,plain,
! [X1634,X1635] :
( hAPP(X1635,esk1_2(X1634,X1635)) != hAPP(X1634,esk1_2(X1634,X1635))
| X1635 = X1634 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_991,plain,
! [X2709] :
( ~ class_Rings_Olinordered__semidom(X2709)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2709,c_Groups_Ozero__class_Ozero(X2709)),c_Groups_Oone__class_Oone(X2709))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_992,plain,
! [X3241,X3242] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X3242),X3241))
| X3242 = X3241 ),
inference(variable_rename,[status(thm)],[i_0_577]) ).
fof(i_0_993,plain,
! [X3161,X3162] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3162,X3161)),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).
fof(i_0_994,plain,
! [X2853] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X2853)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X2853)),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_995,plain,
! [X2892,X2893,X2894] :
( ~ class_Rings_Ocomm__semiring__1(X2894)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2894),X2893),X2892) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2894),X2892),X2893) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_996,plain,
! [X2653] :
( X2653 = 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)),X2653)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_997,plain,
! [X2094,X2095] :
( ~ class_Orderings_Otop(X2095)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2095,X2094),c_Orderings_Otop__class_Otop(X2095))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_998,plain,
! [X2744,X2745] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2745),X2744),X2744) != c_Groups_Ozero__class_Ozero(X2745)
| X2744 = c_Groups_Ozero__class_Ozero(X2745)
| ~ class_Groups_Olinordered__ab__group__add(X2745) )
& ( X2744 != c_Groups_Ozero__class_Ozero(X2745)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2745),X2744),X2744) = c_Groups_Ozero__class_Ozero(X2745)
| ~ class_Groups_Olinordered__ab__group__add(X2745) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_999,plain,
! [X2665,X2666] :
( ( c_Groups_Ozero__class_Ozero(X2666) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2666),X2665),X2665)
| X2665 = c_Groups_Ozero__class_Ozero(X2666)
| ~ class_Groups_Olinordered__ab__group__add(X2666) )
& ( X2665 != c_Groups_Ozero__class_Ozero(X2666)
| c_Groups_Ozero__class_Ozero(X2666) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2666),X2665),X2665)
| ~ class_Groups_Olinordered__ab__group__add(X2666) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_1000,plain,
! [X2895,X2896,X2897] :
( ( X2896 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2897),X2896),X2895)
| X2895 = c_Groups_Ozero__class_Ozero(X2897)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2897) )
& ( X2895 != c_Groups_Ozero__class_Ozero(X2897)
| X2896 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2897),X2896),X2895)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2897) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_1001,plain,
! [X1978,X1979,X1980] :
( ~ class_Orderings_Opreorder(X1980)
| X1979 != X1978
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1980,X1979),X1978)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1002,plain,
! [X3219,X3220,X3221,X3222] : hAPP(hAPP(c_COMBK(X3222,X3221),X3220),X3219) = X3220,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_1003,plain,
! [X2208,X2209] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2209),X2208) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2208),X2209),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_1004,plain,
! [X1960,X1961] :
( ~ class_Orderings_Opreorder(X1961)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1961,X1960),X1960)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1005,plain,
! [X2646] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2646)),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_1006,plain,
! [X2644] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2644)),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_1007,plain,
! [X1751,X1752,X1753] :
( ~ class_Orderings_Otop(X1753)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1752,X1753)),X1751) = c_Orderings_Otop__class_Otop(X1753) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_1008,plain,
! [X2649,X2650] :
( ( X2650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2650),X2649) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2649 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2650),X2649) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2650 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2649 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2650),X2649) = 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_1009,plain,
! [X2297,X2298] :
( X2298 != X2297
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2298),X2297)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1010,plain,
! [X3243,X3244] :
( X3244 != X3243
| hBOOL(hAPP(hAPP(c_fequal,X3244),X3243)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1011,plain,
! [X2651,X2652] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2652),X2651) != X2652
| X2651 = 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_1012,plain,
! [X2294] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2294),X2294)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1013,plain,
! [X2498] :
( ~ class_Finite__Set_Ofinite(X2498)
| c_Finite__Set_Ofinite(X2498,c_Orderings_Otop__class_Otop(tc_fun(X2498,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_1014,plain,
! [X2867,X2868] :
( ~ class_Rings_Ocomm__semiring__1(X2868)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2868),c_Groups_Ozero__class_Ozero(X2868)),X2867) = X2867 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_1015,plain,
! [X2669,X2670] :
( ~ class_Groups_Omonoid__add(X2670)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2670),c_Groups_Ozero__class_Ozero(X2670)),X2669) = X2669 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_1016,plain,
! [X2667,X2668] :
( ~ class_Groups_Ocomm__monoid__add(X2668)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2668),c_Groups_Ozero__class_Ozero(X2668)),X2667) = X2667 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_1017,plain,
! [X2869,X2870] :
( ~ class_Rings_Ocomm__semiring__1(X2870)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2870),X2869),c_Groups_Ozero__class_Ozero(X2870)) = X2869 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_1018,plain,
! [X2663,X2664] :
( ~ class_Groups_Omonoid__add(X2664)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2664),X2663),c_Groups_Ozero__class_Ozero(X2664)) = X2663 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_1019,plain,
! [X2661,X2662] :
( ~ class_Groups_Ocomm__monoid__add(X2662)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2662),X2661),c_Groups_Ozero__class_Ozero(X2662)) = X2661 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_1020,plain,
! [X2852] : hAPP(c_Nat_OSuc,X2852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2852),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1021,plain,
! [X2851] : hAPP(c_Nat_OSuc,X2851) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2851),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1022,plain,
! [X2647] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2647) = X2647,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_1023,plain,
! [X2844] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2844) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2844)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(i_0_1024,plain,
! [X2648] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2648),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2648,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_1025,plain,
! [X3212,X3213] :
( ~ class_Finite__Set_Ofinite(X3213)
| ~ class_Finite__Set_Ofinite(X3212)
| class_Finite__Set_Ofinite(tc_sum(X3213,X3212)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_1026,plain,
! [X3204,X3205] :
( ~ class_Finite__Set_Ofinite(X3205)
| ~ class_Finite__Set_Ofinite(X3204)
| class_Finite__Set_Ofinite(tc_fun(X3205,X3204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_1027,plain,
! [X3215,X3216] :
( ~ class_Finite__Set_Ofinite(X3216)
| ~ class_Finite__Set_Ofinite(X3215)
| class_Finite__Set_Ofinite(tc_prod(X3216,X3215)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_1028,plain,
! [X2800,X2801] :
( ( hAPP(c_Nat_OSuc,X2801) != hAPP(c_Nat_OSuc,X2800)
| X2801 = X2800 )
& ( X2801 != X2800
| hAPP(c_Nat_OSuc,X2801) = hAPP(c_Nat_OSuc,X2800) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1029,plain,
! [X2798,X2799] :
( hAPP(c_Nat_OSuc,X2799) != hAPP(c_Nat_OSuc,X2798)
| X2799 = X2798 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1030,plain,
! [X3210,X3211] :
( ~ class_Orderings_Oord(X3211)
| class_Orderings_Oord(tc_fun(X3210,X3211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1031,plain,
! [X3206,X3207] :
( ~ class_Orderings_Oorder(X3207)
| class_Orderings_Oorder(tc_fun(X3206,X3207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1032,plain,
! [X3202,X3203] :
( ~ class_Orderings_Opreorder(X3203)
| class_Orderings_Opreorder(tc_fun(X3202,X3203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1033,plain,
! [X3208,X3209] :
( ~ class_Orderings_Otop(X3209)
| class_Orderings_Otop(tc_fun(X3208,X3209)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_1034,plain,
! [X2714,X2715] :
( c_Finite__Set_Ofinite(X2715,X2714)
| c_Finite__Set_Ocard(X2715,X2714) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_578])]) ).
fof(i_0_1035,plain,
! [X2755] : hAPP(c_Nat_OSuc,X2755) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1036,plain,
! [X2753] : hAPP(c_Nat_OSuc,X2753) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1037,plain,
! [X2752] : hAPP(c_Nat_OSuc,X2752) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1038,plain,
! [X2754] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2754),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1039,plain,
! [X2751] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2751),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1040,plain,
! [X2750] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2750),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1041,plain,
! [X2485,X2486] :
( ~ class_Finite__Set_Ofinite(X2486)
| c_Finite__Set_Ofinite(X2486,X2485) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(i_0_1042,plain,
! [X2483,X2484] :
( ~ class_Finite__Set_Ofinite(X2484)
| c_Finite__Set_Ofinite(X2484,X2483) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_1043,plain,
! [X2802] : hAPP(c_Nat_OSuc,X2802) != X2802,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1044,plain,
! [X2803] : X2803 != hAPP(c_Nat_OSuc,X2803),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1045,plain,
! [X3217,X3218] : hAPP(c_COMBI(X3218),X3217) = X3217,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1046,plain,
! [X2672] :
( ~ class_Rings_Ozero__neq__one(X2672)
| c_Groups_Oone__class_Oone(X2672) != c_Groups_Ozero__class_Ozero(X2672) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_1047,plain,
! [X2671] :
( ~ class_Rings_Ozero__neq__one(X2671)
| c_Groups_Ozero__class_Ozero(X2671) != c_Groups_Oone__class_Oone(X2671) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_1048,plain,
! [X3214] :
( ~ class_Finite__Set_Ofinite(X3214)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X3214)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_1049,plain,
! [X2857] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X2857) = X2857,
inference(variable_rename,[status(thm)],[fact_nat__size]) ).
fof(i_0_1050,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
cnf(i_0_1051,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,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_579]),
[final] ).
cnf(i_0_1052,negated_conjecture,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_F,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_579]),
[final] ).
cnf(i_0_1053,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_1054,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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),esk29_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_580]),
[final] ).
cnf(i_0_1055,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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),esk27_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_581]),
[final] ).
cnf(i_0_1056,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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_1057,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_582]),
[final] ).
cnf(i_0_1058,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1))),v_Lab____)),v_Lba____))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk29_0)) ),
inference(split_conjunct,[status(thm)],[i_0_580]),
[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_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),esk27_0)) ),
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_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_583]),
[final] ).
cnf(i_0_1061,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_584]),
[final] ).
cnf(i_0_1062,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_584]),
[final] ).
cnf(i_0_1063,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk8_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,esk8_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_585]),
[final] ).
cnf(i_0_1064,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk8_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,esk8_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_585]),
[final] ).
cnf(i_0_1065,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk7_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,esk7_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_586]),
[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),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,esk5_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,esk5_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_587]),
[final] ).
cnf(i_0_1067,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk5_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,esk5_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_587]),
[final] ).
cnf(i_0_1068,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)),X3),X4)),c_Wellfounded_Omax__ext(X1,X2)))
| ~ c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1,c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1069,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_589]),
[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),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,esk8_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,esk8_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_585]),
[final] ).
cnf(i_0_1071,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk8_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,esk8_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_585]),
[final] ).
cnf(i_0_1072,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk7_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,esk7_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_586]),
[final] ).
cnf(i_0_1073,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk5_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,esk5_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_587]),
[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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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(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,esk5_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_587]),
[final] ).
cnf(i_0_1075,plain,
( c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1,c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),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_Omax__ext(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1076,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,esk30_5(X3,X2,X1,X4,X5))),hAPP(X3,esk30_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[final] ).
cnf(i_0_1077,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,esk31_5(X3,X2,X1,X4,X5))),hAPP(X3,esk31_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1078,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk9_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,esk9_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_592]),
[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),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,esk9_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,esk9_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_592]),
[final] ).
cnf(i_0_1080,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk6_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,esk6_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_593]),
[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),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,esk6_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,esk6_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_593]),
[final] ).
cnf(i_0_1082,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk9_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,esk9_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_592]),
[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),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,esk9_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,esk9_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_592]),
[final] ).
cnf(i_0_1084,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk6_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,esk6_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_593]),
[final] ).
cnf(i_0_1085,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),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,esk6_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,esk6_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_593]),
[final] ).
cnf(i_0_1086,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk19_2(X1,X2)),esk20_2(X1,X2))),hAPP(X2,esk18_2(X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_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),esk19_2(X1,X2)),esk20_2(X1,X2))),hAPP(esk18_2(X1,X2),X1)))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1088,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk18_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1089,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk19_2(X1,X2) != esk20_2(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_594]),
[final] ).
cnf(i_0_1090,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_595]),
[final] ).
cnf(i_0_1091,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),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,esk4_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,esk4_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_596]),
[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),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,esk4_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,esk4_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_596]),
[final] ).
cnf(i_0_1093,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(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(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(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(X4,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))),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_597]),
[final] ).
cnf(i_0_1094,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(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(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(X4,esk2_4(X4,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),X1),X2)),hAPP(X3,esk2_4(X4,X3,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_597]),
[final] ).
