%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT163+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 155.69s 125.14s
% Output : CNFRefutation 235.07s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1066)
% Comments :
%------------------------------------------------------------------------------
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,
~ ! [X63] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X63),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> ( ! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53),X63))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X53))),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),X63),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_059_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_folding__image__simple_Oinsert,axiom,
! [X7,X11,X46,X1,X4,X2,X13,X9] :
( c_Finite__Set_Ofolding__image__simple(X9,X13,X2,X4,X1,X46)
=> ( c_Finite__Set_Ofinite(X13,X11)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X7),X11))
=> hAPP(X46,c_Set_Oinsert(X13,X7,X11)) = hAPP(hAPP(X2,hAPP(X1,X7)),hAPP(X46,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
fof(conj_0,conjecture,
! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X65)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X65)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X65)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X65)),v_n____))
=> ( ( hAPP(v_h____,X65) = v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X65)),v_c____),v_e____))) )
& ( hAPP(v_h____,X65) != v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X65)),v_e____))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_pigeonhole,axiom,
! [X11,X2,X13,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X9,c_Set_Oimage(X13,X9,X2,X11))),c_Finite__Set_Ocard(X13,X11)))
=> ~ c_Fun_Oinj__on(X13,X9,X2,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).
fof(fact_card__def,axiom,
! [X11,X9] :
( ( c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) )
& ( ~ c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__def) ).
fof(fact_notin__Lin__iff,axiom,
! [X6,X7,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))
=> ( X7 != X6
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),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),X6),X7)),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X18,X19,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))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),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),X18),X19)),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_PiE,axiom,
! [X7,X10,X11,X2,X13,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X9,X13)),X2),c_FuncSet_OPi(X9,X13,X11,X10)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X7)),hAPP(X10,X7)))
=> ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_in__measures_I1_J,axiom,
! [X6,X7,X9] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_List_Omeasures(X9,c_List_Olist_ONil(tc_fun(X9,tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).
fof(fact_subset__insert,axiom,
! [X10,X11,X7,X9] :
( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),c_Set_Oinsert(X9,X7,X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10)) ) ),
file('/export/starexec/sandbox2/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,
~ ! [X51] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X51))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X51),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__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,
~ ! [X52] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X52))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X52),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X9,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,X13)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,X13),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,X13),X1),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_add__leE,axiom,
! [X17,X56,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X56)),X17))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact__096_B_Bthesis_O_A_I_B_Be_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X27] : ~ c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_c____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_d____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X27,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Be_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_not__add__less1,axiom,
! [X58,X59] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X58)),X59)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X59,X58] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X59)),X59)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_ex__least__nat__less,axiom,
! [X20,X15] :
( ~ hBOOL(hAPP(X15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X15,X20))
=> ? [X61] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),X20))
& ! [X65] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65),X61))
=> ~ hBOOL(hAPP(X15,X65)) )
& hBOOL(hAPP(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_insertCI,axiom,
! [X18,X10,X19,X9] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X9),X19),X10))
=> X19 = X18 )
=> hBOOL(hAPP(hAPP(c_member(X9),X19),c_Set_Oinsert(X9,X18,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_insert__ident,axiom,
! [X10,X11,X7,X9] :
( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X10))
=> ( c_Set_Oinsert(X9,X7,X11) = c_Set_Oinsert(X9,X7,X10)
<=> X11 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_not__less__eq__eq,axiom,
! [X20,X21] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20)),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X20,X21] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_xt1_I9_J,axiom,
! [X35,X34,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),X35))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X6),X7))
| X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_order__less__asym,axiom,
! [X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X34,X35,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_card_Oinsert,axiom,
! [X7,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X9,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert) ).
fof(fact_less__le__not__le,axiom,
! [X6,X7,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X6),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_card__insert__if,axiom,
! [X7,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)) = c_Finite__Set_Ocard(X9,X11) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X9,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).
fof(fact_less__SucE,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X17)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
=> X24 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_less__antisym,axiom,
! [X24,X17] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X24)))
=> X24 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X21,X20] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X21)))
<=> X20 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_linorder__not__less,axiom,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X6),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_leD,axiom,
! [X26,X25,X9] :
( class_Orderings_Olinorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__le,axiom,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X6),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_card__insert__disjoint,axiom,
! [X7,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X9,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_le__SucE,axiom,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),hAPP(c_Nat_OSuc,X17)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
=> X24 = hAPP(c_Nat_OSuc,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X17] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X17)),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
<=> X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_not__one__less__zero,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X25,X26,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( X26 != X25
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__cases,axiom,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ( X26 != X25
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( X26 != X25
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X7,X6,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X6),X7))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_not__leE,axiom,
! [X26,X25,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__one__le__zero,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X25,X26] :
( X26 != X25
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_equalityE,axiom,
! [X9,X10,X11] :
( X11 = X10
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_order__less__irrefl,axiom,
! [X26,X9] :
( class_Orderings_Opreorder(X9)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_linorder__le__cases,axiom,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_less__nat__zero__code,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_not__less0,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__zeroE,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__irrefl__nat,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(help_c__fequal__1,axiom,
! [X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X7),X6))
| X7 = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_card__infinite,axiom,
! [X11,X9] :
( ~ c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/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,
? [X63] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X63),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
& ! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53),X63))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X53))),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),X63),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096) ).
fof(fact_PiProf,axiom,
! [X20] : hBOOL(hAPP(hAPP(c_member(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____)),X20))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiProf) ).
fof(fact_n_I2_J,axiom,
! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X53))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I2_J) ).
fof(fact_pred__subset__eq2,axiom,
! [X31,X12,X13,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_fun(X13,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X9,tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X9,c_COMBC(X13,tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_prod(X9,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),X9,c_COMBB(tc_prod(X9,X13),tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool),X13,c_member(tc_prod(X9,X13)))),c_Product__Type_OPair(X9,X13)))),X12)),hAPP(hAPP(c_COMBC(X9,tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X9,c_COMBC(X13,tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_prod(X9,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),X9,c_COMBB(tc_prod(X9,X13),tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool),X13,c_member(tc_prod(X9,X13)))),c_Product__Type_OPair(X9,X13)))),X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),X12),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact__C2_C,axiom,
! [X64,X15,X29,X30,X18,X19] :
( X19 != X18
=> ( X30 != X29
=> ( X19 != X29
=> ( X18 != X30
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X15),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X64),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(X15,X65)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X30),X29)),hAPP(X64,X65))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(v_F,X15)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X30),X29)),hAPP(v_F,X64))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C2_C) ).
fof(fact__C1_C,axiom,
! [X64,X15,X29,X30,X18,X19] :
( X19 != X18
=> ( X30 != X29
=> ( X19 != X29
=> ( X18 != X30
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X15),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X64),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(X15,X65)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X30),X29)),hAPP(X64,X65))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(v_F,X15)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X30),X29)),hAPP(v_F,X64))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_pairwise__neutrality,axiom,
! [X64,X15,X29,X30,X18,X19] :
( X19 != X18
=> ( X30 != X29
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X15),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X64),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(X15,X65)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X30),X29)),hAPP(X64,X65))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(v_F,X15)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X30),X29)),hAPP(v_F,X64))) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
fof(fact_pred__equals__eq2,axiom,
! [X31,X12,X13,X9] :
( hAPP(hAPP(c_COMBC(X9,tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X9,c_COMBC(X13,tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_prod(X9,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),X9,c_COMBB(tc_prod(X9,X13),tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool),X13,c_member(tc_prod(X9,X13)))),c_Product__Type_OPair(X9,X13)))),X12) = hAPP(hAPP(c_COMBC(X9,tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_fun(X13,tc_HOL_Obool)),X9,c_COMBC(X13,tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X13,tc_prod(X9,X13)),tc_fun(X13,tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool)),X9,c_COMBB(tc_prod(X9,X13),tc_fun(tc_fun(tc_prod(X9,X13),tc_HOL_Obool),tc_HOL_Obool),X13,c_member(tc_prod(X9,X13)))),c_Product__Type_OPair(X9,X13)))),X31)
<=> X12 = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_Pi__mono,axiom,
! [X49,X10,X13,X11,X9] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X9),X3),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),hAPP(X10,X3)),hAPP(X49,X3))) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X9,X13),tc_HOL_Obool),c_FuncSet_OPi(X9,X13,X11,X10)),c_FuncSet_OPi(X9,X13,X11,X49))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_Pi__I,axiom,
! [X10,X2,X13,X11,X9] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X9),X3),X11))
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X3)),hAPP(X10,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X9,X13)),X2),c_FuncSet_OPi(X9,X13,X11,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_IIA__def,axiom,
! [X46] :
( c_Arrow__Order__Mirabelle_OIIA(X46)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X43] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X43),c_Arrow__Order__Mirabelle_OProf))
=> ! [X67,X68] :
( ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X3,X65)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X43,X65))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X46,X3)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X46,X43))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact__C4_C,axiom,
! [X64,X15,X8,X18,X19] :
( X19 != X18
=> ( X18 != X8
=> ( X19 != X8
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X15),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X64),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(X15,X65)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X8)),hAPP(X64,X65))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(v_F,X15)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X8)),hAPP(v_F,X64))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C4_C) ).
fof(fact_dictatorI,axiom,
! [X45,X46] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X46),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin))))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X67,X68] :
( X67 != X68
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X3,X45)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X46,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X46,X45) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_in__lex__prod,axiom,
! [X28,X16,X29,X30,X18,X19,X13,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X9,X13),tc_prod(X9,X13))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X9,X13),tc_prod(X9,X13)),hAPP(hAPP(c_Product__Type_OPair(X9,X13),X19),X18)),hAPP(hAPP(c_Product__Type_OPair(X9,X13),X30),X29))),c_Wellfounded_Olex__prod(X9,X13,X16,X28)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X19),X30)),X16))
| ( X19 = X30
& hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X18),X29)),X28)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact__C3_C,axiom,
! [X64,X15,X18,X19] :
( X19 != X18
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X15),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X64),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(X15,X65)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X19)),hAPP(X64,X65))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),hAPP(v_F,X15)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X19)),hAPP(v_F,X64))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C3_C) ).
fof(fact_folding__image__simple_Oeq__fold__g,axiom,
! [X11,X46,X1,X4,X2,X13,X9] :
( c_Finite__Set_Ofolding__image__simple(X9,X13,X2,X4,X1,X46)
=> ( c_Finite__Set_Ofinite(X13,X11)
=> hAPP(X46,X11) = c_Finite__Set_Ofold__image(X9,X13,X2,X1,X4,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
fof(fact_subset__image__iff,axiom,
! [X11,X2,X13,X10,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),c_Set_Oimage(X13,X9,X2,X11)))
<=> ? [X83] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X83),X11))
& X10 = c_Set_Oimage(X13,X9,X2,X83) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_same__fstI,axiom,
! [X9,X12,X6,X14,X13,X7,X15] :
( hBOOL(hAPP(X15,X7))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X13,X13)),hAPP(hAPP(c_Product__Type_OPair(X13,X13),X14),X6)),hAPP(X12,X7)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X9,X13),tc_prod(X9,X13))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X9,X13),tc_prod(X9,X13)),hAPP(hAPP(c_Product__Type_OPair(X9,X13),X7),X14)),hAPP(hAPP(c_Product__Type_OPair(X9,X13),X7),X6))),c_Recdef_Osame__fst(X9,X13,X15,X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X9,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,X13),X2),X1))
<=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X3)),hAPP(X1,X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_unanimity__def,axiom,
! [X46] :
( c_Arrow__Order__Mirabelle_Ounanimity(X46)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X67,X68] :
( ! [X65] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X3,X65)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X46,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_card__bij,axiom,
! [X1,X10,X11,X2,X13,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X9,X13)),X2),c_FuncSet_OPi(X9,X13,X11,hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X9),X10))))
=> ( c_Fun_Oinj__on(X9,X13,X2,X11)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X9)),X1),c_FuncSet_OPi(X13,X9,X10,hAPP(c_COMBK(tc_fun(X9,tc_HOL_Obool),X13),X11))))
=> ( c_Fun_Oinj__on(X13,X9,X1,X10)
=> ( c_Finite__Set_Ofinite(X9,X11)
=> ( c_Finite__Set_Ofinite(X13,X10)
=> c_Finite__Set_Ocard(X9,X11) = c_Finite__Set_Ocard(X13,X10) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij) ).
fof(fact_pred__subset__eq,axiom,
! [X31,X12,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X9,tc_fun(X9,tc_HOL_Obool),tc_HOL_Obool),c_member(X9)),X12)),hAPP(hAPP(c_COMBC(X9,tc_fun(X9,tc_HOL_Obool),tc_HOL_Obool),c_member(X9)),X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X12),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_in__above,axiom,
! [X6,X7,X5,X18,X19] :
( X19 != X18
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X5),X19),X18)))
<=> ( X7 != X6
& ( X7 = X18
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X6)),X5)) )
& ( X7 != X18
=> ( ( X6 = X18
=> ( X7 = X19
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X19)),X5)) ) )
& ( X6 != X18
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),X5)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_in__below,axiom,
! [X6,X7,X5,X18,X19] :
( X19 != X18
=> ( 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))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),c_Arrow__Order__Mirabelle_Obelow(X5,X19,X18)))
<=> ( X7 != X6
& ( X6 = X19
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X18)),X5)) )
& ( X6 != X19
=> ( ( X7 = X19
=> ( X6 = X18
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X18),X6)),X5)) ) )
& ( X7 != X19
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),X5)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_card_Oeq__fold__g,axiom,
! [X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).
fof(fact_inv__into__into,axiom,
! [X11,X2,X13,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),c_Set_Oimage(X13,X9,X2,X11)))
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(c_Hilbert__Choice_Oinv__into(X13,X9,X11,X2),X7)),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).
fof(fact_inj__image__subset__iff,axiom,
! [X10,X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),c_Set_Oimage(X9,X13,X2,X11)),c_Set_Oimage(X9,X13,X2,X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_in__finite__psubset,axiom,
! [X10,X11,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X9,tc_HOL_Obool),tc_fun(X9,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X9,tc_HOL_Obool),tc_fun(X9,tc_HOL_Obool)),X11),X10)),c_Wellfounded_Ofinite__psubset(X9)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
& c_Finite__Set_Ofinite(X9,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_inv__into__injective,axiom,
! [X6,X7,X2,X11,X13,X9] :
( hAPP(c_Hilbert__Choice_Oinv__into(X9,X13,X11,X2),X7) = hAPP(c_Hilbert__Choice_Oinv__into(X9,X13,X11,X2),X6)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X7),c_Set_Oimage(X9,X13,X2,X11)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X6),c_Set_Oimage(X9,X13,X2,X11)))
=> X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).
fof(fact_Ints__odd__less__0,axiom,
! [X19,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( hBOOL(hAPP(hAPP(c_member(X9),X19),c_Int_Oring__1__class_OInts(X9)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Oone__class_Oone(X9)),X19)),X19)),c_Groups_Ozero__class_Ozero(X9)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X19),c_Groups_Ozero__class_Ozero(X9))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_range__ex1__eq,axiom,
! [X18,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),X18),c_Set_Oimage(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))))
<=> ? [X3] :
( X18 = hAPP(X2,X3)
& ! [X84] :
( X18 = hAPP(X2,X84)
=> X84 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_card__image__le,axiom,
! [X2,X13,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X13,c_Set_Oimage(X9,X13,X2,X11))),c_Finite__Set_Ocard(X9,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).
fof(fact_inj__on__strict__subset,axiom,
! [X11,X10,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X13,tc_HOL_Obool)),c_Set_Oimage(X9,X13,X2,X11)),c_Set_Oimage(X9,X13,X2,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_endo__inj__surj,axiom,
! [X2,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),c_Set_Oimage(X9,X9,X2,X11)),X11))
=> ( c_Fun_Oinj__on(X9,X9,X2,X11)
=> c_Set_Oimage(X9,X9,X2,X11) = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_in__measures_I2_J,axiom,
! [X44,X2,X6,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_List_Omeasures(X9,c_List_Olist_OCons(tc_fun(X9,tc_Nat_Onat),X2,X44))))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X7)),hAPP(X2,X6)))
| ( hAPP(X2,X7) = hAPP(X2,X6)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_List_Omeasures(X9,X44))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
fof(fact_image__iff,axiom,
! [X11,X2,X13,X4,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X4),c_Set_Oimage(X13,X9,X2,X11)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X13),X3),X11))
& X4 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_measures__lesseq,axiom,
! [X44,X9,X6,X7,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X7)),hAPP(X2,X6)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_List_Omeasures(X9,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_List_Omeasures(X9,c_List_Olist_OCons(tc_fun(X9,tc_Nat_Onat),X2,X44)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__lesseq) ).
fof(fact_card__inj,axiom,
! [X10,X11,X2,X13,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X9,X13)),X2),c_FuncSet_OPi(X9,X13,X11,hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X9),X10))))
=> ( c_Fun_Oinj__on(X9,X13,X2,X11)
=> ( c_Finite__Set_Ofinite(X13,X10)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X9,X11)),c_Finite__Set_Ocard(X13,X10))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj) ).
fof(fact_Pi__anti__mono,axiom,
! [X10,X13,X11,X66,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X66),X11))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X9,X13),tc_HOL_Obool),c_FuncSet_OPi(X9,X13,X11,X10)),c_FuncSet_OPi(X9,X13,X66,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_finite__range__imageI,axiom,
! [X2,X42,X1,X13,X9] :
( c_Finite__Set_Ofinite(X9,c_Set_Oimage(X13,X9,X1,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))
=> c_Finite__Set_Ofinite(X42,c_Set_Oimage(X13,X42,hAPP(c_COMBB(X9,X42,X13,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_const__Lin__Prof,axiom,
! [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))
=> hBOOL(hAPP(hAPP(c_member(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),X5)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_funcset__mem,axiom,
! [X7,X10,X11,X2,X13,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X9,X13)),X2),c_FuncSet_OPi(X9,X13,X11,hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X9),X10))))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X7)),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_image__mono,axiom,
! [X2,X13,X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),c_Set_Oimage(X9,X13,X2,X11)),c_Set_Oimage(X9,X13,X2,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_mlex__leq,axiom,
! [X12,X9,X6,X7,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X7)),hAPP(X2,X6)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),X12))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_Wellfounded_Omlex__prod(X9,X2,X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_in__rel__def,axiom,
! [X6,X7,X12,X13,X9] :
( c_FunDef_Oin__rel(X9,X13,X12,X7,X6)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X13)),hAPP(hAPP(c_Product__Type_OPair(X9,X13),X7),X6)),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_f__inv__into__f,axiom,
! [X11,X2,X13,X6,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X6),c_Set_Oimage(X13,X9,X2,X11)))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X13,X9,X11,X2),X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_surj__iff__all,axiom,
! [X2,X9,X13] :
( c_Set_Oimage(X13,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))
<=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X13,X9,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),X3)) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [X16,X9] :
( c_Nitpick_Orefl_H(X9,X16)
<=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X3),X3)),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_inj__on__inv__into,axiom,
! [X11,X2,X13,X10,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),c_Set_Oimage(X13,X9,X2,X11)))
=> c_Fun_Oinj__on(X9,X13,c_Hilbert__Choice_Oinv__into(X13,X9,X11,X2),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
fof(fact_in__mkbot,axiom,
! [X4,X5,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),X7),X6)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X5),X4)))
<=> ( X6 != X4
& ( X7 = X4
=> X7 != 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),X7),X6)),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X4,X5,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),X7),X6)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X5),X4)))
<=> ( X7 != X4
& ( X6 = X4
=> X7 != X6 )
& ( X6 != X4
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(help_c__COMBS__1,axiom,
! [X12,X70,X15,X9,X42,X13] : hAPP(c_COMBS(X13,X42,X9,X15,X70),X12) = hAPP(hAPP(X15,X12),hAPP(X70,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_Pi__mem,axiom,
! [X7,X10,X11,X2,X13,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X9,X13)),X2),c_FuncSet_OPi(X9,X13,X11,X10)))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X7)),hAPP(X10,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_inj__image__mem__iff,axiom,
! [X11,X19,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X19)),c_Set_Oimage(X9,X13,X2,X11)))
<=> hBOOL(hAPP(hAPP(c_member(X9),X19),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_image__surj__f__inv__f,axiom,
! [X11,X2,X9,X13] :
( c_Set_Oimage(X13,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))
=> c_Set_Oimage(X13,X9,X2,c_Set_Oimage(X9,X13,c_Hilbert__Choice_Oinv__into(X13,X9,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),X11)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
fof(fact_image__inv__into__cancel,axiom,
! [X81,X66,X11,X2,X9,X13] :
( c_Set_Oimage(X13,X9,X2,X11) = X66
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X81),X66))
=> c_Set_Oimage(X13,X9,X2,c_Set_Oimage(X9,X13,c_Hilbert__Choice_Oinv__into(X13,X9,X11,X2),X81)) = X81 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_inj__on__def,axiom,
! [X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X9),X3),X11))
=> ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X9),X43),X11))
=> ( hAPP(X2,X3) = hAPP(X2,X43)
=> X3 = X43 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_above__Lin,axiom,
! [X5,X6,X7] :
( X7 != X6
=> ( 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))
=> 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,X5),X7),X6)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_range__composition,axiom,
! [X1,X2,X42,X9,X13] : c_Set_Oimage(X13,X9,hAPP(c_COMBB(X42,X9,X13,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Set_Oimage(X42,X9,X2,c_Set_Oimage(X13,X42,X1,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__composition) ).