cnf(i_0_1095,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_598]),
[final] ).
cnf(i_0_1096,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_595]),
[final] ).
cnf(i_0_1097,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk30_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_590]),
[final] ).
cnf(i_0_1098,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk4_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,esk4_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_596]),
[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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_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,esk4_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_596]),
[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),X1),X2)),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(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(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(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_597]),
[final] ).
cnf(i_0_1101,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),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(X4,esk2_4(X4,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),X1),X2)),hAPP(X3,esk2_4(X4,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),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_597]),
[final] ).
cnf(i_0_1102,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk40_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_599]),
[final] ).
cnf(i_0_1103,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk31_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_591]),
[final] ).
cnf(i_0_1104,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_600]),
[final] ).
cnf(i_0_1105,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_1106,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_595]),
[final] ).
cnf(i_0_1107,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_595]),
[final] ).
cnf(i_0_1108,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,esk21_4(X3,X2,X4,X1))),hAPP(X3,esk21_4(X3,X2,X4,X1))))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1109,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_602]),
[final] ).
cnf(i_0_1110,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_603]),
[final] ).
cnf(i_0_1111,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_604]),
[final] ).
cnf(i_0_1112,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_605]),
[final] ).
cnf(i_0_1113,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_606]),
[final] ).
cnf(i_0_1114,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_607]),
[final] ).
cnf(i_0_1115,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk14_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1116,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_609]),
[final] ).
cnf(i_0_1117,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_610]),
[final] ).
cnf(i_0_1118,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_611]),
[final] ).
cnf(i_0_1119,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_612]),
[final] ).
cnf(i_0_1120,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk42_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_613]),
[final] ).
cnf(i_0_1121,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_614]),
[final] ).
cnf(i_0_1122,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_615]),
[final] ).
cnf(i_0_1123,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_616]),
[final] ).
cnf(i_0_1124,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_617]),
[final] ).
cnf(i_0_1125,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_618]),
[final] ).
cnf(i_0_1126,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_1127,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_619]),
[final] ).
cnf(i_0_1128,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_620]),
[final] ).
cnf(i_0_1129,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_611]),
[final] ).
cnf(i_0_1130,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_621]),
[final] ).
cnf(i_0_1131,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_611]),
[final] ).
cnf(i_0_1132,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_620]),
[final] ).
cnf(i_0_1133,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_622]),
[final] ).
cnf(i_0_1134,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_614]),
[final] ).
cnf(i_0_1135,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_614]),
[final] ).
cnf(i_0_1136,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_614]),
[final] ).
cnf(i_0_1137,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_614]),
[final] ).
cnf(i_0_1138,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_615]),
[final] ).
cnf(i_0_1139,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_615]),
[final] ).
cnf(i_0_1140,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_615]),
[final] ).
cnf(i_0_1141,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_615]),
[final] ).
cnf(i_0_1142,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_610]),
[final] ).
cnf(i_0_1143,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_611]),
[final] ).
cnf(i_0_1144,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk40_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_599]),
[final] ).
cnf(i_0_1145,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_623]),
[final] ).
cnf(i_0_1146,plain,
( X1 = hAPP(X2,esk37_5(X1,X2,X3,X4,X5))
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| X1 != hAPP(X2,X5)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1147,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_625]),
[final] ).
cnf(i_0_1148,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_626]),
[final] ).
cnf(i_0_1149,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_613]),
[final] ).
cnf(i_0_1150,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_627]),
[final] ).
cnf(i_0_1151,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_628]),
[final] ).
cnf(i_0_1152,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_619]),
[final] ).
cnf(i_0_1153,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk39_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_629]),
[final] ).
cnf(i_0_1154,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_614]),
[final] ).
cnf(i_0_1155,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_614]),
[final] ).
cnf(i_0_1156,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_614]),
[final] ).
cnf(i_0_1157,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_630]),
[final] ).
cnf(i_0_1158,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_631]),
[final] ).
cnf(i_0_1159,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_632]),
[final] ).
cnf(i_0_1160,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_620]),
[final] ).
cnf(i_0_1161,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| esk37_5(X1,X2,X3,X4,X5) != X5
| X1 != hAPP(X2,X5)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1162,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_633]),
[final] ).
cnf(i_0_1163,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_614]),
[final] ).
cnf(i_0_1164,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_614]),
[final] ).
cnf(i_0_1165,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_614]),
[final] ).
cnf(i_0_1166,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_614]),
[final] ).
cnf(i_0_1167,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_614]),
[final] ).
cnf(i_0_1168,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_615]),
[final] ).
cnf(i_0_1169,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_634]),
[final] ).
cnf(i_0_1170,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_615]),
[final] ).
cnf(i_0_1171,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),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_615]),
[final] ).
cnf(i_0_1172,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_611]),
[final] ).
cnf(i_0_1173,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_635]),
[final] ).
cnf(i_0_1174,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),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk10_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),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk11_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1175,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_636]),
[final] ).
cnf(i_0_1176,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_615]),
[final] ).
cnf(i_0_1177,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_615]),
[final] ).
cnf(i_0_1178,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_615]),
[final] ).
cnf(i_0_1179,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_615]),
[final] ).
cnf(i_0_1180,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_615]),
[final] ).
cnf(i_0_1181,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_637]),
[final] ).
cnf(i_0_1182,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_638]),
[final] ).
cnf(i_0_1183,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_611]),
[final] ).
cnf(i_0_1184,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,X1)))
| ~ hBOOL(hAPP(hAPP(c_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_611]),
[final] ).
cnf(i_0_1185,plain,
( X1 = hAPP(X2,esk36_4(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1186,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_611]),
[final] ).
cnf(i_0_1187,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_623]),
[final] ).
cnf(i_0_1188,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_639]),
[final] ).
cnf(i_0_1189,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_614]),
[final] ).
cnf(i_0_1190,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_611]),
[final] ).
cnf(i_0_1191,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1)),esk13_1(X1))),hAPP(esk11_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),esk12_1(X1)),esk13_1(X1))),hAPP(esk10_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1192,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1)),esk13_1(X1))),hAPP(esk10_1(X1),X2)))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk12_1(X1)),esk13_1(X1))),hAPP(esk11_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1193,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_639]),
[final] ).
cnf(i_0_1194,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_611]),
[final] ).
cnf(i_0_1195,plain,
( X3 = esk36_4(X1,X2,X4,X5)
| X1 != hAPP(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1196,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_640]),
[final] ).
cnf(i_0_1197,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_630]),
[final] ).
cnf(i_0_1198,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_615]),
[final] ).
cnf(i_0_1199,plain,
( c_Set_Oimage(X2,X3,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))
| hAPP(X1,hAPP(c_Hilbert__Choice_Oinv__into(X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),X1),esk38_3(X1,X3,X2))) != esk38_3(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1200,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk3_2(X2,X1)),esk3_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1201,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_643]),
[final] ).
cnf(i_0_1202,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_644]),
[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),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_645]),
[final] ).
cnf(i_0_1204,plain,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_646]),
[final] ).
cnf(i_0_1205,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_647]),
[final] ).
cnf(i_0_1206,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_648]),
[final] ).
cnf(i_0_1207,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_649]),
[final] ).
cnf(i_0_1208,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_650]),
[final] ).
cnf(i_0_1209,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_645]),
[final] ).
cnf(i_0_1210,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_644]),
[final] ).
cnf(i_0_1211,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_644]),
[final] ).
cnf(i_0_1212,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_645]),
[final] ).
cnf(i_0_1213,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_651]),
[final] ).
cnf(i_0_1214,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk23_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1215,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk22_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[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),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk10_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),esk12_1(X1)),esk13_1(X1))),hAPP(X1,esk11_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1217,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_653]),
[final] ).
cnf(i_0_1218,plain,
( X1 = hAPP(X2,esk39_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_629]),
[final] ).
cnf(i_0_1219,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_614]),
[final] ).
cnf(i_0_1220,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_654]),
[final] ).
cnf(i_0_1221,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_655]),
[final] ).
cnf(i_0_1222,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_656]),
[final] ).
cnf(i_0_1223,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_615]),
[final] ).
cnf(i_0_1224,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_657]),
[final] ).
cnf(i_0_1225,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_658]),
[final] ).
cnf(i_0_1226,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_659]),
[final] ).
cnf(i_0_1227,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_660]),
[final] ).
cnf(i_0_1228,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_661]),
[final] ).
cnf(i_0_1229,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_662]),
[final] ).
cnf(i_0_1230,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_663]),
[final] ).
cnf(i_0_1231,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_664]),
[final] ).
cnf(i_0_1232,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_665]),
[final] ).
cnf(i_0_1233,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_649]),
[final] ).
cnf(i_0_1234,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_599]),
[final] ).
cnf(i_0_1235,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_666]),
[final] ).
cnf(i_0_1236,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_667]),
[final] ).
cnf(i_0_1237,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),esk16_1(X1)),esk17_1(X1))),hAPP(X1,esk15_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1238,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_668]),
[final] ).
cnf(i_0_1239,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_641]),
[final] ).
cnf(i_0_1240,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_669]),
[final] ).
cnf(i_0_1241,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_644]),
[final] ).
cnf(i_0_1242,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_645]),
[final] ).
cnf(i_0_1243,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_645]),
[final] ).
cnf(i_0_1244,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_644]),
[final] ).
cnf(i_0_1245,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_670]),
[final] ).
cnf(i_0_1246,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_661]),
[final] ).
cnf(i_0_1247,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X5,X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1248,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X5)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1249,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_672]),
[final] ).
cnf(i_0_1250,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))),esk24_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1251,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_673]),
[final] ).
cnf(i_0_1252,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_674]),
[final] ).
cnf(i_0_1253,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_675]),
[final] ).
cnf(i_0_1254,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_676]),
[final] ).
cnf(i_0_1255,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
inference(split_conjunct,[status(thm)],[i_0_677]),
[final] ).
cnf(i_0_1256,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_678]),
[final] ).
cnf(i_0_1257,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))),esk15_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1258,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))),esk11_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1259,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk10_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1260,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_679]),
[final] ).
cnf(i_0_1261,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_680]),
[final] ).
cnf(i_0_1262,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_629]),
[final] ).
cnf(i_0_1263,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_1264,plain,
( hAPP(X1,esk22_4(X2,X1,X3,X4)) = hAPP(X1,esk23_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1265,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_681]),
[final] ).
cnf(i_0_1266,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_682]),
[final] ).
cnf(i_0_1267,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_683]),
[final] ).
cnf(i_0_1268,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_684]),
[final] ).
cnf(i_0_1269,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_685]),
[final] ).
cnf(i_0_1270,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_686]),
[final] ).
cnf(i_0_1271,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_687]),
[final] ).
cnf(i_0_1272,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_688]),
[final] ).
cnf(i_0_1273,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_689]),
[final] ).
cnf(i_0_1274,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_690]),
[final] ).
cnf(i_0_1275,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_691]),
[final] ).
cnf(i_0_1276,plain,
( c_Fun_Oinj__on(X1,X2,esk42_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_613]),
[final] ).
cnf(i_0_1277,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk16_1(X1)),esk17_1(X1))),hAPP(esk15_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1278,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_692]),
[final] ).
cnf(i_0_1279,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_693]),
[final] ).
cnf(i_0_1280,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_694]),
[final] ).
cnf(i_0_1281,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_695]),
[final] ).
cnf(i_0_1282,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_696]),
[final] ).
cnf(i_0_1283,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_697]),
[final] ).
cnf(i_0_1284,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_698]),
[final] ).
cnf(i_0_1285,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_699]),
[final] ).
cnf(i_0_1286,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_700]),
[final] ).
cnf(i_0_1287,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_701]),
[final] ).
cnf(i_0_1288,plain,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_702]),
[final] ).
cnf(i_0_1289,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X2))
| ~ c_Nitpick_Orefl_H(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_642]),
[final] ).
cnf(i_0_1290,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_703]),
[final] ).
cnf(i_0_1291,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_704]),
[final] ).
cnf(i_0_1292,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_692]),
[final] ).
cnf(i_0_1293,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_644]),
[final] ).
cnf(i_0_1294,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_645]),
[final] ).
cnf(i_0_1295,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_705]),
[final] ).
cnf(i_0_1296,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_692]),
[final] ).
cnf(i_0_1297,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk22_4(X1,X2,X3,X4) != esk23_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1298,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_706]),
[final] ).
cnf(i_0_1299,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_707]),
[final] ).
cnf(i_0_1300,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_708]),
[final] ).
cnf(i_0_1301,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_709]),
[final] ).
cnf(i_0_1302,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_1303,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_710]),
[final] ).
cnf(i_0_1304,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_711]),
[final] ).
cnf(i_0_1305,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_712]),
[final] ).
cnf(i_0_1306,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_713]),
[final] ).
cnf(i_0_1307,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_714]),
[final] ).
cnf(i_0_1308,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_715]),
[final] ).
cnf(i_0_1309,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_700]),
[final] ).
cnf(i_0_1310,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_716]),
[final] ).
cnf(i_0_1311,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_717]),
[final] ).
cnf(i_0_1312,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_718]),
[final] ).
cnf(i_0_1313,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_719]),
[final] ).
cnf(i_0_1314,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_720]),
[final] ).
cnf(i_0_1315,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_721]),
[final] ).
cnf(i_0_1316,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_722]),
[final] ).
cnf(i_0_1317,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_723]),
[final] ).
cnf(i_0_1318,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_682]),
[final] ).
cnf(i_0_1319,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_724]),
[final] ).
cnf(i_0_1320,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_684]),
[final] ).
cnf(i_0_1321,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_725]),
[final] ).
cnf(i_0_1322,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_726]),
[final] ).
cnf(i_0_1323,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_727]),
[final] ).
cnf(i_0_1324,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_728]),
[final] ).
cnf(i_0_1325,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_729]),
[final] ).
cnf(i_0_1326,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_730]),
[final] ).
cnf(i_0_1327,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk25_0)),
inference(split_conjunct,[status(thm)],[i_0_731]),
[final] ).
cnf(i_0_1328,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_1329,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk26_0)),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1330,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_1331,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_733]),
[final] ).
cnf(i_0_1332,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_733]),
[final] ).
cnf(i_0_1333,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_734]),
[final] ).
cnf(i_0_1334,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_735]),
[final] ).
cnf(i_0_1335,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_736]),
[final] ).
cnf(i_0_1336,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_689]),
[final] ).
cnf(i_0_1337,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_737]),
[final] ).
cnf(i_0_1338,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_691]),
[final] ).
cnf(i_0_1339,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_738]),
[final] ).
cnf(i_0_1340,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_739]),
[final] ).
cnf(i_0_1341,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_710]),
[final] ).
cnf(i_0_1342,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_740]),
[final] ).
cnf(i_0_1343,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_740]),
[final] ).
cnf(i_0_1344,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_741]),
[final] ).
cnf(i_0_1345,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_742]),
[final] ).
cnf(i_0_1346,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_743]),
[final] ).
cnf(i_0_1347,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_696]),
[final] ).
cnf(i_0_1348,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_744]),
[final] ).
cnf(i_0_1349,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_652]),
[final] ).
cnf(i_0_1350,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_745]),
[final] ).
cnf(i_0_1351,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_746]),
[final] ).
cnf(i_0_1352,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_727]),
[final] ).
cnf(i_0_1353,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_747]),
[final] ).
cnf(i_0_1354,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_747]),
[final] ).
cnf(i_0_1355,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_748]),
[final] ).
cnf(i_0_1356,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_749]),
[final] ).
cnf(i_0_1357,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_750]),
[final] ).
cnf(i_0_1358,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_751]),
[final] ).
cnf(i_0_1359,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_705]),
[final] ).
cnf(i_0_1360,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_752]),
[final] ).
cnf(i_0_1361,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_753]),
[final] ).
cnf(i_0_1362,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_754]),
[final] ).
cnf(i_0_1363,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_755]),
[final] ).
cnf(i_0_1364,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_714]),
[final] ).
cnf(i_0_1365,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_715]),
[final] ).
cnf(i_0_1366,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_756]),
[final] ).
cnf(i_0_1367,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_757]),
[final] ).
cnf(i_0_1368,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_758]),
[final] ).
cnf(i_0_1369,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_759]),
[final] ).
cnf(i_0_1370,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_760]),
[final] ).
cnf(i_0_1371,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_761]),
[final] ).
cnf(i_0_1372,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_762]),
[final] ).
cnf(i_0_1373,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_763]),
[final] ).
cnf(i_0_1374,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_740]),
[final] ).
cnf(i_0_1375,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_764]),
[final] ).
cnf(i_0_1376,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_765]),
[final] ).
cnf(i_0_1377,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_766]),
[final] ).
cnf(i_0_1378,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_767]),
[final] ).
cnf(i_0_1379,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_768]),
[final] ).
cnf(i_0_1380,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_769]),
[final] ).
cnf(i_0_1381,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_726]),
[final] ).
cnf(i_0_1382,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_770]),
[final] ).
cnf(i_0_1383,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_771]),
[final] ).
cnf(i_0_1384,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_772]),
[final] ).
cnf(i_0_1385,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_773]),
[final] ).
cnf(i_0_1386,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_774]),
[final] ).
cnf(i_0_1387,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_775]),
[final] ).
cnf(i_0_1388,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_776]),
[final] ).
cnf(i_0_1389,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_777]),
[final] ).
cnf(i_0_1390,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_778]),
[final] ).
cnf(i_0_1391,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_779]),
[final] ).
cnf(i_0_1392,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk26_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_732]),
[final] ).
cnf(i_0_1393,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk25_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_731]),
[final] ).
cnf(i_0_1394,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_1395,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_1396,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_780]),
[final] ).
cnf(i_0_1397,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_781]),
[final] ).
cnf(i_0_1398,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_733]),
[final] ).
cnf(i_0_1399,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_782]),
[final] ).
cnf(i_0_1400,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_774]),
[final] ).
cnf(i_0_1401,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_775]),
[final] ).
cnf(i_0_1402,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_783]),
[final] ).
cnf(i_0_1403,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_761]),
[final] ).
cnf(i_0_1404,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_761]),
[final] ).
cnf(i_0_1405,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_766]),
[final] ).
cnf(i_0_1406,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_784]),
[final] ).
cnf(i_0_1407,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_785]),
[final] ).
cnf(i_0_1408,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_786]),
[final] ).
cnf(i_0_1409,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_787]),
[final] ).
cnf(i_0_1410,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_788]),
[final] ).
cnf(i_0_1411,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_789]),
[final] ).
cnf(i_0_1412,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_790]),
[final] ).
cnf(i_0_1413,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_791]),
[final] ).
cnf(i_0_1414,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_601]),
[final] ).
cnf(i_0_1415,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_792]),
[final] ).
cnf(i_0_1416,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_793]),
[final] ).
cnf(i_0_1417,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_794]),
[final] ).
cnf(i_0_1418,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_795]),
[final] ).
cnf(i_0_1419,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_796]),
[final] ).
cnf(i_0_1420,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_797]),
[final] ).
cnf(i_0_1421,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_797]),
[final] ).
cnf(i_0_1422,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_798]),
[final] ).
cnf(i_0_1423,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_799]),
[final] ).
cnf(i_0_1424,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk35_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_800]),
[final] ).
cnf(i_0_1425,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_801]),
[final] ).
cnf(i_0_1426,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_802]),
[final] ).
cnf(i_0_1427,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_803]),
[final] ).
cnf(i_0_1428,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_776]),
[final] ).
cnf(i_0_1429,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_804]),
[final] ).
cnf(i_0_1430,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_778]),
[final] ).
cnf(i_0_1431,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_805]),
[final] ).
cnf(i_0_1432,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_806]),
[final] ).
cnf(i_0_1433,plain,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk41_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_807]),
[final] ).
cnf(i_0_1434,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_1435,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_775]),
[final] ).
cnf(i_0_1436,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_808]),
[final] ).
cnf(i_0_1437,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_809]),
[final] ).
cnf(i_0_1438,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_810]),
[final] ).
cnf(i_0_1439,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_767]),
[final] ).
cnf(i_0_1440,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_767]),
[final] ).
cnf(i_0_1441,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_811]),
[final] ).
cnf(i_0_1442,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_812]),
[final] ).
cnf(i_0_1443,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_813]),
[final] ).
cnf(i_0_1444,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_814]),
[final] ).
cnf(i_0_1445,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_814]),
[final] ).
cnf(i_0_1446,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_815]),
[final] ).
cnf(i_0_1447,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_816]),
[final] ).
cnf(i_0_1448,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_817]),
[final] ).
cnf(i_0_1449,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_818]),
[final] ).
cnf(i_0_1450,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_819]),
[final] ).
cnf(i_0_1451,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_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_820]),
[final] ).
cnf(i_0_1452,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_821]),
[final] ).
cnf(i_0_1453,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_822]),
[final] ).
cnf(i_0_1454,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_823]),
[final] ).
cnf(i_0_1455,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1456,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_814]),
[final] ).
cnf(i_0_1457,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_825]),
[final] ).
cnf(i_0_1458,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_826]),
[final] ).
cnf(i_0_1459,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_827]),
[final] ).
cnf(i_0_1460,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_828]),
[final] ).
cnf(i_0_1461,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_829]),
[final] ).
cnf(i_0_1462,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_830]),
[final] ).
cnf(i_0_1463,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_831]),
[final] ).
cnf(i_0_1464,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_832]),
[final] ).
cnf(i_0_1465,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_833]),
[final] ).
cnf(i_0_1466,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_834]),
[final] ).
cnf(i_0_1467,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_835]),
[final] ).
cnf(i_0_1468,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_836]),
[final] ).
cnf(i_0_1469,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_837]),
[final] ).
cnf(i_0_1470,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_809]),
[final] ).
cnf(i_0_1471,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_838]),
[final] ).
cnf(i_0_1472,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_839]),
[final] ).
cnf(i_0_1473,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_840]),
[final] ).
cnf(i_0_1474,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_841]),
[final] ).
cnf(i_0_1475,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_842]),
[final] ).
cnf(i_0_1476,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_831]),
[final] ).
cnf(i_0_1477,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_831]),
[final] ).
cnf(i_0_1478,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_843]),
[final] ).
cnf(i_0_1479,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_844]),
[final] ).
cnf(i_0_1480,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_845]),
[final] ).
cnf(i_0_1481,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_846]),
[final] ).
cnf(i_0_1482,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_847]),
[final] ).
cnf(i_0_1483,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_848]),
[final] ).
cnf(i_0_1484,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_849]),
[final] ).
cnf(i_0_1485,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_850]),
[final] ).
cnf(i_0_1486,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_851]),
[final] ).
cnf(i_0_1487,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_852]),
[final] ).
cnf(i_0_1488,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_853]),
[final] ).
cnf(i_0_1489,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_854]),
[final] ).
cnf(i_0_1490,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_855]),
[final] ).
cnf(i_0_1491,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_856]),
[final] ).
cnf(i_0_1492,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_857]),
[final] ).
cnf(i_0_1493,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_858]),
[final] ).
cnf(i_0_1494,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_859]),
[final] ).
cnf(i_0_1495,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_860]),
[final] ).
cnf(i_0_1496,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_861]),
[final] ).
cnf(i_0_1497,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_862]),
[final] ).
cnf(i_0_1498,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk35_2(X2,X3)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1499,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_826]),
[final] ).
cnf(i_0_1500,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_863]),
[final] ).
cnf(i_0_1501,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_864]),
[final] ).
cnf(i_0_1502,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_865]),
[final] ).
cnf(i_0_1503,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk44_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_866]),
[final] ).
cnf(i_0_1504,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_776]),
[final] ).
cnf(i_0_1505,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_804]),
[final] ).
cnf(i_0_1506,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_867]),
[final] ).
cnf(i_0_1507,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1508,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_869]),
[final] ).
cnf(i_0_1509,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_870]),
[final] ).
cnf(i_0_1510,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_871]),
[final] ).
cnf(i_0_1511,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_872]),
[final] ).
cnf(i_0_1512,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk29_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_580]),
[final] ).
cnf(i_0_1513,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk27_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_581]),
[final] ).
cnf(i_0_1514,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_1515,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_846]),
[final] ).
cnf(i_0_1516,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_847]),
[final] ).
cnf(i_0_1517,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1518,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_874]),
[final] ).
cnf(i_0_1519,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_875]),
[final] ).
cnf(i_0_1520,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_820]),
[final] ).
cnf(i_0_1521,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_876]),
[final] ).
cnf(i_0_1522,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_877]),
[final] ).
cnf(i_0_1523,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_878]),
[final] ).
cnf(i_0_1524,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_879]),
[final] ).
cnf(i_0_1525,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_880]),
[final] ).
cnf(i_0_1526,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_881]),
[final] ).
cnf(i_0_1527,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_864]),
[final] ).
cnf(i_0_1528,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk34_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_882]),
[final] ).
cnf(i_0_1529,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_883]),
[final] ).
cnf(i_0_1530,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk46_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_884]),
[final] ).
cnf(i_0_1531,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1532,plain,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk41_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_807]),
[final] ).
cnf(i_0_1533,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_1534,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_865]),
[final] ).
cnf(i_0_1535,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_885]),
[final] ).
cnf(i_0_1536,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_886]),
[final] ).