fof(fact_measures__less,axiom,
! [X44,X9,X6,X7,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X7)),hAPP(X2,X6)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_List_Omeasures(X9,c_List_Olist_OCons(tc_fun(X9,tc_Nat_Onat),X2,X44)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__less) ).
fof(fact_finite__surj__inj,axiom,
! [X2,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),c_Set_Oimage(X9,X9,X2,X11)))
=> c_Fun_Oinj__on(X9,X9,X2,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_dictator__def,axiom,
! [X45,X46] :
( c_Arrow__Order__Mirabelle_Odictator(X46,X45)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> hAPP(X46,X3) = hAPP(X3,X45) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_inj__fun,axiom,
! [X42,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X9,tc_fun(X42,X13),hAPP(c_COMBB(X13,tc_fun(X42,X13),X9,c_COMBK(X13,X42)),X2),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__fun) ).
fof(fact_funcset__id,axiom,
! [X11,X9] : hBOOL(hAPP(hAPP(c_member(tc_fun(X9,X9)),c_COMBI(X9)),c_FuncSet_OPi(X9,X9,X11,hAPP(c_COMBK(tc_fun(X9,tc_HOL_Obool),X9),X11)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_image__image,axiom,
! [X11,X1,X42,X2,X9,X13] : c_Set_Oimage(X13,X9,X2,c_Set_Oimage(X42,X13,X1,X11)) = c_Set_Oimage(X42,X9,hAPP(c_COMBB(X13,X9,X42,X2),X1),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_below__Lin,axiom,
! [X5,X6,X7] :
( X7 != X6
=> ( 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))
=> 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(X5,X7,X6)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_in__measure,axiom,
! [X2,X6,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_Wellfounded_Omeasure(X9,X2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X7)),hAPP(X2,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_inv__into__image__cancel,axiom,
! [X31,X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X31),X11))
=> c_Set_Oimage(X13,X9,c_Hilbert__Choice_Oinv__into(X9,X13,X11,X2),c_Set_Oimage(X9,X13,X2,X31)) = X31 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
fof(fact_finite__surj,axiom,
! [X2,X10,X13,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X13,tc_HOL_Obool),X10),c_Set_Oimage(X9,X13,X2,X11)))
=> c_Finite__Set_Ofinite(X13,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(fact_mktop__Lin,axiom,
! [X7,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))
=> 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,X5),X7)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_mkbot__Lin,axiom,
! [X7,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))
=> 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,X5),X7)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_image__inv__f__f,axiom,
! [X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> c_Set_Oimage(X13,X9,c_Hilbert__Choice_Oinv__into(X9,X13,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),X2),c_Set_Oimage(X9,X13,X2,X11)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
fof(fact_inv__image__comp,axiom,
! [X80,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> c_Set_Oimage(X13,X9,c_Hilbert__Choice_Oinv__into(X9,X13,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),X2),c_Set_Oimage(X9,X13,X2,X80)) = X80 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__comp) ).
fof(fact_surj__f__inv__f,axiom,
! [X6,X2,X9,X13] :
( c_Set_Oimage(X13,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X13,X9,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
fof(fact_mlex__less,axiom,
! [X12,X9,X6,X7,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X7)),hAPP(X2,X6)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_Wellfounded_Omlex__prod(X9,X2,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_surj__imp__inj__inv,axiom,
! [X2,X9,X13] :
( c_Set_Oimage(X13,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))
=> c_Fun_Oinj__on(X9,X13,c_Hilbert__Choice_Oinv__into(X13,X9,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
fof(fact_rangeI,axiom,
! [X13,X7,X2,X9] : hBOOL(hAPP(hAPP(c_member(X9),hAPP(X2,X7)),c_Set_Oimage(X13,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_inj__imp__surj__inv,axiom,
! [X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> c_Set_Oimage(X13,X9,c_Hilbert__Choice_Oinv__into(X9,X13,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
fof(fact_imageI,axiom,
! [X2,X13,X11,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X7)),c_Set_Oimage(X9,X13,X2,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_list_Osimps_I5_J,axiom,
! [X40,X19,X54,X55,X13,X9] : c_List_Olist_Olist__case(X9,X13,X55,X54,c_List_Olist_OCons(X13,X19,X40)) = hAPP(hAPP(X54,X19),X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
fof(fact_range__eqI,axiom,
! [X13,X9,X7,X2,X18] :
( X18 = hAPP(X2,X7)
=> hBOOL(hAPP(hAPP(c_member(X9),X18),c_Set_Oimage(X13,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_image__eqI,axiom,
! [X9,X11,X13,X7,X2,X18] :
( X18 = hAPP(X2,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X13),X7),X11))
=> hBOOL(hAPP(hAPP(c_member(X9),X18),c_Set_Oimage(X13,X9,X2,X11))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X13,X2,X18,X11,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( X18 = hAPP(X2,X7)
=> hBOOL(hAPP(hAPP(c_member(X13),X18),c_Set_Oimage(X9,X13,X2,X11))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__image__eq__iff,axiom,
! [X10,X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( c_Set_Oimage(X9,X13,X2,X11) = c_Set_Oimage(X9,X13,X2,X10)
<=> X11 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_add__less__cancel__right,axiom,
! [X18,X8,X19,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X18),X8)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X19),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X34,X37,X35,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X37)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X18,X19,X8,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X18)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X19),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X34,X35,X37,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X34)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_list_Osimps_I4_J,axiom,
! [X54,X55,X13,X9] : c_List_Olist_Olist__case(X9,X13,X55,X54,c_List_Olist_ONil(X13)) = X55,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_finite__imageD,axiom,
! [X11,X2,X13,X9] :
( c_Finite__Set_Ofinite(X9,c_Set_Oimage(X13,X9,X2,X11))
=> ( c_Fun_Oinj__on(X13,X9,X2,X11)
=> c_Finite__Set_Ofinite(X13,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_psubset__trans,axiom,
! [X49,X10,X11,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X10),X49))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_add__le__imp__le__right,axiom,
! [X34,X37,X35,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X37)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X18,X8,X19,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X18),X8)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X19),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X34,X35,X37,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X34)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X18,X19,X8,X9] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X18)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X19),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_insert__subset,axiom,
! [X10,X11,X7,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),c_Set_Oinsert(X9,X7,X11)),X10))
<=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_inv__f__f,axiom,
! [X7,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> hAPP(c_Hilbert__Choice_Oinv__into(X9,X13,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),X2),hAPP(X2,X7)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__f) ).
fof(fact_inv__f__eq,axiom,
! [X6,X7,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( hAPP(X2,X7) = X6
=> hAPP(c_Hilbert__Choice_Oinv__into(X9,X13,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),X2),X6) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__eq) ).
fof(fact_pred__equals__eq,axiom,
! [X31,X12,X9] :
( hAPP(hAPP(c_COMBC(X9,tc_fun(X9,tc_HOL_Obool),tc_HOL_Obool),c_member(X9)),X12) = hAPP(hAPP(c_COMBC(X9,tc_fun(X9,tc_HOL_Obool),tc_HOL_Obool),c_member(X9)),X31)
<=> X12 = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X20,X21,X60] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_inv__into__f__f,axiom,
! [X7,X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> hAPP(c_Hilbert__Choice_Oinv__into(X9,X13,X11,X2),hAPP(X2,X7)) = X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
fof(fact_inv__into__f__eq,axiom,
! [X6,X7,X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( hAPP(X2,X7) = X6
=> hAPP(c_Hilbert__Choice_Oinv__into(X9,X13,X11,X2),X6) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [X2,X13,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( c_Finite__Set_Ocard(X13,c_Set_Oimage(X9,X13,X2,X11)) = c_Finite__Set_Ocard(X9,X11)
=> c_Fun_Oinj__on(X9,X13,X2,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X13,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( c_Fun_Oinj__on(X9,X13,X2,X11)
<=> c_Finite__Set_Ocard(X13,c_Set_Oimage(X9,X13,X2,X11)) = c_Finite__Set_Ocard(X9,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_insert__mono,axiom,
! [X19,X71,X49,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X49),X71))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),c_Set_Oinsert(X9,X19,X49)),c_Set_Oinsert(X9,X19,X71))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(help_c__COMBB__1,axiom,
! [X12,X70,X15,X42,X9,X13] : hAPP(hAPP(c_COMBB(X13,X9,X42,X15),X70),X12) = hAPP(X15,hAPP(X70,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__strict__mono,axiom,
! [X69,X37,X34,X35,X9] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X37),X69))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X69))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_list_Osize_I2_J,axiom,
! [X40,X19,X78,X9] : c_List_Olist_Olist__size(X9,X78,c_List_Olist_OCons(X9,X19,X40)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X78,X19)),c_List_Olist_Olist__size(X9,X78,X40))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I2_J) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X20,X21,X60] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X21)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X20)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_add__le__less__mono,axiom,
! [X69,X37,X34,X35,X9] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),X34))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X37),X69))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X69))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X69,X37,X34,X35,X9] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X37),X69))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X69))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_subset__psubset__trans,axiom,
! [X49,X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X10),X49))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X49,X10,X11,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),X49))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [X20,X21] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21)),X20))
<=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_insert__image,axiom,
! [X2,X13,X11,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Set_Oinsert(X13,hAPP(X2,X7),c_Set_Oimage(X9,X13,X2,X11)) = c_Set_Oimage(X9,X13,X2,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).
fof(fact_card__psubset,axiom,
! [X11,X10,X9] :
( c_Finite__Set_Ofinite(X9,X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X9,X11)),c_Finite__Set_Ocard(X9,X10)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(fact_third__alt,axiom,
! [X34,X35] :
( X35 != X34
=> ? [X36] : c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X35,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X34,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X36,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_third__alt) ).
fof(fact_add__mono,axiom,
! [X69,X37,X34,X35,X9] :
( class_Groups_Oordered__ab__semigroup__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),X34))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X37),X69))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X69))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X19,X9] :
( class_Groups_Olinordered__ab__group__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X19)),c_Groups_Ozero__class_Ozero(X9)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X19),c_Groups_Ozero__class_Ozero(X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X19,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X19)),c_Groups_Ozero__class_Ozero(X9)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X19),c_Groups_Ozero__class_Ozero(X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_add__less__mono,axiom,
! [X57,X56,X58,X59] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),X58))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X56),X57))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X57))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_image__insert,axiom,
! [X10,X19,X2,X9,X13] : c_Set_Oimage(X13,X9,X2,c_Set_Oinsert(X13,X19,X10)) = c_Set_Oinsert(X9,hAPP(X2,X19),c_Set_Oimage(X13,X9,X2,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [X2,X9] :
( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( c_Set_Oimage(X9,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))
=> c_Fun_Oinj__on(X9,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_subset__inj__on,axiom,
! [X11,X10,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> c_Fun_Oinj__on(X9,X13,X2,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_card__image,axiom,
! [X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
=> c_Finite__Set_Ocard(X13,c_Set_Oimage(X9,X13,X2,X11)) = c_Finite__Set_Ocard(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_add__neg__neg,axiom,
! [X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),c_Groups_Ozero__class_Ozero(X9)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),c_Groups_Ozero__class_Ozero(X9)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34)),c_Groups_Ozero__class_Ozero(X9))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_Ints__add,axiom,
! [X18,X19,X9] :
( class_Rings_Oring__1(X9)
=> ( hBOOL(hAPP(hAPP(c_member(X9),X19),c_Int_Oring__1__class_OInts(X9)))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X18),c_Int_Oring__1__class_OInts(X9)))
=> hBOOL(hAPP(hAPP(c_member(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X18)),c_Int_Oring__1__class_OInts(X9))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__add) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X9] :
( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X9,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> c_Set_Oimage(X9,X9,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_add__strict__right__mono,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X37))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X34))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X19,X9] :
( class_Groups_Olinordered__ab__group__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X19)),c_Groups_Ozero__class_Ozero(X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X19),c_Groups_Ozero__class_Ozero(X9))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_add__nonpos__neg,axiom,
! [X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),c_Groups_Ozero__class_Ozero(X9)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),c_Groups_Ozero__class_Ozero(X9)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34)),c_Groups_Ozero__class_Ozero(X9))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),c_Groups_Ozero__class_Ozero(X9)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),c_Groups_Ozero__class_Ozero(X9)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34)),c_Groups_Ozero__class_Ozero(X9))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__le__mono,axiom,
! [X57,X56,X58,X59] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56),X57))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X57))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_finite__Plus__iff,axiom,
! [X10,X11,X13,X9] :
( c_Finite__Set_Ofinite(tc_sum(X9,X13),c_Sum__Type_OPlus(X9,X13,X11,X10))
<=> ( c_Finite__Set_Ofinite(X9,X11)
& c_Finite__Set_Ofinite(X13,X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X10,X11,X13,X9] :
( c_Finite__Set_Ofinite(tc_sum(X9,X13),c_Sum__Type_OPlus(X9,X13,X11,X10))
=> c_Finite__Set_Ofinite(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [X10,X11,X13,X9] :
( c_Finite__Set_Ofinite(tc_sum(X9,X13),c_Sum__Type_OPlus(X9,X13,X11,X10))
=> c_Finite__Set_Ofinite(X13,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_add__right__mono,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Oordered__ab__semigroup__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X37))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Oordered__ab__semigroup__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X34))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__lessD1,axiom,
! [X56,X58,X59] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X58)),X56))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),c_Groups_Ozero__class_Ozero(X9)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),c_Groups_Ozero__class_Ozero(X9)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34)),c_Groups_Ozero__class_Ozero(X9))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_predicate2D,axiom,
! [X6,X7,X70,X15,X13,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_fun(X13,tc_HOL_Obool)),X15),X70))
=> ( hBOOL(hAPP(hAPP(X15,X7),X6))
=> hBOOL(hAPP(hAPP(X70,X7),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X70,X13,X9,X6,X7,X15] :
( hBOOL(hAPP(hAPP(X15,X7),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_fun(X13,tc_HOL_Obool)),X15),X70))
=> hBOOL(hAPP(hAPP(X70,X7),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_add__less__mono1,axiom,
! [X56,X58,X59] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),X58))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X56))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_inj__on__iff,axiom,
! [X6,X7,X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X6),X11))
=> ( hAPP(X2,X7) = hAPP(X2,X6)
<=> X7 = X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__onD,axiom,
! [X6,X7,X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
=> ( hAPP(X2,X7) = hAPP(X2,X6)
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X6),X11))
=> X7 = X6 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_inj__on__contraD,axiom,
! [X6,X7,X11,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,X11)
=> ( X7 != X6
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X6),X11))
=> hAPP(X2,X7) != hAPP(X2,X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_add__leD1,axiom,
! [X17,X56,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X56)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X17,X56,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X56)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__pos__pos,axiom,
! [X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_ex__nat__less__eq,axiom,
! [X15,X20] :
( ? [X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X53),X20))
& hBOOL(hAPP(X15,X53)) )
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)))
& hBOOL(hAPP(X15,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
fof(fact_add__le__mono1,axiom,
! [X56,X58,X59] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X56)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X56))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_psubsetD,axiom,
! [X8,X10,X11,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X8),X11))
=> hBOOL(hAPP(hAPP(c_member(X9),X8),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_psubset__card__mono,axiom,
! [X11,X10,X9] :
( c_Finite__Set_Ofinite(X9,X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X9,X11)),c_Finite__Set_Ocard(X9,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_inj__on__add__nat,axiom,
! [X62,X60] : 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)),X60),X62),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X69,X37,X34,X35,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X69)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X69)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_all__nat__less__eq,axiom,
! [X15,X20] :
( ! [X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X53),X20))
=> hBOOL(hAPP(X15,X53)) )
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)))
=> hBOOL(hAPP(X15,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_subset__trans,axiom,
! [X49,X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),X49))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_add__nonneg__pos,axiom,
! [X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_card__Plus__conv__if,axiom,
! [X10,X13,X11,X9] :
( ( ( c_Finite__Set_Ofinite(X9,X11)
& c_Finite__Set_Ofinite(X13,X10) )
=> c_Finite__Set_Ocard(tc_sum(X9,X13),c_Sum__Type_OPlus(X9,X13,X11,X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X9,X11)),c_Finite__Set_Ocard(X13,X10)) )
& ( ~ ( c_Finite__Set_Ofinite(X9,X11)
& c_Finite__Set_Ofinite(X13,X10) )
=> c_Finite__Set_Ocard(tc_sum(X9,X13),c_Sum__Type_OPlus(X9,X13,X11,X10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_card__Plus,axiom,
! [X10,X13,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( c_Finite__Set_Ofinite(X13,X10)
=> c_Finite__Set_Ocard(tc_sum(X9,X13),c_Sum__Type_OPlus(X9,X13,X11,X10)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X9,X11)),c_Finite__Set_Ocard(X13,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_pos__add__strict,axiom,
! [X37,X34,X35,X9] :
( class_Rings_Olinordered__semidom(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),X37))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_card__insert__le,axiom,
! [X7,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X9,X11)),c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__le) ).
fof(fact_Ints__odd__nonzero,axiom,
! [X19,X9] :
( class_Int_Oring__char__0(X9)
=> ( hBOOL(hAPP(hAPP(c_member(X9),X19),c_Int_Oring__1__class_OInts(X9)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Oone__class_Oone(X9)),X19)),X19) != c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X19,X9] :
( class_Groups_Olinordered__ab__group__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X19)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_add__gr__0,axiom,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_card__seteq,axiom,
! [X11,X10,X9] :
( c_Finite__Set_Ofinite(X9,X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X9,X10)),c_Finite__Set_Ocard(X9,X11)))
=> X11 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_subset__insertI2,axiom,
! [X18,X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),c_Set_Oinsert(X9,X18,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_add__strict__increasing2,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X35))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),X37))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),X37))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X34))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_splice_Osimps_I3_J,axiom,
! [X50,X25,X41,X26,X9] : c_List_Osplice(X9,c_List_Olist_OCons(X9,X26,X41),c_List_Olist_OCons(X9,X25,X50)) = c_List_Olist_OCons(X9,X26,c_List_Olist_OCons(X9,X25,c_List_Osplice(X9,X41,X50))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).
fof(fact_psubset__eq,axiom,
! [X10,X11,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
& X11 != X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
| X11 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__imp__subset,axiom,
! [X10,X11,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,tc_HOL_Obool)),X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_insert__iff,axiom,
! [X11,X18,X19,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X19),c_Set_Oinsert(X9,X18,X11)))
<=> ( X19 = X18
| hBOOL(hAPP(hAPP(c_member(X9),X19),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X11,X18,X19,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X19),c_Set_Oinsert(X9,X18,X11)))
=> ( X19 != X18
=> hBOOL(hAPP(hAPP(c_member(X9),X19),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X19,X9] :
( class_Groups_Olinordered__ab__group__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X19)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_Pi__UNIV,axiom,
! [X11,X13,X9] : c_FuncSet_OPi(X9,X13,X11,hAPP(c_COMBK(tc_fun(X13,tc_HOL_Obool),X9),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X9,X13),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
fof(fact_add__increasing,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),X37))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X35,X34,X37,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X37))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),X35))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_finite__Plus,axiom,
! [X10,X13,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( c_Finite__Set_Ofinite(X13,X10)
=> c_Finite__Set_Ofinite(tc_sum(X9,X13),c_Sum__Type_OPlus(X9,X13,X11,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(help_c__COMBC__1,axiom,
! [X12,X70,X15,X9,X42,X13] : hAPP(hAPP(hAPP(c_COMBC(X13,X42,X9),X15),X70),X12) = hAPP(hAPP(X15,X12),X70),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_set__eq__subset,axiom,
! [X9,X10,X11] :
( X11 = X10
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),X11))
=> X11 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_set__rev__mp,axiom,
! [X10,X11,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> hBOOL(hAPP(hAPP(c_member(X9),X7),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_set__mp,axiom,
! [X7,X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> hBOOL(hAPP(hAPP(c_member(X9),X7),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_in__mono,axiom,
! [X7,X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> hBOOL(hAPP(hAPP(c_member(X9),X7),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_subsetD,axiom,
! [X8,X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( hBOOL(hAPP(hAPP(c_member(X9),X8),X11))
=> hBOOL(hAPP(hAPP(c_member(X9),X8),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_le__funD,axiom,
! [X7,X1,X2,X9,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,X13),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X7)),hAPP(X1,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X7,X1,X2,X9,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,X13),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X13,hAPP(X2,X7)),hAPP(X1,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_finite__imageI,axiom,
! [X79,X13,X46,X9] :
( c_Finite__Set_Ofinite(X9,X46)
=> c_Finite__Set_Ofinite(X13,c_Set_Oimage(X9,X13,X79,X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_card__mono,axiom,
! [X11,X10,X9] :
( c_Finite__Set_Ofinite(X9,X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X9,X11)),c_Finite__Set_Ocard(X9,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X37,X34,X35,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34)),X37) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_inj__eq,axiom,
! [X6,X7,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( hAPP(X2,X7) = hAPP(X2,X6)
<=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [X6,X7,X2,X13,X9] :
( c_Fun_Oinj__on(X9,X13,X2,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( hAPP(X2,X7) = hAPP(X2,X6)
=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injD) ).