cnf(i_0_1537,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_872]),
[final] ).
cnf(i_0_1538,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_887]),
[final] ).
cnf(i_0_1539,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1540,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk35_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_800]),
[final] ).
cnf(i_0_1541,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_889]),
[final] ).
cnf(i_0_1542,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_890]),
[final] ).
cnf(i_0_1543,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_891]),
[final] ).
cnf(i_0_1544,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_866]),
[final] ).
cnf(i_0_1545,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_892]),
[final] ).
cnf(i_0_1546,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_893]),
[final] ).
cnf(i_0_1547,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_894]),
[final] ).
cnf(i_0_1548,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_895]),
[final] ).
cnf(i_0_1549,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_896]),
[final] ).
cnf(i_0_1550,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_897]),
[final] ).
cnf(i_0_1551,plain,
( X1 = hAPP(c_Nat_OSuc,esk33_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_820]),
[final] ).
cnf(i_0_1552,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_861]),
[final] ).
cnf(i_0_1553,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_898]),
[final] ).
cnf(i_0_1554,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_899]),
[final] ).
cnf(i_0_1555,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_883]),
[final] ).
cnf(i_0_1556,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1557,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_887]),
[final] ).
cnf(i_0_1558,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_901]),
[final] ).
cnf(i_0_1559,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_882]),
[final] ).
cnf(i_0_1560,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk45_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_884]),
[final] ).
cnf(i_0_1561,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_902]),
[final] ).
cnf(i_0_1562,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_903]),
[final] ).
cnf(i_0_1563,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_904]),
[final] ).
cnf(i_0_1564,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_864]),
[final] ).
cnf(i_0_1565,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_905]),
[final] ).
cnf(i_0_1566,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_906]),
[final] ).
cnf(i_0_1567,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_907]),
[final] ).
cnf(i_0_1568,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1569,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_909]),
[final] ).
cnf(i_0_1570,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1571,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_910]),
[final] ).
cnf(i_0_1572,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_911]),
[final] ).
cnf(i_0_1573,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_912]),
[final] ).
cnf(i_0_1574,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_913]),
[final] ).
cnf(i_0_1575,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_902]),
[final] ).
cnf(i_0_1576,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_903]),
[final] ).
cnf(i_0_1577,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_878]),
[final] ).
cnf(i_0_1578,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_914]),
[final] ).
cnf(i_0_1579,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_915]),
[final] ).
cnf(i_0_1580,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_837]),
[final] ).
cnf(i_0_1581,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_916]),
[final] ).
cnf(i_0_1582,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_917]),
[final] ).
cnf(i_0_1583,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_918]),
[final] ).
cnf(i_0_1584,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_919]),
[final] ).
cnf(i_0_1585,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_920]),
[final] ).
cnf(i_0_1586,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_890]),
[final] ).
cnf(i_0_1587,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_871]),
[final] ).
cnf(i_0_1588,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_844]),
[final] ).
cnf(i_0_1589,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_921]),
[final] ).
cnf(i_0_1590,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_922]),
[final] ).
cnf(i_0_1591,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_923]),
[final] ).
cnf(i_0_1592,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_924]),
[final] ).
cnf(i_0_1593,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_925]),
[final] ).
cnf(i_0_1594,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_926]),
[final] ).
cnf(i_0_1595,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_927]),
[final] ).
cnf(i_0_1596,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_928]),
[final] ).
cnf(i_0_1597,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_929]),
[final] ).
cnf(i_0_1598,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_930]),
[final] ).
cnf(i_0_1599,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_931]),
[final] ).
cnf(i_0_1600,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_932]),
[final] ).
cnf(i_0_1601,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_933]),
[final] ).
cnf(i_0_1602,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_855]),
[final] ).
cnf(i_0_1603,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_934]),
[final] ).
cnf(i_0_1604,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_922]),
[final] ).
cnf(i_0_1605,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_923]),
[final] ).
cnf(i_0_1606,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_935]),
[final] ).
cnf(i_0_1607,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_936]),
[final] ).
cnf(i_0_1608,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk46_2(X1,X2)),X1))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_884]),
[final] ).
cnf(i_0_1609,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_866]),
[final] ).
cnf(i_0_1610,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_937]),
[final] ).
cnf(i_0_1611,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_938]),
[final] ).
cnf(i_0_1612,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_939]),
[final] ).
cnf(i_0_1613,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_934]),
[final] ).
cnf(i_0_1614,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_914]),
[final] ).
cnf(i_0_1615,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1616,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_941]),
[final] ).
cnf(i_0_1617,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_942]),
[final] ).
cnf(i_0_1618,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_881]),
[final] ).
cnf(i_0_1619,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_943]),
[final] ).
cnf(i_0_1620,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_880]),
[final] ).
cnf(i_0_1621,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_944]),
[final] ).
cnf(i_0_1622,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_945]),
[final] ).
cnf(i_0_1623,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk28_2(X2,X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1624,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_947]),
[final] ).
cnf(i_0_1625,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_948]),
[final] ).
cnf(i_0_1626,plain,
( X1 = hAPP(c_Nat_OSuc,esk32_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_949]),
[final] ).
cnf(i_0_1627,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_903]),
[final] ).
cnf(i_0_1628,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_855]),
[final] ).
cnf(i_0_1629,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_950]),
[final] ).
cnf(i_0_1630,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_951]),
[final] ).
cnf(i_0_1631,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_952]),
[final] ).
cnf(i_0_1632,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_928]),
[final] ).
cnf(i_0_1633,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_928]),
[final] ).
cnf(i_0_1634,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_953]),
[final] ).
cnf(i_0_1635,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_953]),
[final] ).
cnf(i_0_1636,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_784]),
[final] ).
cnf(i_0_1637,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_784]),
[final] ).
cnf(i_0_1638,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_954]),
[final] ).
cnf(i_0_1639,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_774]),
[final] ).
cnf(i_0_1640,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_955]),
[final] ).
cnf(i_0_1641,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1642,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_1643,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_958]),
[final] ).
cnf(i_0_1644,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_959]),
[final] ).
cnf(i_0_1645,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_960]),
[final] ).
cnf(i_0_1646,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_961]),
[final] ).
cnf(i_0_1647,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_962]),
[final] ).
cnf(i_0_1648,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_963]),
[final] ).
cnf(i_0_1649,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_964]),
[final] ).
cnf(i_0_1650,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_965]),
[final] ).
cnf(i_0_1651,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_966]),
[final] ).
cnf(i_0_1652,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_967]),
[final] ).
cnf(i_0_1653,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_916]),
[final] ).
cnf(i_0_1654,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_968]),
[final] ).
cnf(i_0_1655,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_969]),
[final] ).
cnf(i_0_1656,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_970]),
[final] ).
cnf(i_0_1657,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_971]),
[final] ).
cnf(i_0_1658,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_919]),
[final] ).
cnf(i_0_1659,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1660,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_972]),
[final] ).
cnf(i_0_1661,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_973]),
[final] ).
cnf(i_0_1662,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_974]),
[final] ).
cnf(i_0_1663,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_922]),
[final] ).
cnf(i_0_1664,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1665,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1666,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1667,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_976]),
[final] ).
cnf(i_0_1668,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_946]),
[final] ).
cnf(i_0_1669,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_977]),
[final] ).
cnf(i_0_1670,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_978]),
[final] ).
cnf(i_0_1671,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_979]),
[final] ).
cnf(i_0_1672,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_980]),
[final] ).
cnf(i_0_1673,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1674,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_982]),
[final] ).
cnf(i_0_1675,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_983]),
[final] ).
cnf(i_0_1676,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_820]),
[final] ).
cnf(i_0_1677,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_939]),
[final] ).
cnf(i_0_1678,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_984]),
[final] ).
cnf(i_0_1679,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_872]),
[final] ).
cnf(i_0_1680,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_890]),
[final] ).
cnf(i_0_1681,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk24_2(X2,X1)) != hAPP(esk24_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_656]),
[final] ).
cnf(i_0_1682,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_985]),
[final] ).
cnf(i_0_1683,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1684,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_987]),
[final] ).
cnf(i_0_1685,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_988]),
[final] ).
cnf(i_0_1686,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_989]),
[final] ).
cnf(i_0_1687,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_949]),
[final] ).
cnf(i_0_1688,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_1689,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_991]),
[final] ).
cnf(i_0_1690,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1691,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_988]),
[final] ).
cnf(i_0_1692,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_988]),
[final] ).
cnf(i_0_1693,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_989]),
[final] ).
cnf(i_0_1694,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_989]),
[final] ).
cnf(i_0_1695,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_993]),
[final] ).
cnf(i_0_1696,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_994]),
[final] ).
cnf(i_0_1697,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_995]),
[final] ).
cnf(i_0_1698,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_958]),
[final] ).
cnf(i_0_1699,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_996]),
[final] ).
cnf(i_0_1700,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_988]),
[final] ).
cnf(i_0_1701,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_989]),
[final] ).
cnf(i_0_1702,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_997]),
[final] ).
cnf(i_0_1703,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_998]),
[final] ).
cnf(i_0_1704,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_999]),
[final] ).
cnf(i_0_1705,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_1000]),
[final] ).
cnf(i_0_1706,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_988]),
[final] ).
cnf(i_0_1707,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_988]),
[final] ).
cnf(i_0_1708,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_989]),
[final] ).
cnf(i_0_1709,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_989]),
[final] ).
cnf(i_0_1710,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_897]),
[final] ).
cnf(i_0_1711,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_897]),
[final] ).
cnf(i_0_1712,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_1001]),
[final] ).
cnf(i_0_1713,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_902]),
[final] ).
cnf(i_0_1714,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_1002]),
[final] ).
cnf(i_0_1715,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_1003]),
[final] ).
cnf(i_0_1716,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_1717,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_1005]),
[final] ).
cnf(i_0_1718,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_1006]),
[final] ).
cnf(i_0_1719,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_987]),
[final] ).
cnf(i_0_1720,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_1007]),
[final] ).
cnf(i_0_1721,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_1008]),
[final] ).
cnf(i_0_1722,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_1008]),
[final] ).
cnf(i_0_1723,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1009]),
[final] ).
cnf(i_0_1724,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_923]),
[final] ).
cnf(i_0_1725,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1726,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1010]),
[final] ).
cnf(i_0_1727,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_1011]),
[final] ).
cnf(i_0_1728,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1012]),
[final] ).
cnf(i_0_1729,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_1013]),
[final] ).
cnf(i_0_1730,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_1014]),
[final] ).
cnf(i_0_1731,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_1015]),
[final] ).
cnf(i_0_1732,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_1016]),
[final] ).
cnf(i_0_1733,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_998]),
[final] ).
cnf(i_0_1734,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_999]),
[final] ).
cnf(i_0_1735,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_1000]),
[final] ).
cnf(i_0_1736,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_1017]),
[final] ).
cnf(i_0_1737,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_1018]),
[final] ).
cnf(i_0_1738,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_1019]),
[final] ).
cnf(i_0_1739,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_1020]),
[final] ).
cnf(i_0_1740,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_1021]),
[final] ).
cnf(i_0_1741,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_1742,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_1008]),
[final] ).
cnf(i_0_1743,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_1744,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_1022]),
[final] ).
cnf(i_0_1745,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_1023]),
[final] ).
cnf(i_0_1746,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_1024]),
[final] ).
cnf(i_0_1747,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_1025]),
[final] ).
cnf(i_0_1748,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_1026]),
[final] ).
cnf(i_0_1749,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_1027]),
[final] ).
cnf(i_0_1750,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[final] ).
cnf(i_0_1751,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1752,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1753,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1754,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1755,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1756,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_616]),
[final] ).
cnf(i_0_1757,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_1034]),
[final] ).
cnf(i_0_1758,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1759,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1760,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1761,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1762,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1763,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1764,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1765,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1766,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1767,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1044]),
[final] ).
cnf(i_0_1768,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1769,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_1046]),
[final] ).
cnf(i_0_1770,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_1047]),
[final] ).
cnf(i_0_1771,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_1772,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_1773,plain,
( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1774,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1775,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_1776,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1777,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_1778,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_1779,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_1780,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_1781,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_1782,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_1783,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_1784,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_1785,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_1786,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_1787,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_1788,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_1789,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_1790,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_1791,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_1792,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_1793,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_1794,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1795,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1796,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1797,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1798,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1799,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1800,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1801,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_1802,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1803,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1804,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1805,plain,
v_c____ != v_d____,
inference(split_conjunct,[status(thm)],[fact__096c_A_126_061_Ad_096]),
[final] ).
cnf(i_0_1806,axiom,
X1 = X1 ).