fof(fact_less__add__Suc1,axiom,
! [X24,X59] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X24)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X24,X59] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X59)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_insertI2,axiom,
! [X18,X10,X19,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X19),X10))
=> hBOOL(hAPP(hAPP(c_member(X9),X19),c_Set_Oinsert(X9,X18,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
fof(fact_less__trans__Suc,axiom,
! [X56,X58,X59] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),X58))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X58),X56))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X59)),X56)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [X9] :
( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,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(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_Suc__less__SucD,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),hAPP(c_Nat_OSuc,X17)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__less__eq,axiom,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21)),hAPP(c_Nat_OSuc,X20)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [X13,X9] :
( c_Finite__Set_Ofinite(tc_fun(X9,X13),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X9,X13),tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_order__less__trans,axiom,
! [X38,X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X38))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X38)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X38,X26,X25,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X38),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X38),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X6,X7,X9] :
( class_Groups_Oordered__comm__monoid__add(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),X6))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X7),X6) = c_Groups_Ozero__class_Ozero(X9)
<=> ( X7 = c_Groups_Ozero__class_Ozero(X9)
& X6 = c_Groups_Ozero__class_Ozero(X9) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [X13,X9] : c_Sum__Type_OPlus(X9,X13,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X9,X13),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_trans__less__add1,axiom,
! [X24,X58,X59] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),X58))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X38,X25,X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X38))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add2,axiom,
! [X24,X58,X59] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),X58))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X58))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X25,X38,X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X38))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X38))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)))
<=> ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X76] :
( X21 = hAPP(c_Nat_OSuc,X76)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X37,X34,X35,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34)),X37) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Oab__semigroup__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34)),X37) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X69,X37,X35,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X69)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)),X69) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_insert__code,axiom,
! [X7,X11,X6,X9] :
( hBOOL(hAPP(c_Set_Oinsert(X9,X6,X11),X7))
<=> ( X6 = X7
| hBOOL(hAPP(X11,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_zero__less__two,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Oone__class_Oone(X9)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_Suc__le__mono,axiom,
! [X21,X20] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20)),hAPP(c_Nat_OSuc,X21)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_order__le__less__trans,axiom,
! [X38,X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X38))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X38)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X38,X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X38))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X38)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I8_J,axiom,
! [X38,X26,X25,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X38),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X38),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X38,X26,X25,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X38),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X38),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X13,X9] :
( c_Finite__Set_Ofinite(tc_sum(X9,X13),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X9,X13),tc_HOL_Obool)))
<=> ( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
& c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X13,X9] :
( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(tc_prod(X9,X13),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X9,X13),tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_less__add__eq__less,axiom,
! [X17,X24,X57,X56] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X56),X57))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X56),X17)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_subset__insertI,axiom,
! [X19,X10,X9] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),c_Set_Oinsert(X9,X19,X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_Suc__lessD,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__mono,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),hAPP(c_Nat_OSuc,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_trans__le__add1,axiom,
! [X24,X58,X59] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X38,X25,X26] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X38))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add2,axiom,
! [X24,X58,X59] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X58))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X25,X38,X26] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26),X38))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X38))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X13,X9] :
( c_Finite__Set_Ofinite(tc_fun(X9,X13),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X9,X13),tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(X13,c_Orderings_Otop__class_Otop(tc_fun(X13,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_nat__add__assoc,axiom,
! [X56,X17,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X17)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X56)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_Suc__le__lessD,axiom,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24)),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_Suc__le__eq,axiom,
! [X20,X21] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21)),X20))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__eq__Suc__le,axiom,
! [X21,X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20)),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_predicate1D,axiom,
! [X7,X70,X15,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X15),X70))
=> ( hBOOL(hAPP(X15,X7))
=> hBOOL(hAPP(X70,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X70,X9,X7,X15] :
( hBOOL(hAPP(X15,X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X15),X70))
=> hBOOL(hAPP(X70,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_order__trans,axiom,
! [X38,X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X38))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X38)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X38,X26,X25,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X38),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X38),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_Suc__lessI,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
=> ( hAPP(c_Nat_OSuc,X24) != X17
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__add__one,axiom,
! [X35,X9] :
( class_Rings_Olinordered__semidom(X9)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),c_Groups_Oone__class_Oone(X9)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_le__less__Suc__eq,axiom,
! [X20,X21] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X21)))
<=> X20 = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__leD,axiom,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24)),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_insert__commute,axiom,
! [X11,X6,X7,X9] : c_Set_Oinsert(X9,X7,c_Set_Oinsert(X9,X6,X11)) = c_Set_Oinsert(X9,X6,c_Set_Oinsert(X9,X7,X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_insertI1,axiom,
! [X10,X19,X9] : hBOOL(hAPP(hAPP(c_member(X9),X19),c_Set_Oinsert(X9,X19,X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_less__Suc__eq,axiom,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
| X21 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__leI,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X69,X37,X35,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X69)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X69)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_le__trans,axiom,
! [X56,X58,X59] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59),X58))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X58),X56))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59),X56)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_finite__subset,axiom,
! [X10,X11,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ( c_Finite__Set_Ofinite(X9,X10)
=> c_Finite__Set_Ofinite(X9,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [X11,X10,X9] :
( c_Finite__Set_Ofinite(X9,X10)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> c_Finite__Set_Ofinite(X9,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_less__iff__Suc__add,axiom,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
<=> ? [X61] : X20 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__Suc__eq__le,axiom,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),hAPP(c_Nat_OSuc,X20)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_less__SucI,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [X19,X9] :
( class_Int_Oring__char__0(X9)
=> ( hBOOL(hAPP(hAPP(c_member(X9),X19),c_Int_Oring__1__class_OInts(X9)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X19) = c_Groups_Ozero__class_Ozero(X9)
<=> X19 = c_Groups_Ozero__class_Ozero(X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_nat__case__Suc,axiom,
! [X75,X54,X55,X9] : c_Nat_Onat_Onat__case(X9,X55,X54,hAPP(c_Nat_OSuc,X75)) = hAPP(X54,X75),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_le__Suc__eq,axiom,
! [X20,X21] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),hAPP(c_Nat_OSuc,X20)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
| X21 = hAPP(c_Nat_OSuc,X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_subset__UNIV,axiom,
! [X11,X9] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_nat__less__cases,axiom,
! [X15,X20,X21] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
=> hBOOL(hAPP(hAPP(X15,X20),X21)) )
=> ( ( X21 = X20
=> hBOOL(hAPP(hAPP(X15,X20),X21)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21))
=> hBOOL(hAPP(hAPP(X15,X20),X21)) )
=> hBOOL(hAPP(hAPP(X15,X20),X21)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_nat__add__left__commute,axiom,
! [X38,X25,X26] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),X38)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_order__eq__iff,axiom,
! [X6,X7,X9] :
( class_Orderings_Oorder(X9)
=> ( X7 = X6
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X6),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X7,X6,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X6),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
<=> X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X25,X26,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26))
=> X26 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X26,X25,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
=> X26 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_card__ge__0__finite,axiom,
! [X11,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X9,X11)))
=> c_Finite__Set_Ofinite(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_le__imp__less__Suc,axiom,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X11,X9] :
( c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X9,X11) = c_Finite__Set_Ocard(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))
=> X11 = c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_order__less__le,axiom,
! [X6,X7,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
& X7 != X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__le__less,axiom,
! [X6,X7,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
| X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__imp__le,axiom,
! [X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_le__add1,axiom,
! [X24,X17] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X24))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X24,X17] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_image__ident,axiom,
! [X82,X9] : c_Set_Oimage(X9,X9,c_COMBI(X9),X82) = X82,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_inj__on__id2,axiom,
! [X11,X9] : c_Fun_Oinj__on(X9,X9,c_COMBI(X9),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(fact_order__neq__le__trans,axiom,
! [X34,X35,X9] :
( class_Orderings_Oorder(X9)
=> ( X35 != X34
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),X34))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X25,X26,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
| X26 = X25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [X34,X35,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X35),X34))
=> ( X35 != X34
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [X35,X34,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),X35))
=> ( X35 != X34
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_xt1_I12_J,axiom,
! [X34,X35,X9] :
( class_Orderings_Oorder(X9)
=> ( X35 != X34
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X34),X35))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_less__Suc0,axiom,
! [X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_inj__Suc,axiom,
! [X62] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X62),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_le__antisym,axiom,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X24))
=> X24 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_eq__mem,axiom,
! [X6,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),hAPP(c_fequal,X6)))
<=> X7 = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__SucI,axiom,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),hAPP(c_Nat_OSuc,X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_nat__less__le,axiom,
! [X20,X21] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
& X21 != X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X20,X21] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
| X21 = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_less__imp__le__nat,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X25,X26] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X17,X24] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
| X24 = X17 )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_insert__absorb,axiom,
! [X11,X19,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X19),X11))
=> c_Set_Oinsert(X9,X19,X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_linorder__neq__iff,axiom,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( X7 != X6
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X6),X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
| X26 = X25
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_splice_Osimps_I2_J,axiom,
! [X47,X48,X9] : c_List_Osplice(X9,c_List_Olist_OCons(X9,X48,X47),c_List_Olist_ONil(X9)) = c_List_Olist_OCons(X9,X48,X47),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).
fof(fact_finite__option__UNIV,axiom,
! [X9] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X9),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X9),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_le__neq__implies__less,axiom,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
=> ( X24 != X17
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_insert__absorb2,axiom,
! [X11,X7,X9] : c_Set_Oinsert(X9,X7,c_Set_Oinsert(X9,X7,X11)) = c_Set_Oinsert(X9,X7,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [X7,X9] : hBOOL(hAPP(hAPP(c_member(X9),X7),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_UNIV__I,axiom,
! [X7,X9] : hBOOL(hAPP(hAPP(c_member(X9),X7),c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_finite__insert,axiom,
! [X11,X19,X9] :
( c_Finite__Set_Ofinite(X9,c_Set_Oinsert(X9,X19,X11))
<=> c_Finite__Set_Ofinite(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).
fof(fact_mem__def,axiom,
! [X11,X7,X9] :
( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
<=> hBOOL(hAPP(X11,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_linorder__le__less__linear,axiom,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_add__Suc,axiom,
! [X17,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X17) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_le__iff__add,axiom,
! [X20,X21] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
<=> ? [X61] : X20 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X61) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_nat__neq__iff,axiom,
! [X20,X21] :
( X21 != X20
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_gr0__conv__Suc,axiom,
! [X20] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20))
<=> ? [X53] : X20 = hAPP(c_Nat_OSuc,X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X25,X26,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> X25 != X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X25,X26,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> X26 != X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X25,X26,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> X26 != X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_equalityD1,axiom,
! [X9,X10,X11] :
( X11 = X10
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X9,X10,X11] :
( X11 = X10
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_subset__refl,axiom,
! [X11,X9] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_neq0__conv,axiom,
! [X20] :
( X20 != 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)),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_add__right__imp__eq,axiom,
! [X37,X35,X34,X9] :
( class_Groups_Ocancel__semigroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X34),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X35)
=> X34 = X37 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X8,X19,X18,X9] :
( class_Groups_Ocancel__semigroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X18),X19) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X8),X19)
<=> X18 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Ocancel__ab__semigroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)
=> X34 = X37 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X37,X34,X35,X9] :
( class_Groups_Ocancel__semigroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37)
=> X34 = X37 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X8,X18,X19,X9] :
( class_Groups_Ocancel__semigroup__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X8)
<=> X18 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_list_Oinject,axiom,
! [X39,X30,X40,X19,X9] :
( c_List_Olist_OCons(X9,X19,X40) = c_List_Olist_OCons(X9,X30,X39)
<=> ( X19 = X30
& X40 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
fof(fact_linorder__linear,axiom,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_add__Suc__right,axiom,
! [X17,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X17)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_add__Suc__shift,axiom,
! [X17,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_nat_Osize_I4_J,axiom,
! [X77] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X77)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X77)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
fof(fact_gr__implies__not0,axiom,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
=> X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_nat__le__linear,axiom,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zero__less__Suc,axiom,
! [X17] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_less__not__refl2,axiom,
! [X24,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X24))
=> X24 != X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [X22,X23] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X22))
=> X23 != X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_zero__less__one,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Ozero__class_Ozero(X9)),c_Groups_Oone__class_Oone(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_Ints__0,axiom,
! [X9] :
( class_Rings_Oring__1(X9)
=> hBOOL(hAPP(hAPP(c_member(X9),c_Groups_Ozero__class_Ozero(X9)),c_Int_Oring__1__class_OInts(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(fact_Ints__1,axiom,
! [X9] :
( class_Rings_Oring__1(X9)
=> hBOOL(hAPP(hAPP(c_member(X9),c_Groups_Oone__class_Oone(X9)),c_Int_Oring__1__class_OInts(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(fact_nat__add__right__cancel,axiom,
! [X20,X60,X21] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X60) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20),X60)
<=> X21 = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X20,X21,X60] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X20)
<=> X21 = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_finite_OinsertI,axiom,
! [X19,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ofinite(X9,c_Set_Oinsert(X9,X19,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_lessI,axiom,
! [X17] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_top1I,axiom,
! [X7,X9] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool)),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_le__0__eq,axiom,
! [X20] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_add__is__1,axiom,
! [X20,X21] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X21 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X20 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(fact_one__is__add,axiom,
! [X20,X21] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20)
<=> ( ( X21 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X20 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_zero__le__one,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Ozero__class_Ozero(X9)),c_Groups_Oone__class_Oone(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_nat_Osize_I2_J,axiom,
! [X77] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X77)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X77)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X37,X35,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),X37) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X37),X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_gr0I,axiom,
! [X17] :
( X17 != 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)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_top__greatest,axiom,
! [X26,X9] :
( class_Orderings_Otop(X9)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),c_Orderings_Otop__class_Otop(X9))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_double__eq__0__iff,axiom,
! [X19,X9] :
( class_Groups_Olinordered__ab__group__add(X9)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X19) = c_Groups_Ozero__class_Ozero(X9)
<=> X19 = c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X19,X9] :
( class_Groups_Olinordered__ab__group__add(X9)
=> ( c_Groups_Ozero__class_Ozero(X9) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X19),X19)
<=> X19 = c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__iff,axiom,
! [X19,X18,X9] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X9)
=> ( X18 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X18),X19)
<=> X19 = c_Groups_Ozero__class_Ozero(X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_order__eq__refl,axiom,
! [X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( X26 = X25
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(help_c__COMBK__1,axiom,
! [X88,X87,X13,X9] : hAPP(hAPP(c_COMBK(X9,X13),X87),X88) = X87,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_list_Osimps_I3_J,axiom,
! [X32,X33,X9] : c_List_Olist_OCons(X9,X33,X32) != c_List_Olist_ONil(X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [X32,X33,X9] : c_List_Olist_ONil(X9) != c_List_Olist_OCons(X9,X33,X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_nat__add__commute,axiom,
! [X17,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_order__refl,axiom,
! [X26,X9] :
( class_Orderings_Opreorder(X9)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X17] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X17] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_not__Cons__self2,axiom,
! [X41,X26,X9] : c_List_Olist_OCons(X9,X26,X41) != X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_not__Cons__self,axiom,
! [X26,X9,X41] : X41 != c_List_Olist_OCons(X9,X26,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(fact_top__apply,axiom,
! [X7,X13,X9] :
( class_Orderings_Otop(X9)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X13,X9)),X7) = c_Orderings_Otop__class_Otop(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_add__is__0,axiom,
! [X20,X21] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_eq__imp__le,axiom,
! [X17,X24] :
( X24 = X17
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(help_c__fequal__2,axiom,
! [X6,X7] :
( X7 != X6
| hBOOL(hAPP(hAPP(c_fequal,X7),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_add__eq__self__zero,axiom,
! [X17,X24] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X17) = X24
=> X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_le__refl,axiom,
! [X17] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_finite__UNIV,axiom,
! [X9] :
( class_Finite__Set_Ofinite(X9)
=> c_Finite__Set_Ofinite(X9,c_Orderings_Otop__class_Otop(tc_fun(X9,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X35,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Ozero__class_Ozero(X9)),X35) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0,axiom,
! [X35,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Ozero__class_Ozero(X9)),X35) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [X35,X9] :
( class_Groups_Omonoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),c_Groups_Ozero__class_Ozero(X9)),X35) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X35,X9] :
( class_Rings_Ocomm__semiring__1(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),c_Groups_Ozero__class_Ozero(X9)) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X35,X9] :
( class_Groups_Ocomm__monoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),c_Groups_Ozero__class_Ozero(X9)) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [X35,X9] :
( class_Groups_Omonoid__add(X9)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X9),X35),c_Groups_Ozero__class_Ozero(X9)) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X17] : hAPP(c_Nat_OSuc,X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_list_Osize_I1_J,axiom,
! [X78,X9] : c_List_Olist_Olist__size(X9,X78,c_List_Olist_ONil(X9)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).
fof(fact_Suc__eq__plus1,axiom,
! [X17] : hAPP(c_Nat_OSuc,X17) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_splice_Osimps_I1_J,axiom,
! [X50,X9] : c_List_Osplice(X9,c_List_Olist_ONil(X9),X50) = X50,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
fof(fact_splice__Nil2,axiom,
! [X41,X9] : c_List_Osplice(X9,X41,c_List_Olist_ONil(X9)) = X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X20] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [X86,X85] :
( ( class_Finite__Set_Ofinite(X85)
& class_Finite__Set_Ofinite(X86) )
=> class_Finite__Set_Ofinite(tc_sum(X85,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [X86,X85] :
( ( class_Finite__Set_Ofinite(X85)
& class_Finite__Set_Ofinite(X86) )
=> class_Finite__Set_Ofinite(tc_fun(X85,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X86,X85] :
( ( class_Finite__Set_Ofinite(X85)
& class_Finite__Set_Ofinite(X86) )
=> class_Finite__Set_Ofinite(tc_prod(X85,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(fact_Suc__inject,axiom,
! [X25,X26] :
( hAPP(c_Nat_OSuc,X26) = hAPP(c_Nat_OSuc,X25)
=> X26 = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_nat_Oinject,axiom,
! [X74,X75] :
( hAPP(c_Nat_OSuc,X75) = hAPP(c_Nat_OSuc,X74)
<=> X75 = X74 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X85,X86] :
( class_Orderings_Oord(X86)
=> class_Orderings_Oord(tc_fun(X85,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X85,X86] :
( class_Orderings_Oorder(X86)
=> class_Orderings_Oorder(tc_fun(X85,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X85,X86] :
( class_Orderings_Opreorder(X86)
=> class_Orderings_Opreorder(tc_fun(X85,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Otop,axiom,
! [X85,X86] :
( class_Orderings_Otop(X86)
=> class_Orderings_Otop(tc_fun(X85,X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(fact_Suc__not__Zero,axiom,
! [X24] : hAPP(c_Nat_OSuc,X24) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X72] : hAPP(c_Nat_OSuc,X72) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__neq__Zero,axiom,
! [X24] : hAPP(c_Nat_OSuc,X24) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_Zero__not__Suc,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X73] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X73),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_finite__code,axiom,
! [X11,X9] :
( class_Finite__Set_Ofinite(X9)
=> c_Finite__Set_Ofinite(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_finite,axiom,
! [X11,X9] :
( class_Finite__Set_Ofinite(X9)
=> c_Finite__Set_Ofinite(X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_Suc__n__not__n,axiom,
! [X17] : hAPP(c_Nat_OSuc,X17) != X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X17] : X17 != hAPP(c_Nat_OSuc,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(help_c__COMBI__1,axiom,
! [X87,X9] : hAPP(c_COMBI(X9),X87) = X87,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_distinct_Osimps_I1_J,axiom,
! [X9] : c_List_Odistinct(X9,c_List_Olist_ONil(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact_zero__neq__one,axiom,
! [X9] :
( class_Rings_Ozero__neq__one(X9)
=> c_Groups_Ozero__class_Ozero(X9) != c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X9] :
( class_Rings_Ozero__neq__one(X9)
=> c_Groups_Oone__class_Oone(X9) != c_Groups_Ozero__class_Ozero(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [X86] :
( class_Finite__Set_Ofinite(X86)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X86)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(fact_nat__size,axiom,
! [X17] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omktop),v_P____)),v_e____)),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBS(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_fequal),v_h____)),v_n____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Oabove),v_P____)),v_c____)),v_e____)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_Arrow__Order__Mirabelle_Oindi,c_Arrow__Order__Mirabelle_Omkbot),v_P____)),v_e____)))),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai_A_061_An_Athen_Aabove_A_IP_Ai_J_Ac_Ae_Aelse_Amkbot_A_IP_Ai_J_Ae_J_058_AProf_096) ).
fof(fact_n_I3_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I3_J) ).
fof(fact_assms_I1_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),v_h____),v_n____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_096) ).
fof(fact__096P_A_058_AProf_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
fof(fact_Prof__def,axiom,
c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Prof__def) ).
fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
fof(fact_dist,axiom,
c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_c____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_d____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_e____,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dist) ).
fof(fact__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096) ).
fof(fact__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096) ).
fof(fact_surjh,axiom,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surjh) ).
fof(fact_n_I1_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),v_n____),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I1_J) ).
fof(fact_injh,axiom,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injh) ).
fof(fact_card__UNIV__unit,axiom,
c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
fof(fact_finite__indi,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(fact_nat_Osize_I3_J,axiom,
c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_nat_Osize_I1_J,axiom,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_u) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(fact__096a_A_126_061_Ab_096,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
fof(fact__096c_A_126_061_Ad_096,axiom,
v_c____ != v_d____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_126_061_Ad_096) ).
fof(i_0_519,plain,
~ ! [X63] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X63),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> ( ! [X53] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53),X63))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X53))),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),X63),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_520,plain,
! [X7,X11,X46,X1,X4,X2,X13,X9] :
( c_Finite__Set_Ofolding__image__simple(X9,X13,X2,X4,X1,X46)
=> ( c_Finite__Set_Ofinite(X13,X11)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),X7),X11))
=> hAPP(X46,c_Set_Oinsert(X13,X7,X11)) = hAPP(hAPP(X2,hAPP(X1,X7)),hAPP(X46,X11)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(i_0_521,negated_conjecture,
~ ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X65)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X65)),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X65)),v_e____))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,X65)),v_n____))
=> ( ( hAPP(v_h____,X65) = v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X65)),v_c____),v_e____))) )
& ( hAPP(v_h____,X65) != v_n____
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,X65)),v_e____))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_522,plain,
! [X11,X2,X13,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X9,c_Set_Oimage(X13,X9,X2,X11))),c_Finite__Set_Ocard(X13,X11)))
=> ~ c_Fun_Oinj__on(X13,X9,X2,X11) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).
fof(i_0_523,plain,
! [X11,X9] :
( ( c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X9,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X11) )
& ( ~ c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_simplification,[status(thm)],[fact_card__def]) ).
fof(i_0_524,plain,
! [X6,X7,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))
=> ( X7 != X6
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),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),X6),X7)),X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_525,plain,
! [X18,X19,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))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X19),X18)),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),X18),X19)),X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_526,plain,
! [X7,X10,X11,X2,X13,X9] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X9,X13)),X2),c_FuncSet_OPi(X9,X13,X11,X10)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X13),hAPP(X2,X7)),hAPP(X10,X7)))
=> ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_527,plain,
! [X6,X7,X9] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X6)),c_List_Omeasures(X9,c_List_Olist_ONil(tc_fun(X9,tc_Nat_Onat))))),
inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J]) ).
fof(i_0_528,plain,
! [X10,X11,X7,X9] :
( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),c_Set_Oinsert(X9,X7,X10)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_529,plain,
~ ! [X51] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X51))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X51),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,
~ ! [X52] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X52))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X52),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,X9,X13] :
( class_Orderings_Oord(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X9,X13)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,X13),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,X13),X1),X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_532,plain,
! [X17,X56,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X56)),X17))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56),X17)) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_533,plain,
~ ! [X27] : ~ c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_c____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_d____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X27,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Be_O_Adistinct_A_091c_M_Ad_M_Ae_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(i_0_534,plain,
! [X58,X59] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),X58)),X59)),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_535,plain,
! [X59,X58] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X58),X59)),X59)),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_536,plain,
! [X20,X15] :
( ~ hBOOL(hAPP(X15,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X15,X20))
=> ? [X61] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),X20))
& ! [X65] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65),X61))
=> ~ hBOOL(hAPP(X15,X65)) )
& hBOOL(hAPP(X15,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).
fof(i_0_537,plain,
! [X18,X10,X19,X9] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X9),X19),X10))
=> X19 = X18 )
=> hBOOL(hAPP(hAPP(c_member(X9),X19),c_Set_Oinsert(X9,X18,X10))) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_538,plain,
! [X10,X11,X7,X9] :
( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X10))
=> ( c_Set_Oinsert(X9,X7,X11) = c_Set_Oinsert(X9,X7,X10)
<=> X11 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_539,plain,
! [X20,X21] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21),X20))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X20)),X21)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_540,plain,
! [X20,X21] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21),X20))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X21))) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_541,plain,
! [X35,X34,X9] :
( class_Orderings_Oorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),X35))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34)) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_542,plain,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X6),X7))
| X7 = X6 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_543,plain,
! [X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_544,plain,
! [X34,X35,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X35),X34))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X34),X35)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_545,plain,
! [X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_546,plain,
! [X25,X26,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_547,plain,
! [X7,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X9,X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).
fof(i_0_548,plain,
! [X6,X7,X9] :
( class_Orderings_Opreorder(X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X6),X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_549,plain,
! [X7,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( ( hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)) = c_Finite__Set_Ocard(X9,X11) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X9,X11)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).
fof(i_0_550,plain,
! [X17,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X17)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X17))
=> X24 = X17 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_551,plain,
! [X24,X17] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X24))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X24)))
=> X24 = X17 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_552,plain,
! [X21,X20] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),X21))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20),hAPP(c_Nat_OSuc,X21)))
<=> X20 = X21 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_553,plain,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> X7 = X6 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_554,plain,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X6),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_555,plain,
! [X26,X25,X9] :
( class_Orderings_Olinorder(X9)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_556,plain,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X6),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_557,plain,
! [X7,X11,X9] :
( c_Finite__Set_Ofinite(X9,X11)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X9),X7),X11))
=> c_Finite__Set_Ocard(X9,c_Set_Oinsert(X9,X7,X11)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X9,X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).
fof(i_0_558,plain,
! [X17,X24] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),hAPP(c_Nat_OSuc,X17)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24),X17))
=> X24 = hAPP(c_Nat_OSuc,X17) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_559,plain,
! [X17] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X17)),X17)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_560,plain,
! [X6,X7,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X7),X6))
<=> X7 = X6 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_561,plain,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(X9))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_562,plain,
! [X25,X26,X9] :
( class_Rings_Olinordered__idom(X9)
=> ( X26 != X25
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_563,plain,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> ( X26 != X25
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_564,plain,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( X26 != X25
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X25),X26)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_565,plain,
! [X7,X6,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X6),X7))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X7),X6))
<=> X7 = X6 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_566,plain,
! [X26,X25,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_567,plain,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_568,plain,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,c_Groups_Oone__class_Oone(X9)),c_Groups_Ozero__class_Ozero(X9))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_569,plain,
! [X25,X26] :
( X26 != X25
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X25))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X26)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_570,plain,
! [X9,X10,X11] :
( X11 = X10
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X11),X10))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool),X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_571,plain,
! [X26,X9] :
( class_Orderings_Opreorder(X9)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X9),X26),X26)) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_572,plain,
! [X25,X26,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X26),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X9,X25),X26)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_573,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_574,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_575,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_576,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_577,plain,
! [X17] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X17)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_578,plain,
! [X6,X7] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X7),X6))
| X7 = X6 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_579,plain,
! [X11,X9] :
( ~ c_Finite__Set_Ofinite(X9,X11)
=> c_Finite__Set_Ocard(X9,X11) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
fof(i_0_580,plain,
! [X2316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk18_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,X2316),esk18_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____)),X2316))),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),esk18_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_519])])])]) ).
fof(i_0_581,plain,
! [X2203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2203),esk12_0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X2203))),v_Lab____)),v_Lba____)))) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk12_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[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,
! [X1717] : hBOOL(hAPP(hAPP(c_member(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____)),X1717))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
inference(variable_rename,[status(thm)],[fact_PiProf]) ).
fof(i_0_583,plain,
! [X1937] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1937),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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____)),X1937))),v_Lab____)),v_Lba____)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n_I2_J])]) ).
fof(i_0_584,plain,
! [X2251,X2252,X2253,X2254] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2254,tc_fun(X2253,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2254,tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_fun(X2253,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2253,tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_fun(X2253,tc_HOL_Obool)),X2254,c_COMBC(X2253,tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2253,tc_prod(X2254,X2253)),tc_fun(X2253,tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),X2254,c_COMBB(tc_prod(X2254,X2253),tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool),X2253,c_member(tc_prod(X2254,X2253)))),c_Product__Type_OPair(X2254,X2253)))),X2252)),hAPP(hAPP(c_COMBC(X2254,tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_fun(X2253,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2253,tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_fun(X2253,tc_HOL_Obool)),X2254,c_COMBC(X2253,tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2253,tc_prod(X2254,X2253)),tc_fun(X2253,tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),X2254,c_COMBB(tc_prod(X2254,X2253),tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool),X2253,c_member(tc_prod(X2254,X2253)))),c_Product__Type_OPair(X2254,X2253)))),X2251)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),X2252),X2251)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),X2252),X2251))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2254,tc_fun(X2253,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2254,tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_fun(X2253,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2253,tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_fun(X2253,tc_HOL_Obool)),X2254,c_COMBC(X2253,tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2253,tc_prod(X2254,X2253)),tc_fun(X2253,tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),X2254,c_COMBB(tc_prod(X2254,X2253),tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool),X2253,c_member(tc_prod(X2254,X2253)))),c_Product__Type_OPair(X2254,X2253)))),X2252)),hAPP(hAPP(c_COMBC(X2254,tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_fun(X2253,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2253,tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_fun(X2253,tc_HOL_Obool)),X2254,c_COMBC(X2253,tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2253,tc_prod(X2254,X2253)),tc_fun(X2253,tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool)),X2254,c_COMBB(tc_prod(X2254,X2253),tc_fun(tc_fun(tc_prod(X2254,X2253),tc_HOL_Obool),tc_HOL_Obool),X2253,c_member(tc_prod(X2254,X2253)))),c_Product__Type_OPair(X2254,X2253)))),X2251))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_585,plain,
! [X2229,X2230,X2231,X2232,X2233,X2234] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2234),X2233)),hAPP(v_F,X2230)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2232),X2231)),hAPP(v_F,X2229)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2234),X2233)),hAPP(X2230,esk17_6(X2229,X2230,X2231,X2232,X2233,X2234))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2232),X2231)),hAPP(X2229,esk17_6(X2229,X2230,X2231,X2232,X2233,X2234))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2229),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2230),c_Arrow__Order__Mirabelle_OProf))
| X2233 = X2232
| X2234 = X2231
| X2232 = X2231
| X2234 = X2233 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2232),X2231)),hAPP(v_F,X2229)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2234),X2233)),hAPP(v_F,X2230)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2234),X2233)),hAPP(X2230,esk17_6(X2229,X2230,X2231,X2232,X2233,X2234))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2232),X2231)),hAPP(X2229,esk17_6(X2229,X2230,X2231,X2232,X2233,X2234))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2229),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2230),c_Arrow__Order__Mirabelle_OProf))
| X2233 = X2232
| X2234 = X2231
| X2232 = X2231
| X2234 = X2233 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2234),X2233)),hAPP(v_F,X2230)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2232),X2231)),hAPP(v_F,X2229)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2234),X2233)),hAPP(X2230,esk17_6(X2229,X2230,X2231,X2232,X2233,X2234))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2232),X2231)),hAPP(X2229,esk17_6(X2229,X2230,X2231,X2232,X2233,X2234))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2229),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2230),c_Arrow__Order__Mirabelle_OProf))
| X2233 = X2232
| X2234 = X2231
| X2232 = X2231
| X2234 = X2233 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2232),X2231)),hAPP(v_F,X2229)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2234),X2233)),hAPP(v_F,X2230)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2234),X2233)),hAPP(X2230,esk17_6(X2229,X2230,X2231,X2232,X2233,X2234))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2232),X2231)),hAPP(X2229,esk17_6(X2229,X2230,X2231,X2232,X2233,X2234))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2229),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2230),c_Arrow__Order__Mirabelle_OProf))
| X2233 = X2232
| X2234 = X2231
| X2232 = X2231
| X2234 = X2233 ) ),
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,
! [X2222,X2223,X2224,X2225,X2226,X2227] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2226)),hAPP(X2223,esk16_6(X2222,X2223,X2224,X2225,X2226,X2227))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(X2222,esk16_6(X2222,X2223,X2224,X2225,X2226,X2227))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2226)),hAPP(v_F,X2223)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(v_F,X2222)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2222),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2223),c_Arrow__Order__Mirabelle_OProf))
| X2226 = X2225
| X2227 = X2224
| X2225 = X2224
| X2227 = X2226 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2226)),hAPP(X2223,esk16_6(X2222,X2223,X2224,X2225,X2226,X2227))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(X2222,esk16_6(X2222,X2223,X2224,X2225,X2226,X2227))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2227),X2226)),hAPP(v_F,X2223)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2225),X2224)),hAPP(v_F,X2222)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2222),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2223),c_Arrow__Order__Mirabelle_OProf))
| X2226 = X2225
| X2227 = X2224
| X2225 = X2224
| X2227 = X2226 ) ),
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,
! [X2209,X2210,X2211,X2212,X2213,X2214] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2213)),hAPP(v_F,X2210)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2212),X2211)),hAPP(v_F,X2209)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2213)),hAPP(X2210,esk14_6(X2209,X2210,X2211,X2212,X2213,X2214))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2212),X2211)),hAPP(X2209,esk14_6(X2209,X2210,X2211,X2212,X2213,X2214))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2209),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2210),c_Arrow__Order__Mirabelle_OProf))
| X2212 = X2211
| X2214 = X2213 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2212),X2211)),hAPP(v_F,X2209)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2213)),hAPP(v_F,X2210)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2213)),hAPP(X2210,esk14_6(X2209,X2210,X2211,X2212,X2213,X2214))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2212),X2211)),hAPP(X2209,esk14_6(X2209,X2210,X2211,X2212,X2213,X2214))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2209),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2210),c_Arrow__Order__Mirabelle_OProf))
| X2212 = X2211
| X2214 = X2213 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2213)),hAPP(v_F,X2210)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2212),X2211)),hAPP(v_F,X2209)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2213)),hAPP(X2210,esk14_6(X2209,X2210,X2211,X2212,X2213,X2214))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2212),X2211)),hAPP(X2209,esk14_6(X2209,X2210,X2211,X2212,X2213,X2214))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2209),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2210),c_Arrow__Order__Mirabelle_OProf))
| X2212 = X2211
| X2214 = X2213 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2212),X2211)),hAPP(v_F,X2209)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2213)),hAPP(v_F,X2210)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2214),X2213)),hAPP(X2210,esk14_6(X2209,X2210,X2211,X2212,X2213,X2214))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2212),X2211)),hAPP(X2209,esk14_6(X2209,X2210,X2211,X2212,X2213,X2214))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2209),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2210),c_Arrow__Order__Mirabelle_OProf))
| X2212 = X2211
| X2214 = X2213 ) ),
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,
! [X1698,X1699,X1700,X1701] :
( ( hAPP(hAPP(c_COMBC(X1701,tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_fun(X1700,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1700,tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_fun(X1700,tc_HOL_Obool)),X1701,c_COMBC(X1700,tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1700,tc_prod(X1701,X1700)),tc_fun(X1700,tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),X1701,c_COMBB(tc_prod(X1701,X1700),tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool),X1700,c_member(tc_prod(X1701,X1700)))),c_Product__Type_OPair(X1701,X1700)))),X1699) != hAPP(hAPP(c_COMBC(X1701,tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_fun(X1700,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1700,tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_fun(X1700,tc_HOL_Obool)),X1701,c_COMBC(X1700,tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1700,tc_prod(X1701,X1700)),tc_fun(X1700,tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),X1701,c_COMBB(tc_prod(X1701,X1700),tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool),X1700,c_member(tc_prod(X1701,X1700)))),c_Product__Type_OPair(X1701,X1700)))),X1698)
| X1699 = X1698 )
& ( X1699 != X1698
| hAPP(hAPP(c_COMBC(X1701,tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_fun(X1700,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1700,tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_fun(X1700,tc_HOL_Obool)),X1701,c_COMBC(X1700,tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1700,tc_prod(X1701,X1700)),tc_fun(X1700,tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),X1701,c_COMBB(tc_prod(X1701,X1700),tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool),X1700,c_member(tc_prod(X1701,X1700)))),c_Product__Type_OPair(X1701,X1700)))),X1699) = hAPP(hAPP(c_COMBC(X1701,tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_fun(X1700,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1700,tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_fun(X1700,tc_HOL_Obool)),X1701,c_COMBC(X1700,tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1700,tc_prod(X1701,X1700)),tc_fun(X1700,tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool)),X1701,c_COMBB(tc_prod(X1701,X1700),tc_fun(tc_fun(tc_prod(X1701,X1700),tc_HOL_Obool),tc_HOL_Obool),X1700,c_member(tc_prod(X1701,X1700)))),c_Product__Type_OPair(X1701,X1700)))),X1698) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_589,plain,
! [X2490,X2491,X2492,X2493,X2494] :
( ( hBOOL(hAPP(hAPP(c_member(X2494),esk31_5(X2490,X2491,X2492,X2493,X2494)),X2493))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2494,X2492),tc_HOL_Obool),c_FuncSet_OPi(X2494,X2492,X2493,X2491)),c_FuncSet_OPi(X2494,X2492,X2493,X2490))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2492,tc_HOL_Obool),hAPP(X2491,esk31_5(X2490,X2491,X2492,X2493,X2494))),hAPP(X2490,esk31_5(X2490,X2491,X2492,X2493,X2494))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2494,X2492),tc_HOL_Obool),c_FuncSet_OPi(X2494,X2492,X2493,X2491)),c_FuncSet_OPi(X2494,X2492,X2493,X2490))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_590,plain,
! [X2544,X2545,X2546,X2547,X2548] :
( ( hBOOL(hAPP(hAPP(c_member(X2548),esk32_5(X2544,X2545,X2546,X2547,X2548)),X2547))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2548,X2546)),X2545),c_FuncSet_OPi(X2548,X2546,X2547,X2544))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2546),hAPP(X2545,esk32_5(X2544,X2545,X2546,X2547,X2548))),hAPP(X2544,esk32_5(X2544,X2545,X2546,X2547,X2548))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2548,X2546)),X2545),c_FuncSet_OPi(X2548,X2546,X2547,X2544))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_591,plain,
! [X2462,X2463,X2464,X2465,X2466,X2468,X2473,X2474] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2462,X2463)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2462,X2464)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2463,esk22_5(X2462,X2463,X2464,X2465,X2466))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2464,esk22_5(X2462,X2463,X2464,X2465,X2466))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2464),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2463),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2462) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2462,X2464)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2462,X2463)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2463,esk22_5(X2462,X2463,X2464,X2465,X2466))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2464,esk22_5(X2462,X2463,X2464,X2465,X2466))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2464),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2463),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2462) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2462,X2463)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2462,X2464)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2463,esk22_5(X2462,X2463,X2464,X2465,X2466))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2464,esk22_5(X2462,X2463,X2464,X2465,X2466))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2464),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2463),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2462) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2462,X2464)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2462,X2463)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2463,esk22_5(X2462,X2463,X2464,X2465,X2466))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2465),X2466)),hAPP(X2464,esk22_5(X2462,X2463,X2464,X2465,X2466))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2464),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2463),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2462) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk23_1(X2468)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2468) )
& ( hBOOL(hAPP(hAPP(c_member(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_1(X2468)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2468) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X2468)),esk26_1(X2468))),hAPP(esk23_1(X2468),X2473)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X2468)),esk26_1(X2468))),hAPP(esk24_1(X2468),X2473)))
| c_Arrow__Order__Mirabelle_OIIA(X2468) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X2468)),esk26_1(X2468))),hAPP(esk24_1(X2468),X2474)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X2468)),esk26_1(X2468))),hAPP(esk23_1(X2468),X2474)))
| c_Arrow__Order__Mirabelle_OIIA(X2468) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X2468)),esk26_1(X2468))),hAPP(X2468,esk23_1(X2468))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X2468)),esk26_1(X2468))),hAPP(X2468,esk24_1(X2468))))
| c_Arrow__Order__Mirabelle_OIIA(X2468) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X2468)),esk26_1(X2468))),hAPP(X2468,esk23_1(X2468))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X2468)),esk26_1(X2468))),hAPP(X2468,esk24_1(X2468))))
| c_Arrow__Order__Mirabelle_OIIA(X2468) ) ),
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_592,plain,
! [X2216,X2217,X2218,X2219,X2220] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2220),X2219)),hAPP(v_F,X2217)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2218)),hAPP(v_F,X2216)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2220),X2219)),hAPP(X2217,esk15_5(X2216,X2217,X2218,X2219,X2220))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2218)),hAPP(X2216,esk15_5(X2216,X2217,X2218,X2219,X2220))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2216),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2217),c_Arrow__Order__Mirabelle_OProf))
| X2220 = X2218
| X2219 = X2218
| X2220 = X2219 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2218)),hAPP(v_F,X2216)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2220),X2219)),hAPP(v_F,X2217)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2220),X2219)),hAPP(X2217,esk15_5(X2216,X2217,X2218,X2219,X2220))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2218)),hAPP(X2216,esk15_5(X2216,X2217,X2218,X2219,X2220))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2216),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2217),c_Arrow__Order__Mirabelle_OProf))
| X2220 = X2218
| X2219 = X2218
| X2220 = X2219 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2220),X2219)),hAPP(v_F,X2217)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2218)),hAPP(v_F,X2216)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2220),X2219)),hAPP(X2217,esk15_5(X2216,X2217,X2218,X2219,X2220))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2218)),hAPP(X2216,esk15_5(X2216,X2217,X2218,X2219,X2220))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2216),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2217),c_Arrow__Order__Mirabelle_OProf))
| X2220 = X2218
| X2219 = X2218
| X2220 = X2219 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2218)),hAPP(v_F,X2216)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2220),X2219)),hAPP(v_F,X2217)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2220),X2219)),hAPP(X2217,esk15_5(X2216,X2217,X2218,X2219,X2220))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2219),X2218)),hAPP(X2216,esk15_5(X2216,X2217,X2218,X2219,X2220))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2216),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2217),c_Arrow__Order__Mirabelle_OProf))
| X2220 = X2218
| X2219 = X2218
| X2220 = X2219 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C4_C])])])]) ).