cnf(i_0_1807,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1808,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1809,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1810,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1811,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1812,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1813,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1814,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1815,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1816,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1817,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1818,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_1819,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_1820,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1821,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1822,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_1823,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_1824,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_1825,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_1826,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_1827,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_1828,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1829,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1830,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1831,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1832,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1833,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1834,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1835,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1836,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1837,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1838,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1839,axiom,
( X1 != X2
| esk37_5(X1,X3,X4,X5,X6) = esk37_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1840,axiom,
( X1 != X2
| esk37_5(X3,X1,X4,X5,X6) = esk37_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1841,axiom,
( X1 != X2
| esk37_5(X3,X4,X1,X5,X6) = esk37_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1842,axiom,
( X1 != X2
| esk37_5(X3,X4,X5,X1,X6) = esk37_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1843,axiom,
( X1 != X2
| esk37_5(X3,X4,X5,X6,X1) = esk37_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1844,axiom,
( X1 != X2
| esk36_4(X1,X3,X4,X5) = esk36_4(X2,X3,X4,X5) ) ).
cnf(i_0_1845,axiom,
( X1 != X2
| esk36_4(X3,X1,X4,X5) = esk36_4(X3,X2,X4,X5) ) ).
cnf(i_0_1846,axiom,
( X1 != X2
| esk36_4(X3,X4,X1,X5) = esk36_4(X3,X4,X2,X5) ) ).
cnf(i_0_1847,axiom,
( X1 != X2
| esk36_4(X3,X4,X5,X1) = esk36_4(X3,X4,X5,X2) ) ).
cnf(i_0_1848,axiom,
( X1 != X2
| esk38_3(X1,X3,X4) = esk38_3(X2,X3,X4) ) ).
cnf(i_0_1849,axiom,
( X1 != X2
| esk38_3(X3,X1,X4) = esk38_3(X3,X2,X4) ) ).
cnf(i_0_1850,axiom,
( X1 != X2
| esk38_3(X3,X4,X1) = esk38_3(X3,X4,X2) ) ).
cnf(i_0_1851,axiom,
( X1 != X2
| esk23_4(X1,X3,X4,X5) = esk23_4(X2,X3,X4,X5) ) ).
cnf(i_0_1852,axiom,
( X1 != X2
| esk23_4(X3,X1,X4,X5) = esk23_4(X3,X2,X4,X5) ) ).
cnf(i_0_1853,axiom,
( X1 != X2
| esk23_4(X3,X4,X1,X5) = esk23_4(X3,X4,X2,X5) ) ).
cnf(i_0_1854,axiom,
( X1 != X2
| esk23_4(X3,X4,X5,X1) = esk23_4(X3,X4,X5,X2) ) ).
cnf(i_0_1855,axiom,
( X1 != X2
| esk22_4(X1,X3,X4,X5) = esk22_4(X2,X3,X4,X5) ) ).
cnf(i_0_1856,axiom,
( X1 != X2
| esk22_4(X3,X1,X4,X5) = esk22_4(X3,X2,X4,X5) ) ).
cnf(i_0_1857,axiom,
( X1 != X2
| esk22_4(X3,X4,X1,X5) = esk22_4(X3,X4,X2,X5) ) ).
cnf(i_0_1858,axiom,
( X1 != X2
| esk22_4(X3,X4,X5,X1) = esk22_4(X3,X4,X5,X2) ) ).
cnf(i_0_1859,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1860,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1861,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1862,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_1863,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_1864,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_1865,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_1866,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1867,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1869,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1870,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1871,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
| c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
| c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
| c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
| c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1913,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_1914,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_1915,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_1916,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_1917,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_1918,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_1919,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1922,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_1923,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_1924,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_1925,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_1926,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_1927,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_1928,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1806_001,axiom,
X1 = X1 ).
cnf(i_0_1807_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1808_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1809_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1810_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1811_006,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1812_007,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1813_008,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1814_009,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1815_010,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1816_011,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1817_012,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1818_013,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_1819_014,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_1820_015,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1821_016,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1822_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_1823_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_1824_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_1825_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_1826_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_1827_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_1828_023,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1829_024,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1830_025,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1831_026,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1832_027,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1833_028,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1834_029,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1835_030,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1836_031,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1837_032,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1838_033,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1839_034,axiom,
( X1 != X2
| esk37_5(X1,X3,X4,X5,X6) = esk37_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1840_035,axiom,
( X1 != X2
| esk37_5(X3,X1,X4,X5,X6) = esk37_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1841_036,axiom,
( X1 != X2
| esk37_5(X3,X4,X1,X5,X6) = esk37_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1842_037,axiom,
( X1 != X2
| esk37_5(X3,X4,X5,X1,X6) = esk37_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1843_038,axiom,
( X1 != X2
| esk37_5(X3,X4,X5,X6,X1) = esk37_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1844_039,axiom,
( X1 != X2
| esk36_4(X1,X3,X4,X5) = esk36_4(X2,X3,X4,X5) ) ).
cnf(i_0_1845_040,axiom,
( X1 != X2
| esk36_4(X3,X1,X4,X5) = esk36_4(X3,X2,X4,X5) ) ).
cnf(i_0_1846_041,axiom,
( X1 != X2
| esk36_4(X3,X4,X1,X5) = esk36_4(X3,X4,X2,X5) ) ).
cnf(i_0_1847_042,axiom,
( X1 != X2
| esk36_4(X3,X4,X5,X1) = esk36_4(X3,X4,X5,X2) ) ).
cnf(i_0_1848_043,axiom,
( X1 != X2
| esk38_3(X1,X3,X4) = esk38_3(X2,X3,X4) ) ).
cnf(i_0_1849_044,axiom,
( X1 != X2
| esk38_3(X3,X1,X4) = esk38_3(X3,X2,X4) ) ).
cnf(i_0_1850_045,axiom,
( X1 != X2
| esk38_3(X3,X4,X1) = esk38_3(X3,X4,X2) ) ).
cnf(i_0_1851_046,axiom,
( X1 != X2
| esk23_4(X1,X3,X4,X5) = esk23_4(X2,X3,X4,X5) ) ).
cnf(i_0_1852_047,axiom,
( X1 != X2
| esk23_4(X3,X1,X4,X5) = esk23_4(X3,X2,X4,X5) ) ).
cnf(i_0_1853_048,axiom,
( X1 != X2
| esk23_4(X3,X4,X1,X5) = esk23_4(X3,X4,X2,X5) ) ).
cnf(i_0_1854_049,axiom,
( X1 != X2
| esk23_4(X3,X4,X5,X1) = esk23_4(X3,X4,X5,X2) ) ).
cnf(i_0_1855_050,axiom,
( X1 != X2
| esk22_4(X1,X3,X4,X5) = esk22_4(X2,X3,X4,X5) ) ).
cnf(i_0_1856_051,axiom,
( X1 != X2
| esk22_4(X3,X1,X4,X5) = esk22_4(X3,X2,X4,X5) ) ).
cnf(i_0_1857_052,axiom,
( X1 != X2
| esk22_4(X3,X4,X1,X5) = esk22_4(X3,X4,X2,X5) ) ).
cnf(i_0_1858_053,axiom,
( X1 != X2
| esk22_4(X3,X4,X5,X1) = esk22_4(X3,X4,X5,X2) ) ).
cnf(i_0_1859_054,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1860_055,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1861_056,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1862_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_1863_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_1864_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_1865_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_1866_061,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1867_062,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1868_063,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1869_064,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1870_065,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1871_066,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1872_067,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1873_068,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1874_069,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1875_070,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1876_071,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1877_072,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1878_073,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1879_074,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1880_075,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1881_076,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1882_077,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1883_078,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1884_079,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1885_080,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1886_081,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1887_082,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1888_083,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1889_084,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
| c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).
cnf(i_0_1890_085,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
| c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).
cnf(i_0_1891_086,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
| c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).
cnf(i_0_1892_087,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
| c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).
cnf(i_0_1893_088,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1894_089,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1895_090,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1896_091,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1897_092,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1898_093,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1899_094,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1900_095,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1901_096,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1902_097,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1903_098,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1904_099,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1905_100,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1906_101,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1907_102,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1908_103,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1909_104,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1910_105,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1911_106,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1912_107,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1913_108,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_1914_109,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_1915_110,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_1916_111,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_1917_112,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_1918_113,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_1919_114,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1920_115,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1921_116,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1922_117,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_1923_118,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_1924_119,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_1925_120,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_1926_121,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_1927_122,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_1928_123,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1929_124,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1930_125,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1931_126,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1932,plain,
X1 = X1,
inference(equality_inference,[],[1069]) ).
cnf(i_0_1933,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,[],[1106]) ).
cnf(i_0_1934,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,[],[1133]) ).
cnf(i_0_1935,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,[],[1134]) ).
cnf(i_0_1936,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,[],[1135]) ).
cnf(i_0_1937,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,[],[1138]) ).
cnf(i_0_1938,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,[],[1139]) ).
cnf(i_0_1939,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,[],[1154]) ).
cnf(i_0_1940,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,[],[1156]) ).
cnf(i_0_1941,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,[],[1164]) ).
cnf(i_0_1942,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,[],[1165]) ).
cnf(i_0_1943,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,[],[1167]) ).
cnf(i_0_1944,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,[],[1168]) ).
cnf(i_0_1945,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,[],[1171]) ).
cnf(i_0_1946,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,[],[1177]) ).
cnf(i_0_1947,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,[],[1178]) ).
cnf(i_0_1948,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,[],[1180]) ).
cnf(i_0_1949,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,[],[1189]) ).
cnf(i_0_1950,plain,
( X1 = esk36_4(hAPP(X2,X1),X2,X3,X4)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))) ),
inference(equality_inference,[],[1195]) ).
cnf(i_0_1951,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,[],[1198]) ).
cnf(i_0_1952,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,[],[1213]) ).
cnf(i_0_1953,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,[],[1234]) ).
cnf(i_0_1954,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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,[],[1243]) ).
cnf(i_0_1955,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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,[],[1244]) ).
cnf(i_0_1956,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,[],[1256]) ).
cnf(i_0_1957,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,[],[1262]) ).
cnf(i_0_1958,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1265]) ).
cnf(i_0_1959,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,[],[1280]) ).
cnf(i_0_1960,plain,
X1 = X1,
inference(equality_inference,[],[1281]) ).
cnf(i_0_1961,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,[],[1284]) ).
cnf(i_0_1962,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,[],[1293]) ).
cnf(i_0_1963,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,[],[1294]) ).
cnf(i_0_1964,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,[],[1351]) ).
cnf(i_0_1965,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1419]) ).
cnf(i_0_1966,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,[],[1422]) ).
cnf(i_0_1967,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,[],[1423]) ).
cnf(i_0_1968,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[1435]) ).
cnf(i_0_1969,plain,
( X1 = X1
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(equality_inference,[],[1467]) ).
cnf(i_0_1970,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(equality_inference,[],[1505]) ).
cnf(i_0_1971,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,[],[1520]) ).
cnf(i_0_1972,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,[],[1557]) ).
cnf(i_0_1973,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,[],[1558]) ).
cnf(i_0_1974,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,[],[1559]) ).
cnf(i_0_1975,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(equality_inference,[],[1570]) ).
cnf(i_0_1976,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,[],[1614]) ).
cnf(i_0_1977,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1629]) ).
cnf(i_0_1978,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1631]) ).
cnf(i_0_1979,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1632]) ).
cnf(i_0_1980,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1633]) ).
cnf(i_0_1981,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1639]) ).
cnf(i_0_1982,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1640]) ).
cnf(i_0_1983,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[1645]) ).
cnf(i_0_1984,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[1646]) ).
cnf(i_0_1985,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[1648]) ).
cnf(i_0_1986,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1658]) ).
cnf(i_0_1987,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[1660]) ).
cnf(i_0_1988,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1666]) ).
cnf(i_0_1989,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1667]) ).
cnf(i_0_1990,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,[],[1668]) ).
cnf(i_0_1991,plain,
X1 = X1,
inference(equality_inference,[],[1674]) ).
cnf(i_0_1992,plain,
X1 = X1,
inference(equality_inference,[],[1675]) ).
cnf(i_0_1993,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,[],[1676]) ).
cnf(i_0_1994,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[1679]) ).
cnf(i_0_1995,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,[],[1687]) ).
cnf(i_0_1996,plain,
X1 = X1,
inference(equality_inference,[],[1688]) ).
cnf(i_0_1997,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1711]) ).
cnf(i_0_1998,plain,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1712]) ).
cnf(i_0_1999,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1713]) ).
cnf(i_0_2000,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(equality_inference,[],[1725]) ).
cnf(i_0_2001,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1726]) ).
cnf(i_0_2002,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,[],[1733]) ).
cnf(i_0_2003,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,[],[1734]) ).
cnf(i_0_2004,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,[],[1735]) ).