fof(i_0_593,plain,
! [X2317,X2318] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk19_2(X2317,X2318)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2318,X2317)
| ~ 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))),X2318),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)))) )
& ( esk20_2(X2317,X2318) != esk21_2(X2317,X2318)
| c_Arrow__Order__Mirabelle_Odictator(X2318,X2317)
| ~ 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))),X2318),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),esk20_2(X2317,X2318)),esk21_2(X2317,X2318))),hAPP(esk19_2(X2317,X2318),X2317)))
| c_Arrow__Order__Mirabelle_Odictator(X2318,X2317)
| ~ 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))),X2318),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),esk20_2(X2317,X2318)),esk21_2(X2317,X2318))),hAPP(X2318,esk19_2(X2317,X2318))))
| c_Arrow__Order__Mirabelle_Odictator(X2318,X2317)
| ~ 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))),X2318),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_594,plain,
! [X1688,X1689,X1690,X1691,X1692,X1693,X1694,X1695] :
( ( X1693 = X1691
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1695,X1695)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1695),X1693),X1691)),X1689))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1695,X1694),tc_prod(X1695,X1694))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1695,X1694),tc_prod(X1695,X1694)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1694),X1693),X1692)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1694),X1691),X1690))),c_Wellfounded_Olex__prod(X1695,X1694,X1689,X1688))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1694,X1694)),hAPP(hAPP(c_Product__Type_OPair(X1694,X1694),X1692),X1690)),X1688))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1695,X1695)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1695),X1693),X1691)),X1689))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1695,X1694),tc_prod(X1695,X1694))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1695,X1694),tc_prod(X1695,X1694)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1694),X1693),X1692)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1694),X1691),X1690))),c_Wellfounded_Olex__prod(X1695,X1694,X1689,X1688))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1695,X1695)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1695),X1693),X1691)),X1689))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1695,X1694),tc_prod(X1695,X1694))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1695,X1694),tc_prod(X1695,X1694)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1694),X1693),X1692)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1694),X1691),X1690))),c_Wellfounded_Olex__prod(X1695,X1694,X1689,X1688))) )
& ( X1693 != X1691
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1694,X1694)),hAPP(hAPP(c_Product__Type_OPair(X1694,X1694),X1692),X1690)),X1688))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1695,X1694),tc_prod(X1695,X1694))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1695,X1694),tc_prod(X1695,X1694)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1694),X1693),X1692)),hAPP(hAPP(c_Product__Type_OPair(X1695,X1694),X1691),X1690))),c_Wellfounded_Olex__prod(X1695,X1694,X1689,X1688))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_595,plain,
! [X2204,X2205,X2206,X2207] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2207),X2206)),hAPP(v_F,X2205)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2207)),hAPP(v_F,X2204)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2207),X2206)),hAPP(X2205,esk13_4(X2204,X2205,X2206,X2207))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2207)),hAPP(X2204,esk13_4(X2204,X2205,X2206,X2207))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2204),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2205),c_Arrow__Order__Mirabelle_OProf))
| X2207 = X2206 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2207)),hAPP(v_F,X2204)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2207),X2206)),hAPP(v_F,X2205)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2207),X2206)),hAPP(X2205,esk13_4(X2204,X2205,X2206,X2207))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2207)),hAPP(X2204,esk13_4(X2204,X2205,X2206,X2207))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2204),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2205),c_Arrow__Order__Mirabelle_OProf))
| X2207 = X2206 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2207),X2206)),hAPP(v_F,X2205)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2207)),hAPP(v_F,X2204)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2207),X2206)),hAPP(X2205,esk13_4(X2204,X2205,X2206,X2207))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2207)),hAPP(X2204,esk13_4(X2204,X2205,X2206,X2207))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2204),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2205),c_Arrow__Order__Mirabelle_OProf))
| X2207 = X2206 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2207)),hAPP(v_F,X2204)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2207),X2206)),hAPP(v_F,X2205)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2207),X2206)),hAPP(X2205,esk13_4(X2204,X2205,X2206,X2207))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2206),X2207)),hAPP(X2204,esk13_4(X2204,X2205,X2206,X2207))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2204),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2205),c_Arrow__Order__Mirabelle_OProf))
| X2207 = X2206 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C3_C])])])]) ).
fof(i_0_596,plain,
! [X2912,X2913,X2914,X2915,X2916,X2917,X2918] :
( ~ c_Finite__Set_Ofolding__image__simple(X2918,X2917,X2916,X2915,X2914,X2913)
| ~ c_Finite__Set_Ofinite(X2917,X2912)
| hAPP(X2913,X2912) = c_Finite__Set_Ofold__image(X2918,X2917,X2916,X2914,X2915,X2912) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).
fof(i_0_597,plain,
! [X3092,X3093,X3094,X3095,X3096,X3098,X3099,X3100,X3101,X3102,X3103] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3094,tc_HOL_Obool),esk43_5(X3092,X3093,X3094,X3095,X3096)),X3092))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3096,tc_HOL_Obool),X3095),c_Set_Oimage(X3094,X3096,X3093,X3092))) )
& ( X3095 = c_Set_Oimage(X3094,X3096,X3093,esk43_5(X3092,X3093,X3094,X3095,X3096))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3096,tc_HOL_Obool),X3095),c_Set_Oimage(X3094,X3096,X3093,X3092))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3100,tc_HOL_Obool),X3103),X3098))
| X3101 != c_Set_Oimage(X3100,X3102,X3099,X3103)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3102,tc_HOL_Obool),X3101),c_Set_Oimage(X3100,X3102,X3099,X3098))) ) ),
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_598,plain,
! [X1635,X1636,X1637,X1638,X1639,X1640,X1641] :
( ~ hBOOL(hAPP(X1641,X1640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1639,X1639)),hAPP(hAPP(c_Product__Type_OPair(X1639,X1639),X1638),X1637)),hAPP(X1636,X1640)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1635,X1639),tc_prod(X1635,X1639))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1635,X1639),tc_prod(X1635,X1639)),hAPP(hAPP(c_Product__Type_OPair(X1635,X1639),X1640),X1638)),hAPP(hAPP(c_Product__Type_OPair(X1635,X1639),X1640),X1637))),c_Recdef_Osame__fst(X1635,X1639,X1641,X1636))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_599,plain,
! [X2010,X2011,X2012,X2013,X2014] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2012,X2013),X2011),X2010))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2013,hAPP(X2011,X2014)),hAPP(X2010,X2014)))
| ~ class_Orderings_Oord(X2013) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2013,hAPP(X2011,esk10_4(X2010,X2011,X2012,X2013))),hAPP(X2010,esk10_4(X2010,X2011,X2012,X2013))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2012,X2013),X2011),X2010))
| ~ class_Orderings_Oord(X2013) ) ),
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_600,plain,
! [X2637,X2638,X2639,X2640,X2641,X2642,X2643,X2644] :
( ~ c_Finite__Set_Ofolding__image__simple(X2644,X2643,X2642,X2641,X2640,X2639)
| ~ c_Finite__Set_Ofinite(X2643,X2638)
| hBOOL(hAPP(hAPP(c_member(X2643),X2637),X2638))
| hAPP(X2639,c_Set_Oinsert(X2643,X2637,X2638)) = hAPP(hAPP(X2642,hAPP(X2640,X2637)),hAPP(X2639,X2638)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_520])]) ).
fof(i_0_601,plain,
! [X2475,X2476,X2477,X2478,X2480,X2484] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2475)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2476),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),X2477),X2478)),hAPP(X2476,esk27_4(X2475,X2476,X2477,X2478))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2477),X2478)),hAPP(X2475,X2476))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk28_1(X2480)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X2480) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk29_1(X2480)),esk30_1(X2480))),hAPP(esk28_1(X2480),X2484)))
| c_Arrow__Order__Mirabelle_Ounanimity(X2480) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk29_1(X2480)),esk30_1(X2480))),hAPP(X2480,esk28_1(X2480))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2480) ) ),
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_602,negated_conjecture,
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0))) )
& ( hAPP(v_h____,esk46_0) != v_n____
| hAPP(v_h____,esk46_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk46_0)),v_e____)))
| hAPP(v_h____,esk46_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0))) )
& ( hAPP(v_h____,esk46_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk46_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) )
& ( hAPP(v_h____,esk46_0) != v_n____
| hAPP(v_h____,esk46_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk46_0)),v_e____)))
| hAPP(v_h____,esk46_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) )
& ( hAPP(v_h____,esk46_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk46_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) )
& ( hAPP(v_h____,esk46_0) != v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0))) )
& ( hAPP(v_h____,esk46_0) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_521])])])]) ).
fof(i_0_603,plain,
! [X2496,X2497,X2498,X2499,X2500,X2501] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2501,X2500)),X2499),c_FuncSet_OPi(X2501,X2500,X2498,hAPP(c_COMBK(tc_fun(X2500,tc_HOL_Obool),X2501),X2497))))
| ~ c_Fun_Oinj__on(X2501,X2500,X2499,X2498)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2500,X2501)),X2496),c_FuncSet_OPi(X2500,X2501,X2497,hAPP(c_COMBK(tc_fun(X2501,tc_HOL_Obool),X2500),X2498))))
| ~ c_Fun_Oinj__on(X2500,X2501,X2496,X2497)
| ~ c_Finite__Set_Ofinite(X2501,X2498)
| ~ c_Finite__Set_Ofinite(X2500,X2497)
| c_Finite__Set_Ocard(X2501,X2498) = c_Finite__Set_Ocard(X2500,X2497) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij])]) ).
fof(i_0_604,plain,
! [X2295,X2296,X2297] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2297,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2297,tc_fun(X2297,tc_HOL_Obool),tc_HOL_Obool),c_member(X2297)),X2296)),hAPP(hAPP(c_COMBC(X2297,tc_fun(X2297,tc_HOL_Obool),tc_HOL_Obool),c_member(X2297)),X2295)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2297,tc_HOL_Obool),X2296),X2295)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2297,tc_HOL_Obool),X2296),X2295))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2297,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2297,tc_fun(X2297,tc_HOL_Obool),tc_HOL_Obool),c_member(X2297)),X2296)),hAPP(hAPP(c_COMBC(X2297,tc_fun(X2297,tc_HOL_Obool),tc_HOL_Obool),c_member(X2297)),X2295))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_605,plain,
! [X2965,X2966,X2967,X2968] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2968,c_Set_Oimage(X2967,X2968,X2966,X2965))),c_Finite__Set_Ocard(X2967,X2965)))
| ~ c_Fun_Oinj__on(X2967,X2968,X2966,X2965) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_522])]) ).
fof(i_0_606,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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != 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),X1891),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),X1887)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != 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),X1891)),X1889))
| X1888 = X1890
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1888),X1887)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 = 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 = 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != X1890
| X1888 = X1890
| 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != X1890
| X1887 = X1890
| X1888 = X1890
| 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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
| X1888 = X1890
| 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != X1890
| X1888 != X1891
| X1888 = X1890
| 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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
| X1888 = X1890
| 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != 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),X1891)),X1889))
| X1888 = X1890
| 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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),X1888),X1891)),X1889))
| X1888 = X1890
| 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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != 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),X1891),X1887)),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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != X1890
| 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),X1891),X1887)),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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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),X1891),X1887)),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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != 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),X1891),X1887)),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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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),X1891),X1887)),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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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 != 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),X1891)),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),X1891),X1887)),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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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),X1888),X1891)),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),X1891),X1887)),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)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,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__above])])]) ).
fof(i_0_607,plain,
! [X1892,X1893,X1894,X1895,X1896] :
( ( X1893 != X1892
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1892 != X1896
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1895)),X1894))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1893 != X1896
| X1892 = X1895
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1895),X1892)),X1894))
| X1892 = X1896
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1893 = X1896
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),X1894))
| X1892 = X1896
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1892 != X1896
| X1892 = X1896
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1893 != X1896
| X1893 = X1896
| X1892 = X1896
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),X1894))
| X1893 = X1896
| X1892 = X1896
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1893 != X1896
| X1892 != X1895
| X1892 = X1896
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),X1894))
| X1892 != X1895
| X1892 = X1896
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1893 != X1896
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1895),X1892)),X1894))
| X1892 = X1896
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),X1894))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1895),X1892)),X1894))
| X1892 = X1896
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1892 != X1896
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1895)),X1894))
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1893 != X1896
| X1893 = X1896
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1895)),X1894))
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),X1894))
| X1893 = X1896
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1895)),X1894))
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1893 != X1896
| X1892 != X1895
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1895)),X1894))
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),X1894))
| X1892 != X1895
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1895)),X1894))
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( X1893 != X1896
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1895),X1892)),X1894))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1895)),X1894))
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),X1894))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1895),X1892)),X1894))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1895)),X1894))
| X1893 = X1892
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1893),X1892)),c_Arrow__Order__Mirabelle_Obelow(X1894,X1896,X1895)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1894),c_Arrow__Order__Mirabelle_OLin))
| X1896 = X1895 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_608,plain,
! [X2919,X2920] :
( ( ~ c_Finite__Set_Ofinite(X2920,X2919)
| c_Finite__Set_Ocard(X2920,X2919) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2920,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2920),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2919) )
& ( c_Finite__Set_Ofinite(X2920,X2919)
| c_Finite__Set_Ocard(X2920,X2919) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])]) ).
fof(i_0_609,plain,
! [X2910,X2911] :
( ~ c_Finite__Set_Ofinite(X2911,X2910)
| c_Finite__Set_Ocard(X2911,X2910) = c_Finite__Set_Ofold__image(tc_Nat_Onat,X2911,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X2911),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2910) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).
fof(i_0_610,plain,
! [X3009,X3010,X3011,X3012,X3013] :
( ~ hBOOL(hAPP(hAPP(c_member(X3013),X3012),c_Set_Oimage(X3011,X3013,X3010,X3009)))
| hBOOL(hAPP(hAPP(c_member(X3011),hAPP(c_Hilbert__Choice_Oinv__into(X3011,X3013,X3009,X3010),X3012)),X3009)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).
fof(i_0_611,plain,
! [X3127,X3128,X3129,X3130,X3131] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3130,tc_HOL_Obool),c_Set_Oimage(X3131,X3130,X3129,X3128)),c_Set_Oimage(X3131,X3130,X3129,X3127)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3131,tc_HOL_Obool),X3128),X3127))
| ~ c_Fun_Oinj__on(X3131,X3130,X3129,c_Orderings_Otop__class_Otop(tc_fun(X3131,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3131,tc_HOL_Obool),X3128),X3127))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3130,tc_HOL_Obool),c_Set_Oimage(X3131,X3130,X3129,X3128)),c_Set_Oimage(X3131,X3130,X3129,X3127)))
| ~ c_Fun_Oinj__on(X3131,X3130,X3129,c_Orderings_Otop__class_Otop(tc_fun(X3131,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_612,plain,
! [X2534,X2535,X2536] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2536,tc_HOL_Obool)),X2535),X2534))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2536,tc_HOL_Obool),tc_fun(X2536,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2536,tc_HOL_Obool),tc_fun(X2536,tc_HOL_Obool)),X2535),X2534)),c_Wellfounded_Ofinite__psubset(X2536))) )
& ( c_Finite__Set_Ofinite(X2536,X2534)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2536,tc_HOL_Obool),tc_fun(X2536,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2536,tc_HOL_Obool),tc_fun(X2536,tc_HOL_Obool)),X2535),X2534)),c_Wellfounded_Ofinite__psubset(X2536))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2536,tc_HOL_Obool)),X2535),X2534))
| ~ c_Finite__Set_Ofinite(X2536,X2534)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2536,tc_HOL_Obool),tc_fun(X2536,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2536,tc_HOL_Obool),tc_fun(X2536,tc_HOL_Obool)),X2535),X2534)),c_Wellfounded_Ofinite__psubset(X2536))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).
fof(i_0_613,plain,
! [X3003,X3004,X3005,X3006,X3007,X3008] :
( hAPP(c_Hilbert__Choice_Oinv__into(X3008,X3007,X3006,X3005),X3004) != hAPP(c_Hilbert__Choice_Oinv__into(X3008,X3007,X3006,X3005),X3003)
| ~ hBOOL(hAPP(hAPP(c_member(X3007),X3004),c_Set_Oimage(X3008,X3007,X3005,X3006)))
| ~ hBOOL(hAPP(hAPP(c_member(X3007),X3003),c_Set_Oimage(X3008,X3007,X3005,X3006)))
| X3004 = X3003 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).
fof(i_0_614,plain,
! [X2893,X2894] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2894),c_Groups_Oone__class_Oone(X2894)),X2893)),X2893)),c_Groups_Ozero__class_Ozero(X2894)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2894),X2893),c_Groups_Ozero__class_Ozero(X2894)))
| ~ hBOOL(hAPP(hAPP(c_member(X2894),X2893),c_Int_Oring__1__class_OInts(X2894)))
| ~ class_Rings_Olinordered__idom(X2894) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2894),X2893),c_Groups_Ozero__class_Ozero(X2894)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2894),c_Groups_Oone__class_Oone(X2894)),X2893)),X2893)),c_Groups_Ozero__class_Ozero(X2894)))
| ~ hBOOL(hAPP(hAPP(c_member(X2894),X2893),c_Int_Oring__1__class_OInts(X2894)))
| ~ class_Rings_Olinordered__idom(X2894) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).
fof(i_0_615,plain,
! [X3147,X3148,X3149,X3150,X3152,X3153] :
( ( X3147 = hAPP(X3148,esk44_4(X3147,X3148,X3149,X3150))
| ~ hBOOL(hAPP(hAPP(c_member(X3149),X3147),c_Set_Oimage(X3150,X3149,X3148,c_Orderings_Otop__class_Otop(tc_fun(X3150,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X3150,X3149,X3148,c_Orderings_Otop__class_Otop(tc_fun(X3150,tc_HOL_Obool))) )
& ( X3147 != hAPP(X3148,X3152)
| X3152 = esk44_4(X3147,X3148,X3149,X3150)
| ~ hBOOL(hAPP(hAPP(c_member(X3149),X3147),c_Set_Oimage(X3150,X3149,X3148,c_Orderings_Otop__class_Otop(tc_fun(X3150,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X3150,X3149,X3148,c_Orderings_Otop__class_Otop(tc_fun(X3150,tc_HOL_Obool))) )
& ( X3147 = hAPP(X3148,esk45_5(X3147,X3148,X3149,X3150,X3153))
| X3147 != hAPP(X3148,X3153)
| hBOOL(hAPP(hAPP(c_member(X3149),X3147),c_Set_Oimage(X3150,X3149,X3148,c_Orderings_Otop__class_Otop(tc_fun(X3150,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X3150,X3149,X3148,c_Orderings_Otop__class_Otop(tc_fun(X3150,tc_HOL_Obool))) )
& ( esk45_5(X3147,X3148,X3149,X3150,X3153) != X3153
| X3147 != hAPP(X3148,X3153)
| hBOOL(hAPP(hAPP(c_member(X3149),X3147),c_Set_Oimage(X3150,X3149,X3148,c_Orderings_Otop__class_Otop(tc_fun(X3150,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X3150,X3149,X3148,c_Orderings_Otop__class_Otop(tc_fun(X3150,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_616,plain,
! [X3123,X3124,X3125,X3126] :
( ~ c_Finite__Set_Ofinite(X3126,X3125)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3124,c_Set_Oimage(X3126,X3124,X3123,X3125))),c_Finite__Set_Ocard(X3126,X3125))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_617,plain,
! [X3041,X3042,X3043,X3044,X3045] :
( ~ c_Fun_Oinj__on(X3045,X3044,X3043,X3042)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3045,tc_HOL_Obool)),X3041),X3042))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3044,tc_HOL_Obool)),c_Set_Oimage(X3045,X3044,X3043,X3041)),c_Set_Oimage(X3045,X3044,X3043,X3042))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_618,plain,
! [X3139,X3140,X3141] :
( ~ c_Finite__Set_Ofinite(X3141,X3140)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3141,tc_HOL_Obool),c_Set_Oimage(X3141,X3141,X3139,X3140)),X3140))
| ~ c_Fun_Oinj__on(X3141,X3141,X3139,X3140)
| c_Set_Oimage(X3141,X3141,X3139,X3140) = X3140 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_619,plain,
! [X1905,X1906,X1907,X1908,X1909] :
( ( hAPP(X1906,X1908) = hAPP(X1906,X1907)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1906,X1908)),hAPP(X1906,X1907)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1909,X1909)),hAPP(hAPP(c_Product__Type_OPair(X1909,X1909),X1908),X1907)),c_List_Omeasures(X1909,c_List_Olist_OCons(tc_fun(X1909,tc_Nat_Onat),X1906,X1905)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1909,X1909)),hAPP(hAPP(c_Product__Type_OPair(X1909,X1909),X1908),X1907)),c_List_Omeasures(X1909,X1905)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1906,X1908)),hAPP(X1906,X1907)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1909,X1909)),hAPP(hAPP(c_Product__Type_OPair(X1909,X1909),X1908),X1907)),c_List_Omeasures(X1909,c_List_Olist_OCons(tc_fun(X1909,tc_Nat_Onat),X1906,X1905)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1906,X1908)),hAPP(X1906,X1907)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1909,X1909)),hAPP(hAPP(c_Product__Type_OPair(X1909,X1909),X1908),X1907)),c_List_Omeasures(X1909,c_List_Olist_OCons(tc_fun(X1909,tc_Nat_Onat),X1906,X1905)))) )
& ( hAPP(X1906,X1908) != hAPP(X1906,X1907)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1909,X1909)),hAPP(hAPP(c_Product__Type_OPair(X1909,X1909),X1908),X1907)),c_List_Omeasures(X1909,X1905)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1909,X1909)),hAPP(hAPP(c_Product__Type_OPair(X1909,X1909),X1908),X1907)),c_List_Omeasures(X1909,c_List_Olist_OCons(tc_fun(X1909,tc_Nat_Onat),X1906,X1905)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).
fof(i_0_620,plain,
! [X3067,X3068,X3069,X3070,X3071,X3073,X3074,X3075,X3076,X3077,X3078] :
( ( hBOOL(hAPP(hAPP(c_member(X3069),esk42_4(X3067,X3068,X3069,X3070)),X3067))
| ~ hBOOL(hAPP(hAPP(c_member(X3071),X3070),c_Set_Oimage(X3069,X3071,X3068,X3067))) )
& ( X3070 = hAPP(X3068,esk42_4(X3067,X3068,X3069,X3070))
| ~ hBOOL(hAPP(hAPP(c_member(X3071),X3070),c_Set_Oimage(X3069,X3071,X3068,X3067))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3075),X3077),X3073))
| X3076 != hAPP(X3074,X3077)
| hBOOL(hAPP(hAPP(c_member(X3078),X3076),c_Set_Oimage(X3075,X3078,X3074,X3073))) ) ),
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_621,plain,
! [X1938,X1939,X1940,X1941,X1942] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1942,X1941)),hAPP(X1942,X1940)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1939,X1939)),hAPP(hAPP(c_Product__Type_OPair(X1939,X1939),X1941),X1940)),c_List_Omeasures(X1939,X1938)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1939,X1939)),hAPP(hAPP(c_Product__Type_OPair(X1939,X1939),X1941),X1940)),c_List_Omeasures(X1939,c_List_Olist_OCons(tc_fun(X1939,tc_Nat_Onat),X1942,X1938)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).
fof(i_0_622,plain,
! [X1869,X1870,X1871] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1870),X1869)),X1871))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1869),X1870)),X1871))
| X1870 = X1869
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1871),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),X1869),X1870)),X1871))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1870),X1869)),X1871))
| X1870 = X1869
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1871),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])])]) ).
fof(i_0_623,plain,
! [X1866,X1867,X1868] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1868),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),X1867),X1866)),X1868))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1866),X1867)),X1868)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])]) ).
fof(i_0_624,plain,
! [X2485,X2486,X2487,X2488,X2489] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2489,X2488)),X2487),c_FuncSet_OPi(X2489,X2488,X2486,hAPP(c_COMBK(tc_fun(X2488,tc_HOL_Obool),X2489),X2485))))
| ~ c_Fun_Oinj__on(X2489,X2488,X2487,X2486)
| ~ c_Finite__Set_Ofinite(X2488,X2485)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2489,X2486)),c_Finite__Set_Ocard(X2488,X2485))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj])]) ).
fof(i_0_625,plain,
! [X2246,X2247,X2248,X2249,X2250] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2250,tc_HOL_Obool),X2249),X2248))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2250,X2247),tc_HOL_Obool),c_FuncSet_OPi(X2250,X2247,X2248,X2246)),c_FuncSet_OPi(X2250,X2247,X2249,X2246))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_626,plain,
! [X3046,X3047,X3048,X3049,X3050] :
( ~ c_Finite__Set_Ofinite(X3050,c_Set_Oimage(X3049,X3050,X3048,c_Orderings_Otop__class_Otop(tc_fun(X3049,tc_HOL_Obool))))
| c_Finite__Set_Ofinite(X3047,c_Set_Oimage(X3049,X3047,hAPP(c_COMBB(X3050,X3047,X3049,X3046),X3048),c_Orderings_Otop__class_Otop(tc_fun(X3049,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).
fof(i_0_627,plain,
! [X1884] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1884),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),X1884)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_628,plain,
! [X2309,X2310,X2311,X2312,X2313,X2314] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2314,X2313)),X2312),c_FuncSet_OPi(X2314,X2313,X2311,hAPP(c_COMBK(tc_fun(X2313,tc_HOL_Obool),X2314),X2310))))
| ~ hBOOL(hAPP(hAPP(c_member(X2314),X2309),X2311))
| hBOOL(hAPP(hAPP(c_member(X2313),hAPP(X2312,X2309)),X2310)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_629,plain,
! [X3104,X3105,X3106,X3107,X3108] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3108,tc_HOL_Obool),X3107),X3106))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3105,tc_HOL_Obool),c_Set_Oimage(X3108,X3105,X3104,X3107)),c_Set_Oimage(X3108,X3105,X3104,X3106))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_630,plain,
! [X2197,X2198,X2199,X2200,X2201] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2201,X2200)),hAPP(X2201,X2199)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2198,X2198)),hAPP(hAPP(c_Product__Type_OPair(X2198,X2198),X2200),X2199)),X2197))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2198,X2198)),hAPP(hAPP(c_Product__Type_OPair(X2198,X2198),X2200),X2199)),c_Wellfounded_Omlex__prod(X2198,X2201,X2197))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_631,plain,
! [X1630,X1631,X1632,X1633,X1634] :
( ( ~ c_FunDef_Oin__rel(X1634,X1633,X1632,X1631,X1630)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1634,X1633)),hAPP(hAPP(c_Product__Type_OPair(X1634,X1633),X1631),X1630)),X1632)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1634,X1633)),hAPP(hAPP(c_Product__Type_OPair(X1634,X1633),X1631),X1630)),X1632))
| c_FunDef_Oin__rel(X1634,X1633,X1632,X1631,X1630) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_632,plain,
! [X3014,X3015,X3016,X3017,X3018] :
( ~ hBOOL(hAPP(hAPP(c_member(X3018),X3017),c_Set_Oimage(X3016,X3018,X3015,X3014)))
| hAPP(X3015,hAPP(c_Hilbert__Choice_Oinv__into(X3016,X3018,X3014,X3015),X3017)) = X3017 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).
fof(i_0_633,plain,
! [X3033,X3034,X3035,X3036,X3037,X3038,X3039] :
( ( c_Set_Oimage(X3035,X3034,X3033,c_Orderings_Otop__class_Otop(tc_fun(X3035,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3034,tc_HOL_Obool))
| hAPP(X3033,hAPP(c_Hilbert__Choice_Oinv__into(X3035,X3034,c_Orderings_Otop__class_Otop(tc_fun(X3035,tc_HOL_Obool)),X3033),X3036)) = X3036 )
& ( hAPP(X3037,hAPP(c_Hilbert__Choice_Oinv__into(X3039,X3038,c_Orderings_Otop__class_Otop(tc_fun(X3039,tc_HOL_Obool)),X3037),esk41_3(X3037,X3038,X3039))) != esk41_3(X3037,X3038,X3039)
| c_Set_Oimage(X3039,X3038,X3037,c_Orderings_Otop__class_Otop(tc_fun(X3039,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3038,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_634,plain,
! [X1646,X1647,X1648,X1649,X1650] :
( ( ~ c_Nitpick_Orefl_H(X1647,X1646)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1647,X1647)),hAPP(hAPP(c_Product__Type_OPair(X1647,X1647),X1648),X1648)),X1646)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1650,X1650)),hAPP(hAPP(c_Product__Type_OPair(X1650,X1650),esk2_2(X1649,X1650)),esk2_2(X1649,X1650))),X1649))
| c_Nitpick_Orefl_H(X1650,X1649) ) ),
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_635,plain,
! [X2938,X2939,X2940,X2941,X2942] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2942,tc_HOL_Obool),X2941),c_Set_Oimage(X2940,X2942,X2939,X2938)))
| c_Fun_Oinj__on(X2942,X2940,c_Hilbert__Choice_Oinv__into(X2940,X2942,X2938,X2939),X2941) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).
fof(i_0_636,plain,
! [X1618,X1619,X1620,X1621] :
( ( X1620 != X1618
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1619),X1618))) )
& ( X1621 != X1618
| X1621 != X1620
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1619),X1618))) )
& ( X1621 = X1618
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),X1619))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1619),X1618))) )
& ( X1621 != X1618
| X1621 = X1618
| X1620 = X1618
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1619),X1618))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),X1619))
| X1621 = X1618
| X1620 = X1618
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1619),X1618))) )
& ( X1621 != X1618
| X1621 = X1620
| X1620 = X1618
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1619),X1618))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),X1619))
| X1621 = X1620
| X1620 = X1618
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1621),X1620)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1619),X1618))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_637,plain,
! [X1622,X1623,X1624,X1625] :
( ( X1625 != X1622
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1623),X1622))) )
& ( X1624 != X1622
| X1625 != X1624
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1623),X1622))) )
& ( X1624 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),X1623))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1623),X1622))) )
& ( X1624 != X1622
| X1624 = X1622
| X1625 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1623),X1622))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),X1623))
| X1624 = X1622
| X1625 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1623),X1622))) )
& ( X1624 != X1622
| X1625 = X1624
| X1625 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1623),X1622))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),X1623))
| X1625 = X1624
| X1625 = X1622
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1625),X1624)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1623),X1622))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_638,plain,
! [X3192,X3193,X3194,X3195,X3196,X3197] : hAPP(c_COMBS(X3197,X3196,X3195,X3194,X3193),X3192) = hAPP(hAPP(X3194,X3192),hAPP(X3193,X3192)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_639,plain,
! [X2303,X2304,X2305,X2306,X2307,X2308] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2308,X2307)),X2306),c_FuncSet_OPi(X2308,X2307,X2305,X2304)))
| ~ hBOOL(hAPP(hAPP(c_member(X2308),X2303),X2305))
| hBOOL(hAPP(hAPP(c_member(X2307),hAPP(X2306,X2303)),hAPP(X2304,X2303))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_640,plain,
! [X2236,X2237,X2238,X2239,X2240,X2241] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2241,X2240)),X2239),c_FuncSet_OPi(X2241,X2240,X2238,X2237)))
| hBOOL(hAPP(hAPP(c_member(X2240),hAPP(X2239,X2236)),hAPP(X2237,X2236)))
| ~ hBOOL(hAPP(hAPP(c_member(X2241),X2236),X2238)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_526])]) ).
fof(i_0_641,plain,
! [X3142,X3143,X3144,X3145,X3146] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3145),hAPP(X3144,X3143)),c_Set_Oimage(X3146,X3145,X3144,X3142)))
| hBOOL(hAPP(hAPP(c_member(X3146),X3143),X3142))
| ~ c_Fun_Oinj__on(X3146,X3145,X3144,c_Orderings_Otop__class_Otop(tc_fun(X3146,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3146),X3143),X3142))
| hBOOL(hAPP(hAPP(c_member(X3145),hAPP(X3144,X3143)),c_Set_Oimage(X3146,X3145,X3144,X3142)))
| ~ c_Fun_Oinj__on(X3146,X3145,X3144,c_Orderings_Otop__class_Otop(tc_fun(X3146,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_642,plain,
! [X3025,X3026,X3027,X3028] :
( c_Set_Oimage(X3028,X3027,X3026,c_Orderings_Otop__class_Otop(tc_fun(X3028,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3027,tc_HOL_Obool))
| c_Set_Oimage(X3028,X3027,X3026,c_Set_Oimage(X3027,X3028,c_Hilbert__Choice_Oinv__into(X3028,X3027,c_Orderings_Otop__class_Otop(tc_fun(X3028,tc_HOL_Obool)),X3026),X3025)) = X3025 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).
fof(i_0_643,plain,
! [X3019,X3020,X3021,X3022,X3023,X3024] :
( c_Set_Oimage(X3024,X3023,X3022,X3021) != X3020
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3023,tc_HOL_Obool),X3019),X3020))
| c_Set_Oimage(X3024,X3023,X3022,c_Set_Oimage(X3023,X3024,c_Hilbert__Choice_Oinv__into(X3024,X3023,X3021,X3022),X3019)) = X3019 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).
fof(i_0_644,plain,
! [X1872,X1873,X1874,X1875,X1876,X1877,X1878,X1879,X1880,X1881] :
( ( ~ c_Fun_Oinj__on(X1875,X1874,X1873,X1872)
| ~ hBOOL(hAPP(hAPP(c_member(X1875),X1876),X1872))
| ~ hBOOL(hAPP(hAPP(c_member(X1875),X1877),X1872))
| hAPP(X1873,X1876) != hAPP(X1873,X1877)
| X1876 = X1877 )
& ( hBOOL(hAPP(hAPP(c_member(X1881),esk5_4(X1878,X1879,X1880,X1881)),X1878))
| c_Fun_Oinj__on(X1881,X1880,X1879,X1878) )
& ( hBOOL(hAPP(hAPP(c_member(X1881),esk6_4(X1878,X1879,X1880,X1881)),X1878))
| c_Fun_Oinj__on(X1881,X1880,X1879,X1878) )
& ( hAPP(X1879,esk5_4(X1878,X1879,X1880,X1881)) = hAPP(X1879,esk6_4(X1878,X1879,X1880,X1881))
| c_Fun_Oinj__on(X1881,X1880,X1879,X1878) )
& ( esk5_4(X1878,X1879,X1880,X1881) != esk6_4(X1878,X1879,X1880,X1881)
| c_Fun_Oinj__on(X1881,X1880,X1879,X1878) ) ),
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_645,plain,
! [X1863,X1864,X1865] :
( 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))
| 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,X1863),X1865),X1864)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_646,plain,
! [X3079,X3080,X3081,X3082,X3083] : c_Set_Oimage(X3083,X3082,hAPP(c_COMBB(X3081,X3082,X3083,X3080),X3079),c_Orderings_Otop__class_Otop(tc_fun(X3083,tc_HOL_Obool))) = c_Set_Oimage(X3081,X3082,X3080,c_Set_Oimage(X3083,X3081,X3079,c_Orderings_Otop__class_Otop(tc_fun(X3083,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_range__composition]) ).
fof(i_0_647,plain,
! [X1900,X1901,X1902,X1903,X1904] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1904,X1903)),hAPP(X1904,X1902)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1901,X1901)),hAPP(hAPP(c_Product__Type_OPair(X1901,X1901),X1903),X1902)),c_List_Omeasures(X1901,c_List_Olist_OCons(tc_fun(X1901,tc_Nat_Onat),X1904,X1900)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).
fof(i_0_648,plain,
! [X3136,X3137,X3138] :
( ~ c_Finite__Set_Ofinite(X3138,X3137)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3138,tc_HOL_Obool),X3137),c_Set_Oimage(X3138,X3138,X3136,X3137)))
| c_Fun_Oinj__on(X3138,X3138,X3136,X3137) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_649,plain,
! [X1910,X1911,X1912,X1913,X1914] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X1911,X1910)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1912),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X1911,X1912) = hAPP(X1912,X1910) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk7_2(X1913,X1914)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X1914,X1913) )
& ( hAPP(X1914,esk7_2(X1913,X1914)) != hAPP(esk7_2(X1913,X1914),X1913)
| c_Arrow__Order__Mirabelle_Odictator(X1914,X1913) ) ),
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_650,plain,
! [X1932,X1933,X1934] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1934,X1934)),hAPP(hAPP(c_Product__Type_OPair(X1934,X1934),X1933),X1932)),c_List_Omeasures(X1934,c_List_Olist_ONil(tc_fun(X1934,tc_Nat_Onat))))),
inference(variable_rename,[status(thm)],[i_0_527]) ).
fof(i_0_651,plain,
! [X1823,X1824,X1825,X1826] :
( ~ c_Fun_Oinj__on(X1826,X1825,X1824,c_Orderings_Otop__class_Otop(tc_fun(X1826,tc_HOL_Obool)))
| c_Fun_Oinj__on(X1826,tc_fun(X1823,X1825),hAPP(c_COMBB(X1825,tc_fun(X1823,X1825),X1826,c_COMBK(X1825,X1823)),X1824),c_Orderings_Otop__class_Otop(tc_fun(X1826,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).
fof(i_0_652,plain,
! [X2298,X2299] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2299,X2299)),c_COMBI(X2299)),c_FuncSet_OPi(X2299,X2299,X2298,hAPP(c_COMBK(tc_fun(X2299,tc_HOL_Obool),X2299),X2298)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_653,plain,
! [X3086,X3087,X3088,X3089,X3090,X3091] : c_Set_Oimage(X3091,X3090,X3089,c_Set_Oimage(X3088,X3091,X3087,X3086)) = c_Set_Oimage(X3088,X3090,hAPP(c_COMBB(X3091,X3090,X3088,X3089),X3087),X3086),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_654,plain,
! [X1897,X1898,X1899] :
( X1899 = X1898
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1897),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X1897,X1899,X1898)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_655,plain,
! [X1642,X1643,X1644,X1645] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1645,X1645)),hAPP(hAPP(c_Product__Type_OPair(X1645,X1645),X1644),X1643)),c_Wellfounded_Omeasure(X1645,X1642)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1642,X1644)),hAPP(X1642,X1643))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1642,X1644)),hAPP(X1642,X1643)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1645,X1645)),hAPP(hAPP(c_Product__Type_OPair(X1645,X1645),X1644),X1643)),c_Wellfounded_Omeasure(X1645,X1642))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_656,plain,
! [X2933,X2934,X2935,X2936,X2937] :
( ~ c_Fun_Oinj__on(X2937,X2936,X2935,X2934)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2937,tc_HOL_Obool),X2933),X2934))
| c_Set_Oimage(X2936,X2937,c_Hilbert__Choice_Oinv__into(X2937,X2936,X2934,X2935),c_Set_Oimage(X2937,X2936,X2935,X2933)) = X2933 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).
fof(i_0_657,plain,
! [X2969,X2970,X2971,X2972,X2973] :
( ~ c_Finite__Set_Ofinite(X2973,X2972)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2971,tc_HOL_Obool),X2970),c_Set_Oimage(X2973,X2971,X2969,X2972)))
| c_Finite__Set_Ofinite(X2971,X2970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
fof(i_0_658,plain,
! [X1859,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_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1860),X1859)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_659,plain,
! [X1861,X1862] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1862),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,X1862),X1861)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_660,plain,
! [X2950,X2951,X2952,X2953] :
( ~ c_Fun_Oinj__on(X2953,X2952,X2951,c_Orderings_Otop__class_Otop(tc_fun(X2953,tc_HOL_Obool)))
| c_Set_Oimage(X2952,X2953,c_Hilbert__Choice_Oinv__into(X2953,X2952,c_Orderings_Otop__class_Otop(tc_fun(X2953,tc_HOL_Obool)),X2951),c_Set_Oimage(X2953,X2952,X2951,X2950)) = X2950 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).
fof(i_0_661,plain,
! [X2946,X2947,X2948,X2949] :
( ~ c_Fun_Oinj__on(X2949,X2948,X2947,c_Orderings_Otop__class_Otop(tc_fun(X2949,tc_HOL_Obool)))
| c_Set_Oimage(X2948,X2949,c_Hilbert__Choice_Oinv__into(X2949,X2948,c_Orderings_Otop__class_Otop(tc_fun(X2949,tc_HOL_Obool)),X2947),c_Set_Oimage(X2949,X2948,X2947,X2946)) = X2946 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).
fof(i_0_662,plain,
! [X3029,X3030,X3031,X3032] :
( c_Set_Oimage(X3032,X3031,X3030,c_Orderings_Otop__class_Otop(tc_fun(X3032,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3031,tc_HOL_Obool))
| hAPP(X3030,hAPP(c_Hilbert__Choice_Oinv__into(X3032,X3031,c_Orderings_Otop__class_Otop(tc_fun(X3032,tc_HOL_Obool)),X3030),X3029)) = X3029 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).