cnf(i_0_2005,plain,
X1 = X1,
inference(equality_inference,[],[1751]) ).
cnf(i_0_2006,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_1954,i_0_1188]) ).
cnf(i_0_2007,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_1188]) ).
cnf(i_0_2008,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_1954,i_0_1986,i_0_1188,i_0_1193]) ).
cnf(i_0_2009,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_1986]) ).
cnf(i_0_2010,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_1193]) ).
cnf(i_0_2011,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_1954,i_0_1986,i_0_2009,i_0_1188,i_0_1193,i_0_1253]) ).
cnf(i_0_2012,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_1253]) ).
cnf(i_0_2013,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1466,i_0_1188,i_0_1193,i_0_1253,i_0_1292]) ).
cnf(i_0_2014,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_1466]) ).
cnf(i_0_2015,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_1292]) ).
cnf(i_0_2016,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_1954,i_0_1986,i_0_2009,i_0_1466,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304]) ).
cnf(i_0_2017,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_1304]) ).
cnf(i_0_2018,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,hAPP(c_fequal,X2)))),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1466,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429]) ).
cnf(i_0_2019,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_1429]) ).
cnf(i_0_2020,plain,
c_Set_Oinsert(X1,X2,hAPP(c_fequal,X2)) = hAPP(c_fequal,X2),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1466,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595]) ).
cnf(i_0_2021,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Set_Oinsert(X1,X2,X3) = X3 ),
inference(rename_variables,[],[i_0_1595]) ).
cnf(i_0_2022,plain,
hBOOL(hAPP(c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(X3,X4))),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1466,i_0_1251,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615]) ).
cnf(i_0_2023,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1615]) ).
cnf(i_0_2024,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_1954,i_0_1986,i_0_2009,i_0_1466,i_0_1251,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659]) ).
cnf(i_0_2025,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1659]) ).
cnf(i_0_2026,plain,
c_Nitpick_Orefl_H(X1,c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1466,i_0_1611,i_0_1251,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200]) ).
cnf(i_0_2027,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2028,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk3_2(X2,X1)),esk3_2(X2,X1))),X2))
| c_Nitpick_Orefl_H(X1,X2) ),
inference(rename_variables,[],[i_0_1200]) ).
cnf(i_0_2029,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_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1466,i_0_1611,i_0_1251,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239]) ).
cnf(i_0_2030,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2031,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_1239]) ).
cnf(i_0_2032,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_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1466,i_0_1611,i_0_1251,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249]) ).
cnf(i_0_2033,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1567]) ).
cnf(i_0_2034,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_1249]) ).
cnf(i_0_2035,plain,
X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1466,i_0_1673,i_0_1611,i_0_1251,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559]) ).
cnf(i_0_2036,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_1559]) ).
cnf(i_0_2037,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_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1466,i_0_1673,i_0_1611,i_0_1251,i_0_1514,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660]) ).
cnf(i_0_2038,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_1660]) ).
cnf(i_0_2039,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_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1466,i_0_1673,i_0_1611,i_0_1251,i_0_1514,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666]) ).
cnf(i_0_2040,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_1666]) ).
cnf(i_0_2041,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_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1466,i_0_1673,i_0_1611,i_0_1251,i_0_1514,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667]) ).
cnf(i_0_2042,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1667]) ).
cnf(i_0_2043,plain,
X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1466,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668]) ).
cnf(i_0_2044,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_1668]) ).
cnf(i_0_2045,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_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1466,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1369,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676]) ).
cnf(i_0_2046,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_1369]) ).
cnf(i_0_2047,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_1676]) ).
cnf(i_0_2048,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1466,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679]) ).
cnf(i_0_2049,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_1369]) ).
cnf(i_0_2050,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_1679]) ).
cnf(i_0_2051,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_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1739,i_0_1466,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688]) ).
cnf(i_0_2052,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_1739]) ).
cnf(i_0_2053,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(rename_variables,[],[i_0_1688]) ).
cnf(i_0_2054,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_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1567,i_0_1739,i_0_1466,i_0_1642,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952]) ).
cnf(i_0_2055,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1642]) ).
cnf(i_0_2056,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_1952]) ).
cnf(i_0_2057,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_1642,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807]) ).
cnf(i_0_2058,plain,
X1 != hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X1,X2))),
inference(scs_inference,[],[i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_1642,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809]) ).
cnf(i_0_2059,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_1642,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128]) ).
cnf(i_0_2060,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_1128]) ).
cnf(i_0_2061,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_1642,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130]) ).
cnf(i_0_2062,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_1130]) ).
cnf(i_0_2063,plain,
c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk40_5(X4,X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_1642,i_0_2055,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144]) ).
cnf(i_0_2064,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1642]) ).
cnf(i_0_2065,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,esk40_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_1144]) ).
cnf(i_0_2066,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1642,i_0_2055,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162]) ).
cnf(i_0_2067,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(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_1162]) ).
cnf(i_0_2068,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1642,i_0_2055,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181]) ).
cnf(i_0_2069,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_1181]) ).
cnf(i_0_2070,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1642,i_0_2055,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196]) ).
cnf(i_0_2071,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_1196]) ).
cnf(i_0_2072,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201]) ).
cnf(i_0_2073,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1642]) ).
cnf(i_0_2074,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_1201]) ).
cnf(i_0_2075,plain,
hAPP(X1,X2) = hAPP(X1,esk39_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218]) ).
cnf(i_0_2076,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
| X2 = hAPP(X4,esk39_4(X5,X4,X3,X2)) ),
inference(rename_variables,[],[i_0_1218]) ).
cnf(i_0_2077,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228]) ).
cnf(i_0_2078,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2079,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_1228]) ).
cnf(i_0_2080,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,esk26_0),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231]) ).
cnf(i_0_2081,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_1231]) ).
cnf(i_0_2082,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,esk26_0),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232]) ).
cnf(i_0_2083,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_1232]) ).
cnf(i_0_2084,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1682,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240]) ).
cnf(i_0_2085,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1682]) ).
cnf(i_0_2086,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_1240]) ).
cnf(i_0_2087,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246]) ).
cnf(i_0_2088,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1682]) ).
cnf(i_0_2089,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_1246]) ).
cnf(i_0_2090,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287]) ).
cnf(i_0_2091,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_1287]) ).
cnf(i_0_2092,plain,
~ c_Nitpick_Orefl_H(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2)),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289]) ).
cnf(i_0_2093,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_1954]) ).
cnf(i_0_2094,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),X3))
| ~ c_Nitpick_Orefl_H(X1,X3) ),
inference(rename_variables,[],[i_0_1289]) ).
cnf(i_0_2095,plain,
~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2)),hAPP(X1,X2))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303]) ).
cnf(i_0_2096,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2097,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_1303]) ).
cnf(i_0_2098,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339]) ).
cnf(i_0_2099,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_1426]) ).
cnf(i_0_2100,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_1339]) ).
cnf(i_0_2101,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341]) ).
cnf(i_0_2102,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2103,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_1341]) ).
cnf(i_0_2104,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355]) ).
cnf(i_0_2105,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_1565]) ).
cnf(i_0_2106,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_1355]) ).
cnf(i_0_2107,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_2105,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356]) ).
cnf(i_0_2108,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_1565]) ).
cnf(i_0_2109,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_1356]) ).
cnf(i_0_2110,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_2105,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380]) ).
cnf(i_0_2111,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_1380]) ).
cnf(i_0_2112,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_2105,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437]) ).
cnf(i_0_2113,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_1437]) ).
cnf(i_0_2114,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_2105,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448]) ).
cnf(i_0_2115,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(rename_variables,[],[i_0_1370]) ).
cnf(i_0_2116,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_1448]) ).
cnf(i_0_2117,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_2105,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450]) ).
cnf(i_0_2118,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_1370]) ).
cnf(i_0_2119,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_1450]) ).
cnf(i_0_2120,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_2105,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468]) ).
cnf(i_0_2121,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1682]) ).
cnf(i_0_2122,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_1468]) ).
cnf(i_0_2123,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469]) ).
cnf(i_0_2124,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_1565]) ).
cnf(i_0_2125,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_1469]) ).
cnf(i_0_2126,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471]) ).
cnf(i_0_2127,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_1471]) ).
cnf(i_0_2128,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473]) ).
cnf(i_0_2129,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2130,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_1473]) ).
cnf(i_0_2131,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475]) ).
cnf(i_0_2132,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2133,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_1475]) ).
cnf(i_0_2134,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479]) ).
cnf(i_0_2135,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_1479]) ).
cnf(i_0_2136,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483]) ).
cnf(i_0_2137,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_1565]) ).
cnf(i_0_2138,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_1483]) ).
cnf(i_0_2139,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497]) ).
cnf(i_0_2140,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2141,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_1497]) ).
cnf(i_0_2142,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499]) ).
cnf(i_0_2143,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_1499]) ).
cnf(i_0_2144,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)),esk34_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528]) ).
cnf(i_0_2145,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),esk34_2(X2,X1))) ),
inference(rename_variables,[],[i_0_1528]) ).
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),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529]) ).
cnf(i_0_2147,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_1529]) ).
cnf(i_0_2148,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537]) ).
cnf(i_0_2149,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_1537]) ).
cnf(i_0_2150,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556]) ).
cnf(i_0_2151,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_1556]) ).
cnf(i_0_2152,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586]) ).
cnf(i_0_2153,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2154,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_1586]) ).
cnf(i_0_2155,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588]) ).
cnf(i_0_2156,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_1588]) ).
cnf(i_0_2157,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_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594]) ).
cnf(i_0_2158,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_1594]) ).
cnf(i_0_2159,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk28_2(X1,X1)),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623]) ).
cnf(i_0_2160,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),esk28_2(X2,X1)) ),
inference(rename_variables,[],[i_0_1623]) ).
cnf(i_0_2161,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,esk32_1(hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626]) ).
cnf(i_0_2162,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,esk32_1(X1)) ),
inference(rename_variables,[],[i_0_1626]) ).
cnf(i_0_2163,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661]) ).
cnf(i_0_2164,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_1661]) ).
cnf(i_0_2165,plain,
~ class_Orderings_Otop(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702]) ).
cnf(i_0_2166,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2167,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_1702]) ).
cnf(i_0_2168,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765]) ).
cnf(i_0_2169,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1765]) ).
cnf(i_0_2170,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk26_0)),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158]) ).
cnf(i_0_2171,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_1158]) ).
cnf(i_0_2172,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Wellfounded_Omlex__prod(X1,X3,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2))))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_1986,i_0_2009,i_0_1760,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182]) ).
cnf(i_0_2173,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_1986]) ).
cnf(i_0_2174,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2175,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_1182]) ).
cnf(i_0_2176,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_1968,i_0_1954,i_0_2093,i_0_1986,i_0_2009,i_0_1766,i_0_1760,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202]) ).
cnf(i_0_2177,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_1954]) ).
cnf(i_0_2178,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1202]) ).
cnf(i_0_2179,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1968,i_0_1954,i_0_2093,i_0_2177,i_0_1986,i_0_2009,i_0_1766,i_0_1760,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203]) ).
cnf(i_0_2180,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_1954]) ).
cnf(i_0_2181,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_1203]) ).
cnf(i_0_2182,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_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_1986,i_0_2009,i_0_2173,i_0_1766,i_0_1760,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206]) ).
cnf(i_0_2183,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_1986]) ).
cnf(i_0_2184,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_1954]) ).
cnf(i_0_2185,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_1206]) ).
cnf(i_0_2186,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_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_1766,i_0_1760,i_0_1568,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207]) ).
cnf(i_0_2187,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1568]) ).
cnf(i_0_2188,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_1207]) ).
cnf(i_0_2189,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_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_1766,i_0_1760,i_0_1568,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262]) ).
cnf(i_0_2190,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2191,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_1262]) ).
cnf(i_0_2192,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_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_1766,i_0_1760,i_0_1568,i_0_2187,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283]) ).
cnf(i_0_2193,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_1986]) ).
cnf(i_0_2194,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1568]) ).
cnf(i_0_2195,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_1283]) ).
cnf(i_0_2196,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X2,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),c_Set_Oinsert(X1,X3,X2))))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_1766,i_0_1760,i_0_1568,i_0_2187,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411]) ).
cnf(i_0_2197,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X2,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))),
inference(rename_variables,[],[i_0_1225]) ).
cnf(i_0_2198,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_1411]) ).
cnf(i_0_2199,plain,
hBOOL(hAPP(c_Set_Oimage(X1,X2,X3,c_Set_Oinsert(X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),hAPP(X3,X5))),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_1766,i_0_1760,i_0_1568,i_0_2187,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485]) ).
cnf(i_0_2200,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_1485]) ).
cnf(i_0_2201,plain,
c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Set_Oinsert(tc_Product__Type_Ounit,X1,hAPP(c_fequal,X1))) = c_Finite__Set_Ocard(tc_Product__Type_Ounit,hAPP(c_fequal,X1)),
inference(scs_inference,[],[i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1760,i_0_1568,i_0_2187,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502]) ).
cnf(i_0_2202,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_1986]) ).
cnf(i_0_2203,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_1502]) ).
cnf(i_0_2204,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1760,i_0_1568,i_0_2187,i_0_1774,i_0_1784,i_0_1567,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873]) ).
cnf(i_0_2205,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),c_Set_Oimage(X1,X1,c_Hilbert__Choice_Oinv__into(X1,X1,c_Set_Oinsert(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),c_COMBI(X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1760,i_0_1568,i_0_2187,i_0_1774,i_0_1784,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213]) ).
cnf(i_0_2206,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_1466]) ).
cnf(i_0_2207,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1567]) ).
cnf(i_0_2208,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_1213]) ).
cnf(i_0_2209,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1760,i_0_1568,i_0_2187,i_0_1774,i_0_2190,i_0_1784,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234]) ).
cnf(i_0_2210,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2211,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_1234]) ).
cnf(i_0_2212,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Hilbert__Choice_Oinv__into(tc_Nat_Onat,tc_Nat_Onat,X1,c_Nat_OSuc),c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1)) = X1,
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1760,i_0_1568,i_0_2187,i_0_1774,i_0_2190,i_0_1582,i_0_1784,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265]) ).
cnf(i_0_2213,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2214,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_1265]) ).
cnf(i_0_2215,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_1784,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280]) ).
cnf(i_0_2216,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2217,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1568]) ).
cnf(i_0_2218,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_1280]) ).
cnf(i_0_2219,plain,
hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Nat_OSuc),hAPP(c_Nat_OSuc,X3)) = X3,
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419]) ).
cnf(i_0_2220,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2221,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_1419]) ).
cnf(i_0_2222,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465]) ).
cnf(i_0_2223,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_1465]) ).
cnf(i_0_2224,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520]) ).
cnf(i_0_2225,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2226,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_1520]) ).
cnf(i_0_2227,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))) != esk27_0,
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629]) ).
cnf(i_0_2228,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1629]) ).
cnf(i_0_2229,plain,
esk27_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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631]) ).
cnf(i_0_2230,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1631]) ).
cnf(i_0_2231,plain,
esk29_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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1798,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632]) ).
cnf(i_0_2232,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1632]) ).
cnf(i_0_2233,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))) != esk29_0,
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1798,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633]) ).
cnf(i_0_2234,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1633]) ).
cnf(i_0_2235,plain,
esk28_2(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1798,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701]) ).
cnf(i_0_2236,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2237,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1701]) ).
cnf(i_0_2238,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1798,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711]) ).
cnf(i_0_2239,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1711]) ).
cnf(i_0_2240,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712]) ).
cnf(i_0_2241,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2242,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713]) ).
cnf(i_0_2243,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1713]) ).
cnf(i_0_2244,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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,esk26_0),hAPP(c_Nat_OSuc,X2)),X2))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949]) ).
cnf(i_0_2245,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_1949]) ).
cnf(i_0_2246,plain,
X1 = esk36_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950]) ).
cnf(i_0_2247,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2248,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_1251]) ).
cnf(i_0_2249,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))
| X4 = esk36_4(hAPP(X3,X4),X3,X2,X1) ),
inference(rename_variables,[],[i_0_1950]) ).
cnf(i_0_2250,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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(esk26_0,hAPP(c_Nat_OSuc,X2),X2))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951]) ).
cnf(i_0_2251,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_1951]) ).
cnf(i_0_2252,plain,
hAPP(c_Nat_OSuc,X1) != c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808]) ).
cnf(i_0_2253,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2254,plain,
c_Arrow__Order__Mirabelle_Ounanimity(esk36_4(hAPP(c_Nat_OSuc,v_F),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874]) ).
cnf(i_0_2255,plain,
~ c_FunDef_Oin__rel(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2),X2,X2),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876]) ).
cnf(i_0_2256,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2257,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2),X2,X2),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877]) ).
cnf(i_0_2258,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2259,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2)),X2,X2),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878]) ).
cnf(i_0_2260,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2261,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2),X2),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879]) ).
cnf(i_0_2262,plain,
~ c_FunDef_Oin__rel(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),X2),X2,c_Nat_Osize__class_Osize(tc_Nat_Onat,X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880]) ).
cnf(i_0_2263,plain,
~ c_Nitpick_Orefl_H(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),tc_Arrow__Order__Mirabelle_Oalt)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881]) ).
cnf(i_0_2264,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2265,plain,
~ c_Nitpick_Orefl_H(tc_Arrow__Order__Mirabelle_Oalt,c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1),tc_Arrow__Order__Mirabelle_Oalt))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882]) ).
cnf(i_0_2266,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2267,plain,
tc_HOL_Obool != tc_Nat_Onat,
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902]) ).
cnf(i_0_2268,plain,
c_Arrow__Order__Mirabelle_OIIA(esk36_4(hAPP(c_Nat_OSuc,v_F),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903]) ).
cnf(i_0_2269,plain,
~ c_Finite__Set_Ofolding__image__simple(X1,tc_Nat_Onat,X2,X3,X4,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Finite__Set_Ofold__image(X1,tc_Nat_Onat,X2,X4,X3,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X5,X6))))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095]) ).
cnf(i_0_2270,plain,
( hAPP(X1,X2) = c_Finite__Set_Ofold__image(X3,X4,X5,X6,X7,X2)
| ~ c_Finite__Set_Ofolding__image__simple(X3,X4,X5,X7,X6,X1)
| ~ c_Finite__Set_Ofinite(X4,X2) ),
inference(rename_variables,[],[i_0_1095]) ).
cnf(i_0_2271,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),X2),X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108]) ).
cnf(i_0_2272,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2273,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk21_4(X3,X2,X4,X1))),hAPP(X3,esk21_4(X3,X2,X4,X1))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_1108]) ).
cnf(i_0_2274,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112]) ).
cnf(i_0_2275,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_1112]) ).
cnf(i_0_2276,plain,
hAPP(c_COMBI(X1),X2) = hAPP(c_COMBI(X1),esk36_4(hAPP(c_COMBI(X1),X2),c_COMBI(X1),X1,X1)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185]) ).
cnf(i_0_2277,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_1251]) ).
cnf(i_0_2278,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1568]) ).
cnf(i_0_2279,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))
| X2 = hAPP(X4,esk36_4(X2,X4,X1,X3))
| ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1185]) ).
cnf(i_0_2280,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(esk26_0,hAPP(c_Nat_OSuc,X1),X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227]) ).
cnf(i_0_2281,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_1227]) ).
cnf(i_0_2282,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229]) ).
cnf(i_0_2283,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_1466]) ).
cnf(i_0_2284,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1568]) ).
cnf(i_0_2285,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_1229]) ).
cnf(i_0_2286,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230]) ).
cnf(i_0_2287,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1642]) ).
cnf(i_0_2288,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_1230]) ).
cnf(i_0_2289,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273]) ).
cnf(i_0_2290,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_1273]) ).
cnf(i_0_2291,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317]) ).
cnf(i_0_2292,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_1317]) ).
cnf(i_0_2293,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407]) ).
cnf(i_0_2294,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_1466]) ).
cnf(i_0_2295,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_1543]) ).
cnf(i_0_2296,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_1407]) ).
cnf(i_0_2297,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414]) ).
cnf(i_0_2298,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_1414]) ).
cnf(i_0_2299,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,X1)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416]) ).
cnf(i_0_2300,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_1543]) ).
cnf(i_0_2301,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_1416]) ).
cnf(i_0_2302,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489]) ).
cnf(i_0_2303,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_1489]) ).
cnf(i_0_2304,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490]) ).
cnf(i_0_2305,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_1490]) ).
cnf(i_0_2306,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)))),esk27_0)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494]) ).
cnf(i_0_2307,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_1494]) ).
cnf(i_0_2308,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496]) ).
cnf(i_0_2309,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1))
| X1 = X2 ),
inference(rename_variables,[],[i_0_1496]) ).
cnf(i_0_2310,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,esk27_0))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509]) ).
cnf(i_0_2311,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_1509]) ).
cnf(i_0_2312,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511]) ).
cnf(i_0_2313,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_1369]) ).
cnf(i_0_2314,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_1511]) ).
cnf(i_0_2315,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519]) ).
cnf(i_0_2316,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2317,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_1519]) ).
cnf(i_0_2318,plain,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,X1),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522]) ).
cnf(i_0_2319,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2320,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_1522]) ).
cnf(i_0_2321,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)))),esk27_0)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526]) ).
cnf(i_0_2322,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_1526]) ).
cnf(i_0_2323,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)))),esk29_0)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527]) ).
cnf(i_0_2324,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_1527]) ).
cnf(i_0_2325,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544]) ).
cnf(i_0_2326,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2327,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2328,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk43_1(X2)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(rename_variables,[],[i_0_1544]) ).
cnf(i_0_2329,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,esk33_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_1251,i_0_2248,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551]) ).
cnf(i_0_2330,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2331,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 = hAPP(c_Nat_OSuc,esk33_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1551]) ).
cnf(i_0_2332,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560]) ).
cnf(i_0_2333,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_1251]) ).
cnf(i_0_2334,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2335,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk45_1(X2)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(rename_variables,[],[i_0_1560]) ).
cnf(i_0_2336,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk27_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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562]) ).
cnf(i_0_2337,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_1562]) ).
cnf(i_0_2338,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk29_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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564]) ).
cnf(i_0_2339,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_1564]) ).
cnf(i_0_2340,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606]) ).
cnf(i_0_2341,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_1369]) ).
cnf(i_0_2342,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_1606]) ).
cnf(i_0_2343,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620]) ).
cnf(i_0_2344,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_1620]) ).
cnf(i_0_2345,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625]) ).
cnf(i_0_2346,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1369]) ).
cnf(i_0_2347,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_1625]) ).
cnf(i_0_2348,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650]) ).
cnf(i_0_2349,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_1650]) ).
cnf(i_0_2350,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_2216,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284]) ).
cnf(i_0_2351,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1611]) ).
cnf(i_0_2352,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2353,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(rename_variables,[],[i_0_1714]) ).
cnf(i_0_2354,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_1284]) ).
cnf(i_0_2355,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk35_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_2216,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498]) ).
cnf(i_0_2356,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2357,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2358,plain,
( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk35_2(X3,X1)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(rename_variables,[],[i_0_1498]) ).
cnf(i_0_2359,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk26_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940]) ).
cnf(i_0_2360,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2361,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_1940]) ).
cnf(i_0_2362,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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(esk26_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945]) ).
cnf(i_0_2363,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2364,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_1945]) ).
cnf(i_0_2365,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk26_0),hAPP(c_Nat_OSuc,X2)),X2))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189]) ).
cnf(i_0_2366,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_1189]) ).
cnf(i_0_2367,plain,
X1 = esk36_4(hAPP(c_COMBI(X2),hAPP(c_COMBI(X2),X1)),c_COMBI(X2),X2,X2),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195]) ).
cnf(i_0_2368,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_1251]) ).
cnf(i_0_2369,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1568]) ).
cnf(i_0_2370,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1768]) ).
cnf(i_0_2371,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 = esk36_4(X2,X4,X1,X3) ),
inference(rename_variables,[],[i_0_1195]) ).
cnf(i_0_2372,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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(esk26_0,hAPP(c_Nat_OSuc,X2),X2))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198]) ).
cnf(i_0_2373,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_1198]) ).
cnf(i_0_2374,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614]) ).
cnf(i_0_2375,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_1656]) ).
cnf(i_0_2376,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_1746]) ).
cnf(i_0_2377,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_1614]) ).
cnf(i_0_2378,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,X1)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Set_Oinsert(tc_Arrow__Order__Mirabelle_Oindi,X2,c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_COMBI(tc_Arrow__Order__Mirabelle_Oindi),X1))))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151]) ).
cnf(i_0_2379,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_1466]) ).
cnf(i_0_2380,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1568]) ).
cnf(i_0_2381,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_1151]) ).
cnf(i_0_2382,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,esk42_4(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2),tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2),tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276]) ).
cnf(i_0_2383,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2384,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,esk42_4(X4,X3,X2,X1),X2)
| ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1276]) ).
cnf(i_0_2385,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X1)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1792,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298]) ).
cnf(i_0_2386,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_1369]) ).
cnf(i_0_2387,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_1298]) ).
cnf(i_0_2388,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1792,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299]) ).
cnf(i_0_2389,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_1370]) ).
cnf(i_0_2390,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_1299]) ).
cnf(i_0_2391,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373]) ).