fof(i_0_663,plain,
! [X1652,X1653,X1654,X1655,X1656] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1656,X1655)),hAPP(X1656,X1654)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1653,X1653)),hAPP(hAPP(c_Product__Type_OPair(X1653,X1653),X1655),X1654)),c_Wellfounded_Omlex__prod(X1653,X1656,X1652))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_664,plain,
! [X2943,X2944,X2945] :
( c_Set_Oimage(X2945,X2944,X2943,c_Orderings_Otop__class_Otop(tc_fun(X2945,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2944,tc_HOL_Obool))
| c_Fun_Oinj__on(X2944,X2945,c_Hilbert__Choice_Oinv__into(X2945,X2944,c_Orderings_Otop__class_Otop(tc_fun(X2945,tc_HOL_Obool)),X2943),c_Orderings_Otop__class_Otop(tc_fun(X2944,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).
fof(i_0_665,plain,
! [X3114,X3115,X3116,X3117] : hBOOL(hAPP(hAPP(c_member(X3117),hAPP(X3116,X3115)),c_Set_Oimage(X3114,X3117,X3116,c_Orderings_Otop__class_Otop(tc_fun(X3114,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_666,plain,
! [X2954,X2955,X2956] :
( ~ c_Fun_Oinj__on(X2956,X2955,X2954,c_Orderings_Otop__class_Otop(tc_fun(X2956,tc_HOL_Obool)))
| c_Set_Oimage(X2955,X2956,c_Hilbert__Choice_Oinv__into(X2956,X2955,c_Orderings_Otop__class_Otop(tc_fun(X2956,tc_HOL_Obool)),X2954),c_Orderings_Otop__class_Otop(tc_fun(X2955,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2956,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).
fof(i_0_667,plain,
! [X3062,X3063,X3064,X3065,X3066] :
( ~ hBOOL(hAPP(hAPP(c_member(X3066),X3065),X3064))
| hBOOL(hAPP(hAPP(c_member(X3063),hAPP(X3062,X3065)),c_Set_Oimage(X3066,X3063,X3062,X3064))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_668,plain,
! [X1947,X1948,X1949,X1950,X1951,X1952] : c_List_Olist_Olist__case(X1952,X1951,X1950,X1949,c_List_Olist_OCons(X1951,X1948,X1947)) = hAPP(hAPP(X1949,X1948),X1947),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).
fof(i_0_669,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_670,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_671,plain,
! [X3109,X3110,X3111,X3112,X3113] :
( X3113 != hAPP(X3112,X3111)
| hBOOL(hAPP(hAPP(c_member(X3110),X3113),c_Set_Oimage(X3109,X3110,X3112,c_Orderings_Otop__class_Otop(tc_fun(X3109,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_672,plain,
! [X2923,X2924,X2925,X2926,X2927,X2928] :
( X2928 != hAPP(X2927,X2926)
| ~ hBOOL(hAPP(hAPP(c_member(X2925),X2926),X2924))
| hBOOL(hAPP(hAPP(c_member(X2923),X2928),c_Set_Oimage(X2925,X2923,X2927,X2924))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_673,plain,
! [X3056,X3057,X3058,X3059,X3060,X3061] :
( ~ hBOOL(hAPP(hAPP(c_member(X3061),X3060),X3059))
| X3058 != hAPP(X3057,X3060)
| hBOOL(hAPP(hAPP(c_member(X3056),X3058),c_Set_Oimage(X3061,X3056,X3057,X3059))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_674,plain,
! [X2994,X2995,X2996,X2997,X2998] :
( ( c_Set_Oimage(X2998,X2997,X2996,X2995) != c_Set_Oimage(X2998,X2997,X2996,X2994)
| X2995 = X2994
| ~ c_Fun_Oinj__on(X2998,X2997,X2996,c_Orderings_Otop__class_Otop(tc_fun(X2998,tc_HOL_Obool))) )
& ( X2995 != X2994
| c_Set_Oimage(X2998,X2997,X2996,X2995) = c_Set_Oimage(X2998,X2997,X2996,X2994)
| ~ c_Fun_Oinj__on(X2998,X2997,X2996,c_Orderings_Otop__class_Otop(tc_fun(X2998,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_675,plain,
! [X2458,X2459,X2460,X2461] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2461),X2460),X2459)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2461),X2458),X2459)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2461),X2460),X2458))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2461) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2461),X2460),X2458))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2461),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2461),X2460),X2459)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2461),X2458),X2459)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2461) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_676,plain,
! [X2437,X2438,X2439,X2440] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2440)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2440),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2440),X2439),X2438)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2440),X2437),X2438)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2440),X2439),X2437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_677,plain,
! [X2454,X2455,X2456,X2457] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2457),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2457),X2456),X2455)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2457),X2456),X2454)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2457),X2455),X2454))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2457) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2457),X2455),X2454))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2457),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2457),X2456),X2455)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2457),X2456),X2454)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2457) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_678,plain,
! [X2433,X2434,X2435,X2436] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2436)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2436),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2436),X2435),X2434)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2436),X2435),X2433)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2436),X2434),X2433)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_679,plain,
! [X1943,X1944,X1945,X1946] : c_List_Olist_Olist__case(X1946,X1945,X1944,X1943,c_List_Olist_ONil(X1945)) = X1944,
inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).
fof(i_0_680,plain,
! [X2974,X2975,X2976,X2977] :
( ~ c_Finite__Set_Ofinite(X2977,c_Set_Oimage(X2976,X2977,X2975,X2974))
| ~ c_Fun_Oinj__on(X2976,X2977,X2975,X2974)
| c_Finite__Set_Ofinite(X2976,X2974) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_681,plain,
! [X1919,X1920,X1921,X1922] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1922,tc_HOL_Obool)),X1921),X1920))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1922,tc_HOL_Obool)),X1920),X1919))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1922,tc_HOL_Obool)),X1921),X1919)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_682,plain,
! [X2425,X2426,X2427,X2428] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2428)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2428),X2427),X2426)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2428),X2425),X2426)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2428,X2427),X2425)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_683,plain,
! [X2404,X2405,X2406,X2407] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2407,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2407),X2406),X2405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2407),X2404),X2405)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2407,X2406),X2404))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2407) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2407,X2406),X2404))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2407,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2407),X2406),X2405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2407),X2404),X2405)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2407) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_684,plain,
! [X2429,X2430,X2431,X2432] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2432)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2432,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2432),X2431),X2430)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2432),X2431),X2429)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2432,X2430),X2429)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_685,plain,
! [X2408,X2409,X2410,X2411] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2411,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2411),X2410),X2409)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2411),X2410),X2408)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2411,X2409),X2408))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2411) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2411,X2409),X2408))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2411,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2411),X2410),X2409)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2411),X2410),X2408)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2411) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_686,plain,
! [X2624,X2625,X2626,X2627] :
( ( hBOOL(hAPP(hAPP(c_member(X2627),X2626),X2624))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2627,tc_HOL_Obool),c_Set_Oinsert(X2627,X2626,X2625)),X2624)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2627,tc_HOL_Obool),X2625),X2624))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2627,tc_HOL_Obool),c_Set_Oinsert(X2627,X2626,X2625)),X2624)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2627),X2626),X2624))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2627,tc_HOL_Obool),X2625),X2624))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2627,tc_HOL_Obool),c_Set_Oinsert(X2627,X2626,X2625)),X2624)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_687,plain,
! [X1808,X1809,X1810,X1811] :
( ~ c_Fun_Oinj__on(X1811,X1810,X1809,c_Orderings_Otop__class_Otop(tc_fun(X1811,tc_HOL_Obool)))
| hAPP(c_Hilbert__Choice_Oinv__into(X1811,X1810,c_Orderings_Otop__class_Otop(tc_fun(X1811,tc_HOL_Obool)),X1809),hAPP(X1809,X1808)) = X1808 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).
fof(i_0_688,plain,
! [X1803,X1804,X1805,X1806,X1807] :
( ~ c_Fun_Oinj__on(X1807,X1806,X1805,c_Orderings_Otop__class_Otop(tc_fun(X1807,tc_HOL_Obool)))
| hAPP(X1805,X1804) != X1803
| hAPP(c_Hilbert__Choice_Oinv__into(X1807,X1806,c_Orderings_Otop__class_Otop(tc_fun(X1807,tc_HOL_Obool)),X1805),X1803) = X1804 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).
fof(i_0_689,plain,
! [X1800,X1801,X1802] :
( ( hAPP(hAPP(c_COMBC(X1802,tc_fun(X1802,tc_HOL_Obool),tc_HOL_Obool),c_member(X1802)),X1801) != hAPP(hAPP(c_COMBC(X1802,tc_fun(X1802,tc_HOL_Obool),tc_HOL_Obool),c_member(X1802)),X1800)
| X1801 = X1800 )
& ( X1801 != X1800
| hAPP(hAPP(c_COMBC(X1802,tc_fun(X1802,tc_HOL_Obool),tc_HOL_Obool),c_member(X1802)),X1801) = hAPP(hAPP(c_COMBC(X1802,tc_fun(X1802,tc_HOL_Obool),tc_HOL_Obool),c_member(X1802)),X1800) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_690,plain,
! [X2176,X2177,X2178] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2178),X2177)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2178),X2176)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2177),X2176)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2177),X2176))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2178),X2177)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2178),X2176))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_691,plain,
! [X1818,X1819,X1820,X1821,X1822] :
( ~ c_Fun_Oinj__on(X1822,X1821,X1820,X1819)
| ~ hBOOL(hAPP(hAPP(c_member(X1822),X1818),X1819))
| hAPP(c_Hilbert__Choice_Oinv__into(X1822,X1821,X1819,X1820),hAPP(X1820,X1818)) = X1818 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).
fof(i_0_692,plain,
! [X1812,X1813,X1814,X1815,X1816,X1817] :
( ~ c_Fun_Oinj__on(X1817,X1816,X1815,X1814)
| ~ hBOOL(hAPP(hAPP(c_member(X1817),X1813),X1814))
| hAPP(X1815,X1813) != X1812
| hAPP(c_Hilbert__Choice_Oinv__into(X1817,X1816,X1814,X1815),X1812) = X1813 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).
fof(i_0_693,plain,
! [X2961,X2962,X2963,X2964] :
( ~ 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) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_694,plain,
! [X2957,X2958,X2959,X2960] :
( ( ~ c_Fun_Oinj__on(X2960,X2958,X2957,X2959)
| c_Finite__Set_Ocard(X2958,c_Set_Oimage(X2960,X2958,X2957,X2959)) = c_Finite__Set_Ocard(X2960,X2959)
| ~ 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)
| ~ c_Finite__Set_Ofinite(X2960,X2959) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).
fof(i_0_695,plain,
! [X2564,X2565,X2566,X2567] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2567,tc_HOL_Obool),X2566),X2565))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2567,tc_HOL_Obool),c_Set_Oinsert(X2567,X2564,X2566)),c_Set_Oinsert(X2567,X2564,X2565))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(i_0_696,plain,
! [X3180,X3181,X3182,X3183,X3184,X3185] : hAPP(hAPP(c_COMBB(X3185,X3184,X3183,X3182),X3181),X3180) = hAPP(X3182,hAPP(X3181,X3180)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_697,plain,
! [X2441,X2442,X2443,X2444,X2445] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2445)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2445),X2444),X2443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2445),X2442),X2441))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2445),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2445),X2444),X2442)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2445),X2443),X2441))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_698,plain,
! [X2889,X2890,X2891,X2892] : c_List_Olist_Olist__size(X2892,X2891,c_List_Olist_OCons(X2892,X2890,X2889)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2891,X2890)),c_List_Olist_Olist__size(X2892,X2891,X2889))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_list_Osize_I2_J]) ).
fof(i_0_699,plain,
! [X2051,X2052,X2053] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2053),X2052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2053),X2051)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2052),X2051)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2052),X2051))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2053),X2052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2053),X2051))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_700,plain,
! [X2324,X2325,X2326,X2327,X2328] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2328)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2328,X2327),X2326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2328),X2325),X2324))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2328),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2328),X2327),X2325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2328),X2326),X2324))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_701,plain,
! [X2329,X2330,X2331,X2332,X2333] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2333)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2333),X2332),X2331))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2333,X2330),X2329))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2333),X2332),X2330)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2333),X2331),X2329))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_702,plain,
! [X2278,X2279,X2280,X2281] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2281,tc_HOL_Obool),X2280),X2279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2281,tc_HOL_Obool)),X2279),X2278))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2281,tc_HOL_Obool)),X2280),X2278)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_703,plain,
! [X2282,X2283,X2284,X2285] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2285,tc_HOL_Obool)),X2284),X2283))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2285,tc_HOL_Obool),X2283),X2282))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2285,tc_HOL_Obool)),X2284),X2282)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_704,plain,
! [X2921,X2922] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2922)),X2921))
| hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2922),X2921)) )
& ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2922),X2921))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2922)),X2921)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_705,plain,
! [X3118,X3119,X3120,X3121,X3122] :
( ~ hBOOL(hAPP(hAPP(c_member(X3122),X3121),X3120))
| c_Set_Oinsert(X3119,hAPP(X3118,X3121),c_Set_Oimage(X3122,X3119,X3118,X3120)) = c_Set_Oimage(X3122,X3119,X3118,X3120) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
fof(i_0_706,plain,
! [X2502,X2503,X2504] :
( ~ c_Finite__Set_Ofinite(X2504,X2503)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2504,tc_HOL_Obool),X2502),X2503))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2504,X2502)),c_Finite__Set_Ocard(X2504,X2503)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2504,tc_HOL_Obool)),X2502),X2503)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_707,plain,
! [X1714,X1715] :
( X1715 = X1714
| c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X1715,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X1714,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,esk4_2(X1714,X1715),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_third__alt])])]) ).
fof(i_0_708,plain,
! [X2420,X2421,X2422,X2423,X2424] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2424)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2424,X2423),X2422))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2424,X2421),X2420))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2424,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2424),X2423),X2421)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2424),X2422),X2420))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_709,plain,
! [X2698,X2699] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2699),X2698),X2698)),c_Groups_Ozero__class_Ozero(X2699)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2699),X2698),c_Groups_Ozero__class_Ozero(X2699)))
| ~ class_Groups_Olinordered__ab__group__add(X2699) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2699),X2698),c_Groups_Ozero__class_Ozero(X2699)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2699),X2698),X2698)),c_Groups_Ozero__class_Ozero(X2699)))
| ~ class_Groups_Olinordered__ab__group__add(X2699) ) ),
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_710,plain,
! [X2742,X2743] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2743),X2742),X2742)),c_Groups_Ozero__class_Ozero(X2743)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2743),X2742),c_Groups_Ozero__class_Ozero(X2743)))
| ~ class_Rings_Olinordered__idom(X2743) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2743),X2742),c_Groups_Ozero__class_Ozero(X2743)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2743),X2742),X2742)),c_Groups_Ozero__class_Ozero(X2743)))
| ~ class_Rings_Olinordered__idom(X2743) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_711,plain,
! [X2157,X2158,X2159,X2160] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2160),X2159))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2158),X2157))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2160),X2158)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2159),X2157))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_712,plain,
! [X3051,X3052,X3053,X3054,X3055] : c_Set_Oimage(X3055,X3054,X3053,c_Set_Oinsert(X3055,X3052,X3051)) = c_Set_Oinsert(X3054,hAPP(X3053,X3052),c_Set_Oimage(X3055,X3054,X3053,X3051)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
fof(i_0_713,plain,
! [X3132,X3133] :
( ~ c_Finite__Set_Ofinite(X3133,c_Orderings_Otop__class_Otop(tc_fun(X3133,tc_HOL_Obool)))
| c_Set_Oimage(X3133,X3133,X3132,c_Orderings_Otop__class_Otop(tc_fun(X3133,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3133,tc_HOL_Obool))
| c_Fun_Oinj__on(X3133,X3133,X3132,c_Orderings_Otop__class_Otop(tc_fun(X3133,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_714,plain,
! [X2269,X2270,X2271,X2272,X2273] :
( ~ c_Fun_Oinj__on(X2273,X2272,X2271,X2270)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2273,tc_HOL_Obool),X2269),X2270))
| c_Fun_Oinj__on(X2273,X2272,X2271,X2269) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_715,plain,
! [X2999,X3000,X3001,X3002] :
( ~ c_Fun_Oinj__on(X3002,X3001,X3000,X2999)
| c_Finite__Set_Ocard(X3001,c_Set_Oimage(X3002,X3001,X3000,X2999)) = c_Finite__Set_Ocard(X3002,X2999) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_716,plain,
! [X2707,X2708,X2709] :
( ~ class_Groups_Oordered__comm__monoid__add(X2709)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2709),X2708),c_Groups_Ozero__class_Ozero(X2709)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2709),X2707),c_Groups_Ozero__class_Ozero(X2709)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2709),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2709),X2708),X2707)),c_Groups_Ozero__class_Ozero(X2709))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_717,plain,
! [X2896,X2897,X2898] :
( ~ class_Rings_Oring__1(X2898)
| ~ hBOOL(hAPP(hAPP(c_member(X2898),X2897),c_Int_Oring__1__class_OInts(X2898)))
| ~ hBOOL(hAPP(hAPP(c_member(X2898),X2896),c_Int_Oring__1__class_OInts(X2898)))
| hBOOL(hAPP(hAPP(c_member(X2898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2898),X2897),X2896)),c_Int_Oring__1__class_OInts(X2898))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).
fof(i_0_718,plain,
! [X3134,X3135] :
( ~ c_Finite__Set_Ofinite(X3135,c_Orderings_Otop__class_Otop(tc_fun(X3135,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X3135,X3135,X3134,c_Orderings_Otop__class_Otop(tc_fun(X3135,tc_HOL_Obool)))
| c_Set_Oimage(X3135,X3135,X3134,c_Orderings_Otop__class_Otop(tc_fun(X3135,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3135,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_719,plain,
! [X2450,X2451,X2452,X2453] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2453)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2453),X2452),X2451))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2453),X2452),X2450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2453),X2451),X2450))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_720,plain,
! [X2446,X2447,X2448,X2449] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2449)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2449),X2448),X2447))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2449),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2449),X2446),X2448)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2449),X2446),X2447))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_721,plain,
! [X2677,X2678] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2678,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2678),X2677),X2677)),c_Groups_Ozero__class_Ozero(X2678)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2678,X2677),c_Groups_Ozero__class_Ozero(X2678)))
| ~ class_Groups_Olinordered__ab__group__add(X2678) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2678,X2677),c_Groups_Ozero__class_Ozero(X2678)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2678,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2678),X2677),X2677)),c_Groups_Ozero__class_Ozero(X2678)))
| ~ class_Groups_Olinordered__ab__group__add(X2678) ) ),
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_722,plain,
! [X2620,X2621,X2622,X2623] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2623,tc_HOL_Obool),X2621),c_Set_Oinsert(X2623,X2622,X2620)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2623,tc_HOL_Obool),X2621),X2620))
| hBOOL(hAPP(hAPP(c_member(X2623),X2622),X2621)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2623,tc_HOL_Obool),X2621),X2620))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2623,tc_HOL_Obool),X2621),c_Set_Oinsert(X2623,X2622,X2620)))
| hBOOL(hAPP(hAPP(c_member(X2623),X2622),X2621)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])]) ).
fof(i_0_723,plain,
! [X2735,X2736,X2737] :
( ~ class_Groups_Oordered__comm__monoid__add(X2737)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2737,X2736),c_Groups_Ozero__class_Ozero(X2737)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2737),X2735),c_Groups_Ozero__class_Ozero(X2737)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2737),X2736),X2735)),c_Groups_Ozero__class_Ozero(X2737))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_724,plain,
! [X2732,X2733,X2734] :
( ~ class_Groups_Oordered__comm__monoid__add(X2734)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2734),X2733),c_Groups_Ozero__class_Ozero(X2734)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2734,X2732),c_Groups_Ozero__class_Ozero(X2734)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2734),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2734),X2733),X2732)),c_Groups_Ozero__class_Ozero(X2734))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_725,plain,
! [X2025,X2026,X2027,X2028] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2028),X2027))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2026),X2025))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2028),X2026)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2027),X2025))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_726,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk8_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk8_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])])]) ).
fof(i_0_727,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk9_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk9_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])])]) ).