cnf(i_0_2392,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(rename_variables,[],[i_0_1373]) ).
cnf(i_0_2393,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X3))),X3)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383]) ).
cnf(i_0_2394,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_1370]) ).
cnf(i_0_2395,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1383]) ).
cnf(i_0_2396,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))),X1)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396]) ).
cnf(i_0_2397,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2398,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_1396]) ).
cnf(i_0_2399,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397]) ).
cnf(i_0_2400,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2401,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_1397]) ).
cnf(i_0_2402,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)))),esk29_0)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441]) ).
cnf(i_0_2403,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2404,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_1441]) ).
cnf(i_0_2405,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459]) ).
cnf(i_0_2406,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1673]) ).
cnf(i_0_2407,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_1459]) ).
cnf(i_0_2408,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X3)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460]) ).
cnf(i_0_2409,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1682]) ).
cnf(i_0_2410,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_1460]) ).
cnf(i_0_2411,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)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461]) ).
cnf(i_0_2412,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_1656]) ).
cnf(i_0_2413,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_1461]) ).
cnf(i_0_2414,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462]) ).
cnf(i_0_2415,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_1369]) ).
cnf(i_0_2416,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_1462]) ).
cnf(i_0_2417,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),v_n____)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486]) ).
cnf(i_0_2418,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1554]) ).
cnf(i_0_2419,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1486]) ).
cnf(i_0_2420,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X3)),X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487]) ).
cnf(i_0_2421,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_1487]) ).
cnf(i_0_2422,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk35_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501]) ).
cnf(i_0_2423,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
inference(rename_variables,[],[i_0_1718]) ).
cnf(i_0_2424,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1501]) ).
cnf(i_0_2425,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550]) ).
cnf(i_0_2426,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
inference(rename_variables,[],[i_0_1718]) ).
cnf(i_0_2427,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_Oorder(X1)
| X3 = X2 ),
inference(rename_variables,[],[i_0_1550]) ).
cnf(i_0_2428,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = esk35_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576]) ).
cnf(i_0_2429,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
inference(rename_variables,[],[i_0_1718]) ).
cnf(i_0_2430,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X2 = X3 ),
inference(rename_variables,[],[i_0_1576]) ).
cnf(i_0_2431,plain,
esk35_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579]) ).
cnf(i_0_2432,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
inference(rename_variables,[],[i_0_1718]) ).
cnf(i_0_2433,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1)
| X3 = X2 ),
inference(rename_variables,[],[i_0_1579]) ).
cnf(i_0_2434,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk26_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156]) ).
cnf(i_0_2435,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2436,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2437,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_1156]) ).
cnf(i_0_2438,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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(esk26_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171]) ).
cnf(i_0_2439,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2440,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2441,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_1171]) ).
cnf(i_0_2442,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422]) ).
cnf(i_0_2443,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1682]) ).
cnf(i_0_2444,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2445,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_1422]) ).
cnf(i_0_2446,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423]) ).
cnf(i_0_2447,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1682]) ).
cnf(i_0_2448,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2449,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_1423]) ).
cnf(i_0_2450,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444]) ).
cnf(i_0_2451,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_1566]) ).
cnf(i_0_2452,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_1444]) ).
cnf(i_0_2453,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk26_0),hAPP(c_Nat_OSuc,X1))),hAPP(c_Nat_OSuc,X1)),X1))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155]) ).
cnf(i_0_2454,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_1955]) ).
cnf(i_0_2455,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_1155]) ).
cnf(i_0_2456,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X1))),c_Arrow__Order__Mirabelle_Obelow(hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,esk26_0),hAPP(c_Nat_OSuc,X1)),X1,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1392,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170]) ).
cnf(i_0_2457,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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_1955]) ).
cnf(i_0_2458,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2459,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2460,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_1170]) ).
cnf(i_0_2461,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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,esk25_0),v_a____),hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936]) ).
cnf(i_0_2462,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1767]) ).
cnf(i_0_2463,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_1936]) ).
cnf(i_0_2464,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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(esk25_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938]) ).
cnf(i_0_2465,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2466,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_1938]) ).
cnf(i_0_2467,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk26_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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944]) ).
cnf(i_0_2468,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X3),X1))),
inference(rename_variables,[],[i_0_1954]) ).
cnf(i_0_2469,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2470,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1766]) ).
cnf(i_0_2471,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2472,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_1944]) ).
cnf(i_0_2473,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_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456]) ).
cnf(i_0_2474,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_1565]) ).
cnf(i_0_2475,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_1746]) ).
cnf(i_0_2476,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_1456]) ).
cnf(i_0_2477,plain,
hAPP(c_Nat_OSuc,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_Nat_OSuc),esk38_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi))) != esk38_3(c_Nat_OSuc,tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oindi),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456,i_0_1199]) ).
cnf(i_0_2478,plain,
( c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| hAPP(X3,hAPP(c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),esk38_3(X3,X2,X1))) != esk38_3(X3,X2,X1) ),
inference(rename_variables,[],[i_0_1199]) ).
cnf(i_0_2479,plain,
esk35_2(hAPP(c_Nat_OSuc,X1),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != hAPP(c_Nat_OSuc,X2),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456,i_0_1199,i_0_1687]) ).
cnf(i_0_2480,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(rename_variables,[],[i_0_1687]) ).
cnf(i_0_2481,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456,i_0_1199,i_0_1687,i_0_1725]) ).
cnf(i_0_2482,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1725]) ).
cnf(i_0_2483,plain,
v_F = esk39_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,v_F)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456,i_0_1199,i_0_1687,i_0_1725,i_0_1751]) ).
cnf(i_0_2484,plain,
( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1751]) ).
cnf(i_0_2485,plain,
hAPP(c_Nat_OSuc,hAPP(c_Hilbert__Choice_Oinv__into(X1,X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_COMBI(X1)),hAPP(c_COMBI(X1),X2))) != X2,
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456,i_0_1199,i_0_1687,i_0_1725,i_0_1751,i_0_1810]) ).
cnf(i_0_2486,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X2)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456,i_0_1199,i_0_1687,i_0_1725,i_0_1751,i_0_1810,i_0_1358]) ).
cnf(i_0_2487,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(rename_variables,[],[i_0_1358]) ).
cnf(i_0_2488,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X3)),
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456,i_0_1199,i_0_1687,i_0_1725,i_0_1751,i_0_1810,i_0_1358,i_0_1359]) ).
cnf(i_0_2489,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(rename_variables,[],[i_0_1359]) ).
cnf(i_0_2490,plain,
$false,
inference(scs_inference,[],[i_0_1975,i_0_1968,i_0_1954,i_0_2093,i_0_2177,i_0_2180,i_0_2184,i_0_1955,i_0_2454,i_0_1986,i_0_2009,i_0_2173,i_0_2183,i_0_2193,i_0_1766,i_0_2236,i_0_2330,i_0_2363,i_0_2439,i_0_2444,i_0_2448,i_0_2459,i_0_2465,i_0_2458,i_0_1767,i_0_2216,i_0_2352,i_0_2360,i_0_2435,i_0_1760,i_0_2030,i_0_1804,i_0_1568,i_0_2187,i_0_2194,i_0_2217,i_0_2278,i_0_2284,i_0_2369,i_0_1774,i_0_2190,i_0_2210,i_0_2253,i_0_2256,i_0_2258,i_0_2260,i_0_2264,i_0_2266,i_0_2436,i_0_1582,i_0_2213,i_0_2220,i_0_1779,i_0_1784,i_0_1791,i_0_1792,i_0_1793,i_0_1794,i_0_1795,i_0_1797,i_0_1798,i_0_1800,i_0_1801,i_0_1802,i_0_1803,i_0_1567,i_0_2033,i_0_1768,i_0_1746,i_0_2376,i_0_1695,i_0_1714,i_0_1743,i_0_1739,i_0_1466,i_0_2014,i_0_2206,i_0_2283,i_0_2294,i_0_1728,i_0_2102,i_0_2140,i_0_2174,i_0_2272,i_0_2357,i_0_2383,i_0_2397,i_0_1662,i_0_1682,i_0_2085,i_0_2088,i_0_2121,i_0_2409,i_0_2443,i_0_1656,i_0_2375,i_0_1642,i_0_2055,i_0_2064,i_0_2073,i_0_1673,i_0_2078,i_0_2225,i_0_2327,i_0_2356,i_0_2403,i_0_1543,i_0_2295,i_0_2300,i_0_1611,i_0_2027,i_0_2326,i_0_1718,i_0_2423,i_0_2426,i_0_2429,i_0_1554,i_0_2096,i_0_2129,i_0_2132,i_0_2153,i_0_2166,i_0_2316,i_0_2334,i_0_2418,i_0_1251,i_0_2248,i_0_2277,i_0_2333,i_0_1565,i_0_2105,i_0_2108,i_0_2124,i_0_2137,i_0_1566,i_0_1514,i_0_1513,i_0_1512,i_0_1225,i_0_1369,i_0_2046,i_0_2049,i_0_2313,i_0_2341,i_0_2346,i_0_2386,i_0_1370,i_0_2115,i_0_2118,i_0_2389,i_0_1426,i_0_1329,i_0_1327,i_0_1392,i_0_1393,i_0_1188,i_0_1193,i_0_1253,i_0_1292,i_0_1304,i_0_1429,i_0_1595,i_0_1615,i_0_1659,i_0_1200,i_0_1239,i_0_1249,i_0_1559,i_0_1660,i_0_1666,i_0_1667,i_0_1668,i_0_1676,i_0_1679,i_0_1688,i_0_1952,i_0_1807,i_0_1809,i_0_1128,i_0_1130,i_0_1144,i_0_1162,i_0_1181,i_0_1196,i_0_1201,i_0_1218,i_0_1228,i_0_1231,i_0_1232,i_0_1240,i_0_1246,i_0_1287,i_0_1289,i_0_1303,i_0_1339,i_0_1341,i_0_1355,i_0_1356,i_0_1380,i_0_1437,i_0_1448,i_0_1450,i_0_1468,i_0_1469,i_0_1471,i_0_1473,i_0_1475,i_0_1479,i_0_1483,i_0_1497,i_0_1499,i_0_1528,i_0_1529,i_0_1537,i_0_1556,i_0_1586,i_0_1588,i_0_1594,i_0_1623,i_0_1626,i_0_1661,i_0_1702,i_0_1765,i_0_1158,i_0_1182,i_0_1202,i_0_1203,i_0_1206,i_0_1207,i_0_1262,i_0_1283,i_0_1411,i_0_1485,i_0_1502,i_0_1873,i_0_1213,i_0_1234,i_0_1265,i_0_1280,i_0_1419,i_0_1465,i_0_1520,i_0_1629,i_0_1631,i_0_1632,i_0_1633,i_0_1701,i_0_1711,i_0_1712,i_0_1713,i_0_1949,i_0_1950,i_0_1951,i_0_1808,i_0_1874,i_0_1876,i_0_1877,i_0_1878,i_0_1879,i_0_1880,i_0_1881,i_0_1882,i_0_1902,i_0_1903,i_0_1095,i_0_1108,i_0_1112,i_0_1185,i_0_1227,i_0_1229,i_0_1230,i_0_1273,i_0_1317,i_0_1407,i_0_1414,i_0_1416,i_0_1489,i_0_1490,i_0_1494,i_0_1496,i_0_1509,i_0_1511,i_0_1519,i_0_1522,i_0_1526,i_0_1527,i_0_1544,i_0_1551,i_0_1560,i_0_1562,i_0_1564,i_0_1606,i_0_1620,i_0_1625,i_0_1650,i_0_1284,i_0_1498,i_0_1940,i_0_1945,i_0_1189,i_0_1195,i_0_1198,i_0_1614,i_0_1151,i_0_1276,i_0_1298,i_0_1299,i_0_1373,i_0_1383,i_0_1396,i_0_1397,i_0_1441,i_0_1459,i_0_1460,i_0_1461,i_0_1462,i_0_1486,i_0_1487,i_0_1501,i_0_1550,i_0_1576,i_0_1579,i_0_1156,i_0_1171,i_0_1422,i_0_1423,i_0_1444,i_0_1155,i_0_1170,i_0_1936,i_0_1938,i_0_1944,i_0_1456,i_0_1199,i_0_1687,i_0_1725,i_0_1751,i_0_1810,i_0_1358,i_0_1359,i_0_1415]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SCT164+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 01:59:01 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 4.07/5.57 % Version : CSE_E---1.7
% 4.07/5.57 % Problem : theBenchmark.p
% 4.07/5.57 % SZS status Theorem for theBenchmark.p
% 4.07/5.57 % SZS output start CNFRefutation
% See solution above
% 12.77/12.85 % Total time : 5.323s
%------------------------------------------------------------------------------