fof(i_0_728,plain,
! [X2604,X2605,X2606,X2607] :
( ( c_Finite__Set_Ofinite(X2607,X2605)
| ~ c_Finite__Set_Ofinite(tc_sum(X2607,X2606),c_Sum__Type_OPlus(X2607,X2606,X2605,X2604)) )
& ( c_Finite__Set_Ofinite(X2606,X2604)
| ~ c_Finite__Set_Ofinite(tc_sum(X2607,X2606),c_Sum__Type_OPlus(X2607,X2606,X2605,X2604)) )
& ( ~ c_Finite__Set_Ofinite(X2607,X2605)
| ~ c_Finite__Set_Ofinite(X2606,X2604)
| c_Finite__Set_Ofinite(tc_sum(X2607,X2606),c_Sum__Type_OPlus(X2607,X2606,X2605,X2604)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_729,plain,
! [X2612,X2613,X2614,X2615] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2615,X2614),c_Sum__Type_OPlus(X2615,X2614,X2613,X2612))
| c_Finite__Set_Ofinite(X2615,X2613) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_730,plain,
! [X2616,X2617,X2618,X2619] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2619,X2618),c_Sum__Type_OPlus(X2619,X2618,X2617,X2616))
| c_Finite__Set_Ofinite(X2618,X2616) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_731,plain,
! [X2412,X2413,X2414,X2415] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2415)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2415,X2414),X2413))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2415,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2415),X2414),X2412)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2415),X2413),X2412))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_732,plain,
! [X2416,X2417,X2418,X2419] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2419)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2419,X2418),X2417))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2419,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2419),X2416),X2418)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2419),X2416),X2417))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_733,plain,
! [X2150,X2151,X2152] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2152),X2151)),X2150))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2152),X2150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_734,plain,
! [X2693,X2694,X2695] :
( ~ class_Groups_Oordered__comm__monoid__add(X2695)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2695,X2694),c_Groups_Ozero__class_Ozero(X2695)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2695,X2693),c_Groups_Ozero__class_Ozero(X2695)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2695,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2695),X2694),X2693)),c_Groups_Ozero__class_Ozero(X2695))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_735,plain,
! [X2274,X2275,X2276,X2277] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2276,X2277),X2275),X2274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2276,X2277)),X2275),X2274))
| ~ class_Orderings_Oord(X2277) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2276,X2277),X2274),X2275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2276,X2277)),X2275),X2274))
| ~ class_Orderings_Oord(X2277) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2276,X2277),X2275),X2274))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2276,X2277),X2274),X2275))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2276,X2277)),X2275),X2274))
| ~ class_Orderings_Oord(X2277) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_531])])]) ).
fof(i_0_736,plain,
! [X2343,X2344,X2345,X2346,X2347,X2348] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2348,tc_fun(X2347,tc_HOL_Obool)),X2346),X2345))
| ~ hBOOL(hAPP(hAPP(X2346,X2344),X2343))
| hBOOL(hAPP(hAPP(X2345,X2344),X2343)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_737,plain,
! [X2337,X2338,X2339,X2340,X2341,X2342] :
( ~ hBOOL(hAPP(hAPP(X2342,X2341),X2340))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2339,tc_fun(X2338,tc_HOL_Obool)),X2342),X2337))
| hBOOL(hAPP(hAPP(X2337,X2341),X2340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_738,plain,
! [X2161,X2162,X2163] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2163),X2162))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2163),X2161)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2162),X2161))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_739,plain,
! [X1843,X1844,X1845,X1846,X1847,X1848] :
( ( hAPP(X1846,X1844) != hAPP(X1846,X1843)
| X1844 = X1843
| ~ hBOOL(hAPP(hAPP(c_member(X1848),X1843),X1845))
| ~ hBOOL(hAPP(hAPP(c_member(X1848),X1844),X1845))
| ~ c_Fun_Oinj__on(X1848,X1847,X1846,X1845) )
& ( X1844 != X1843
| hAPP(X1846,X1844) = hAPP(X1846,X1843)
| ~ hBOOL(hAPP(hAPP(c_member(X1848),X1843),X1845))
| ~ hBOOL(hAPP(hAPP(c_member(X1848),X1844),X1845))
| ~ c_Fun_Oinj__on(X1848,X1847,X1846,X1845) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_740,plain,
! [X1849,X1850,X1851,X1852,X1853,X1854] :
( ~ c_Fun_Oinj__on(X1854,X1853,X1852,X1851)
| hAPP(X1852,X1850) != hAPP(X1852,X1849)
| ~ hBOOL(hAPP(hAPP(c_member(X1854),X1850),X1851))
| ~ hBOOL(hAPP(hAPP(c_member(X1854),X1849),X1851))
| X1850 = X1849 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_741,plain,
! [X1837,X1838,X1839,X1840,X1841,X1842] :
( ~ c_Fun_Oinj__on(X1842,X1841,X1840,X1839)
| X1838 = X1837
| ~ hBOOL(hAPP(hAPP(c_member(X1842),X1838),X1839))
| ~ hBOOL(hAPP(hAPP(c_member(X1842),X1837),X1839))
| hAPP(X1840,X1838) != hAPP(X1840,X1837) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_742,plain,
! [X2016,X2017,X2018] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2018),X2016))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2018),X2017)),X2016)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2017),X2016))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2018),X2017)),X2016)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_532])])]) ).
fof(i_0_743,plain,
! [X2019,X2020,X2021] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2021),X2020)),X2019))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2021),X2019)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_744,plain,
! [X2022,X2023,X2024] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2024),X2023)),X2022))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2023),X2022)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_745,plain,
! [X2700,X2701,X2702] :
( ~ class_Groups_Oordered__comm__monoid__add(X2702)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2702),c_Groups_Ozero__class_Ozero(X2702)),X2701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2702),c_Groups_Ozero__class_Ozero(X2702)),X2700))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2702),c_Groups_Ozero__class_Ozero(X2702)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2702),X2701),X2700))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_746,plain,
c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_c____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_d____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,esk3_0,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_533])])]) ).
fof(i_0_747,plain,
! [X2986,X2987,X2988,X2990,X2991,X2992] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk39_2(X2986,X2987)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2988),X2987))
| ~ hBOOL(hAPP(X2986,X2988)) )
& ( hBOOL(hAPP(X2986,esk39_2(X2986,X2987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2988),X2987))
| ~ hBOOL(hAPP(X2986,X2988)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk40_2(X2990,X2991)),X2991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2992),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2991)))
| ~ hBOOL(hAPP(X2990,X2992)) )
& ( hBOOL(hAPP(X2990,esk40_2(X2990,X2991)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2992),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2991)))
| ~ hBOOL(hAPP(X2990,X2992)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq])])])])])]) ).
fof(i_0_748,plain,
! [X2034,X2035,X2036] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2036),X2035))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2036),X2034)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2035),X2034))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_749,plain,
! [X1855,X1856,X1857,X1858] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1858,tc_HOL_Obool)),X1857),X1856))
| ~ hBOOL(hAPP(hAPP(c_member(X1858),X1855),X1857))
| hBOOL(hAPP(hAPP(c_member(X1858),X1855),X1856)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_750,plain,
! [X2505,X2506,X2507] :
( ~ c_Finite__Set_Ofinite(X2507,X2506)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2507,tc_HOL_Obool)),X2505),X2506))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2507,X2505)),c_Finite__Set_Ocard(X2507,X2506))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_751,plain,
! [X2081,X2082] : 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)),X2082),X2081),
inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).
fof(i_0_752,plain,
! [X2847,X2848,X2849,X2850,X2851] :
( ~ class_Rings_Ocomm__semiring__1(X2851)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),X2850),X2849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),X2848),X2847)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),X2850),X2848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2851),X2849),X2847)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_753,plain,
! [X2978,X2979,X2981,X2982,X2983,X2985] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk37_2(X2978,X2979)),X2979))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2981),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2979)))
| hBOOL(hAPP(X2978,X2981)) )
& ( ~ hBOOL(hAPP(X2978,esk37_2(X2978,X2979)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2981),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2979)))
| hBOOL(hAPP(X2978,X2981)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk38_2(X2982,X2983)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2983)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2985),X2983))
| hBOOL(hAPP(X2982,X2985)) )
& ( ~ hBOOL(hAPP(X2982,esk38_2(X2982,X2983)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2985),X2983))
| hBOOL(hAPP(X2982,X2985)) ) ),
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_all__nat__less__eq])])])])])]) ).
fof(i_0_754,plain,
! [X2360,X2361,X2362,X2363] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2363,tc_HOL_Obool),X2362),X2361))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2363,tc_HOL_Obool),X2361),X2360))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2363,tc_HOL_Obool),X2362),X2360)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_755,plain,
! [X2721,X2722,X2723] :
( ~ class_Groups_Oordered__comm__monoid__add(X2723)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2723,c_Groups_Ozero__class_Ozero(X2723)),X2722))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2723),c_Groups_Ozero__class_Ozero(X2723)),X2721))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2723),c_Groups_Ozero__class_Ozero(X2723)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2723),X2722),X2721))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_756,plain,
! [X2718,X2719,X2720] :
( ~ class_Groups_Oordered__comm__monoid__add(X2720)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2720),c_Groups_Ozero__class_Ozero(X2720)),X2719))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2720,c_Groups_Ozero__class_Ozero(X2720)),X2718))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2720),c_Groups_Ozero__class_Ozero(X2720)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2720),X2719),X2718))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_757,plain,
! [X2181,X2182] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2182),X2181)),X2182)),
inference(variable_rename,[status(thm)],[i_0_534]) ).
fof(i_0_758,plain,
! [X2179,X2180] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2180),X2179)),X2179)),
inference(variable_rename,[status(thm)],[i_0_535]) ).
fof(i_0_759,plain,
! [X2633,X2634,X2635,X2636] :
( ( ~ c_Finite__Set_Ofinite(X2636,X2635)
| ~ c_Finite__Set_Ofinite(X2634,X2633)
| c_Finite__Set_Ocard(tc_sum(X2636,X2634),c_Sum__Type_OPlus(X2636,X2634,X2635,X2633)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2636,X2635)),c_Finite__Set_Ocard(X2634,X2633)) )
& ( c_Finite__Set_Ofinite(X2636,X2635)
| c_Finite__Set_Ocard(tc_sum(X2636,X2634),c_Sum__Type_OPlus(X2636,X2634,X2635,X2633)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X2634,X2633)
| c_Finite__Set_Ocard(tc_sum(X2636,X2634),c_Sum__Type_OPlus(X2636,X2634,X2635,X2633)) = 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_760,plain,
! [X2537,X2538,X2539,X2540] :
( ~ c_Finite__Set_Ofinite(X2540,X2539)
| ~ c_Finite__Set_Ofinite(X2538,X2537)
| c_Finite__Set_Ocard(tc_sum(X2540,X2538),c_Sum__Type_OPlus(X2540,X2538,X2539,X2537)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2540,X2539)),c_Finite__Set_Ocard(X2538,X2537)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_761,plain,
! [X2703,X2704,X2705,X2706] :
( ~ class_Rings_Olinordered__semidom(X2706)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2706),c_Groups_Ozero__class_Ozero(X2706)),X2705))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2706),X2704),X2703))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2706),X2704),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2706),X2705),X2703))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_762,plain,
! [X2628,X2629,X2630] :
( ~ c_Finite__Set_Ofinite(X2630,X2629)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2630,X2629)),c_Finite__Set_Ocard(X2630,c_Set_Oinsert(X2630,X2628,X2629)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).
fof(i_0_763,plain,
! [X2904,X2905] :
( ~ class_Int_Oring__char__0(X2905)
| ~ hBOOL(hAPP(hAPP(c_member(X2905),X2904),c_Int_Oring__1__class_OInts(X2905)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2905),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2905),c_Groups_Oone__class_Oone(X2905)),X2904)),X2904) != c_Groups_Ozero__class_Ozero(X2905) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).
fof(i_0_764,plain,
! [X2696,X2697] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2697),c_Groups_Ozero__class_Ozero(X2697)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2697),X2696),X2696)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2697),c_Groups_Ozero__class_Ozero(X2697)),X2696))
| ~ class_Groups_Olinordered__ab__group__add(X2697) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2697),c_Groups_Ozero__class_Ozero(X2697)),X2696))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2697),c_Groups_Ozero__class_Ozero(X2697)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2697),X2696),X2696)))
| ~ class_Groups_Olinordered__ab__group__add(X2697) ) ),
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_765,plain,
! [X2714,X2715] :
( ( ~ 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),X2715),X2714)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2715))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2714)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2715))
| 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),X2715),X2714))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2714))
| 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),X2715),X2714))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_766,plain,
! [X2508,X2509,X2510] :
( ~ c_Finite__Set_Ofinite(X2510,X2509)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2510,tc_HOL_Obool),X2508),X2509))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2510,X2509)),c_Finite__Set_Ocard(X2510,X2508)))
| X2508 = X2509 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_767,plain,
! [X2568,X2569,X2570,X2571] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2571,tc_HOL_Obool),X2570),X2569))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2571,tc_HOL_Obool),X2570),c_Set_Oinsert(X2571,X2568,X2569))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_768,plain,
! [X2728,X2729,X2730,X2731] :
( ~ class_Groups_Oordered__comm__monoid__add(X2731)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2731,c_Groups_Ozero__class_Ozero(X2731)),X2730))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2731),X2729),X2728))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2731),X2729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2731),X2730),X2728))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_769,plain,
! [X2724,X2725,X2726,X2727] :
( ~ class_Groups_Oordered__comm__monoid__add(X2727)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2727),c_Groups_Ozero__class_Ozero(X2727)),X2726))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2727,X2725),X2724))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2727),X2725),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2727),X2726),X2724))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_770,plain,
! [X2679,X2680,X2681] :
( ~ class_Groups_Oordered__comm__monoid__add(X2681)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2681,c_Groups_Ozero__class_Ozero(X2681)),X2680))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2681,c_Groups_Ozero__class_Ozero(X2681)),X2679))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2681,c_Groups_Ozero__class_Ozero(X2681)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2681),X2680),X2679))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_771,plain,
! [X1923,X1924,X1925,X1926,X1927] : c_List_Osplice(X1927,c_List_Olist_OCons(X1927,X1926,X1925),c_List_Olist_OCons(X1927,X1924,X1923)) = c_List_Olist_OCons(X1927,X1926,c_List_Olist_OCons(X1927,X1924,c_List_Osplice(X1927,X1925,X1923))),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).
fof(i_0_772,plain,
! [X2292,X2293,X2294] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2294,tc_HOL_Obool),X2293),X2292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2294,tc_HOL_Obool)),X2293),X2292)) )
& ( X2293 != X2292
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2294,tc_HOL_Obool)),X2293),X2292)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2294,tc_HOL_Obool),X2293),X2292))
| X2293 = X2292
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2294,tc_HOL_Obool)),X2293),X2292)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_773,plain,
! [X2289,X2290,X2291] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2291,tc_HOL_Obool),X2290),X2289))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2291,tc_HOL_Obool)),X2290),X2289))
| X2290 = X2289 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2291,tc_HOL_Obool)),X2290),X2289))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2291,tc_HOL_Obool),X2290),X2289)) )
& ( X2290 != X2289
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2291,tc_HOL_Obool),X2290),X2289)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_774,plain,
! [X2286,X2287,X2288] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2288,tc_HOL_Obool)),X2287),X2286))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2288,tc_HOL_Obool),X2287),X2286)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_775,plain,
! [X2597,X2598,X2599,X2600] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2600),X2599),c_Set_Oinsert(X2600,X2598,X2597)))
| X2599 = X2598
| hBOOL(hAPP(hAPP(c_member(X2600),X2599),X2597)) )
& ( X2599 != X2598
| hBOOL(hAPP(hAPP(c_member(X2600),X2599),c_Set_Oinsert(X2600,X2598,X2597))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2600),X2599),X2597))
| hBOOL(hAPP(hAPP(c_member(X2600),X2599),c_Set_Oinsert(X2600,X2598,X2597))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_776,plain,
! [X2554,X2555,X2556,X2557] :
( ~ hBOOL(hAPP(hAPP(c_member(X2557),X2556),c_Set_Oinsert(X2557,X2555,X2554)))
| X2556 = X2555
| hBOOL(hAPP(hAPP(c_member(X2557),X2556),X2554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
fof(i_0_777,plain,
! [X2675,X2676] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2676,c_Groups_Ozero__class_Ozero(X2676)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2676),X2675),X2675)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2676,c_Groups_Ozero__class_Ozero(X2676)),X2675))
| ~ class_Groups_Olinordered__ab__group__add(X2676) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2676,c_Groups_Ozero__class_Ozero(X2676)),X2675))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2676,c_Groups_Ozero__class_Ozero(X2676)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2676),X2675),X2675)))
| ~ class_Groups_Olinordered__ab__group__add(X2676) ) ),
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_778,plain,
! [X2300,X2301,X2302] : c_FuncSet_OPi(X2302,X2301,X2300,hAPP(c_COMBK(tc_fun(X2301,tc_HOL_Obool),X2302),c_Orderings_Otop__class_Otop(tc_fun(X2301,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2302,X2301),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pi__UNIV]) ).
fof(i_0_779,plain,
! [X2685,X2686,X2687,X2688] :
( ~ class_Groups_Oordered__comm__monoid__add(X2688)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2688,c_Groups_Ozero__class_Ozero(X2688)),X2687))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2688,X2686),X2685))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2688,X2686),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2688),X2687),X2685))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_780,plain,
! [X2689,X2690,X2691,X2692] :
( ~ class_Groups_Oordered__comm__monoid__add(X2692)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2692,c_Groups_Ozero__class_Ozero(X2692)),X2691))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2692,X2690),X2689))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2692,X2690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2692),X2689),X2691))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_781,plain,
! [X2608,X2609,X2610,X2611] :
( ~ c_Finite__Set_Ofinite(X2611,X2610)
| ~ c_Finite__Set_Ofinite(X2609,X2608)
| c_Finite__Set_Ofinite(tc_sum(X2611,X2609),c_Sum__Type_OPlus(X2611,X2609,X2610,X2608)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_782,plain,
! [X3186,X3187,X3188,X3189,X3190,X3191] : hAPP(hAPP(hAPP(c_COMBC(X3191,X3190,X3189),X3188),X3187),X3186) = hAPP(hAPP(X3188,X3186),X3187),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_783,plain,
! [X2370,X2371,X2372] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2370,tc_HOL_Obool),X2372),X2371))
| X2372 != X2371 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2370,tc_HOL_Obool),X2371),X2372))
| X2372 != X2371 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2370,tc_HOL_Obool),X2372),X2371))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2370,tc_HOL_Obool),X2371),X2372))
| X2372 = X2371 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_784,plain,
! [X2334,X2335,X2336] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2336,tc_HOL_Obool),X2335),X2334))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2336,tc_HOL_Obool),X2334),X2335))
| X2335 = X2334 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_785,plain,
! [X2259,X2260,X2261,X2262] :
( ~ hBOOL(hAPP(hAPP(c_member(X2262),X2261),X2260))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2262,tc_HOL_Obool),X2260),X2259))
| hBOOL(hAPP(hAPP(c_member(X2262),X2261),X2259)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_786,plain,
! [X2263,X2264,X2265,X2266] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2266,tc_HOL_Obool),X2265),X2264))
| ~ hBOOL(hAPP(hAPP(c_member(X2266),X2263),X2265))
| hBOOL(hAPP(hAPP(c_member(X2266),X2263),X2264)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_787,plain,
! [X2255,X2256,X2257,X2258] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2258,tc_HOL_Obool),X2257),X2256))
| ~ hBOOL(hAPP(hAPP(c_member(X2258),X2255),X2257))
| hBOOL(hAPP(hAPP(c_member(X2258),X2255),X2256)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_788,plain,
! [X2242,X2243,X2244,X2245] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2245,tc_HOL_Obool),X2244),X2243))
| ~ hBOOL(hAPP(hAPP(c_member(X2245),X2242),X2244))
| hBOOL(hAPP(hAPP(c_member(X2245),X2242),X2243)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_789,plain,
! [X1996,X1997,X1998,X1999,X2000] :
( ~ class_Orderings_Oord(X2000)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1999,X2000),X1998),X1997))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2000,hAPP(X1998,X1996)),hAPP(X1997,X1996))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_790,plain,
! [X1958,X1959,X1960,X1961,X1962] :
( ~ class_Orderings_Oord(X1962)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1961,X1962),X1960),X1959))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1962,hAPP(X1960,X1958)),hAPP(X1959,X1958))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_791,plain,
! [X2929,X2930,X2931,X2932] :
( ~ c_Finite__Set_Ofinite(X2932,X2931)
| c_Finite__Set_Ofinite(X2930,c_Set_Oimage(X2932,X2930,X2929,X2931)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
fof(i_0_792,plain,
! [X2511,X2512,X2513] :
( ~ c_Finite__Set_Ofinite(X2513,X2512)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2513,tc_HOL_Obool),X2511),X2512))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2513,X2511)),c_Finite__Set_Ocard(X2513,X2512))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_793,plain,
! [X2852,X2853,X2854,X2855] :
( ~ class_Rings_Ocomm__semiring__1(X2855)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2855),X2854),X2853)),X2852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2855),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2855),X2854),X2852)),X2853) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_794,plain,
! [X1832,X1833,X1834,X1835,X1836] :
( ( hAPP(X1834,X1833) != hAPP(X1834,X1832)
| X1833 = X1832
| ~ c_Fun_Oinj__on(X1836,X1835,X1834,c_Orderings_Otop__class_Otop(tc_fun(X1836,tc_HOL_Obool))) )
& ( X1833 != X1832
| hAPP(X1834,X1833) = hAPP(X1834,X1832)
| ~ c_Fun_Oinj__on(X1836,X1835,X1834,c_Orderings_Otop__class_Otop(tc_fun(X1836,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_795,plain,
! [X1827,X1828,X1829,X1830,X1831] :
( ~ c_Fun_Oinj__on(X1831,X1830,X1829,c_Orderings_Otop__class_Otop(tc_fun(X1831,tc_HOL_Obool)))
| hAPP(X1829,X1828) != hAPP(X1829,X1827)
| X1828 = X1827 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_796,plain,
! [X2906,X2907,X2909] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk36_2(X2906,X2907)),X2906))
| ~ hBOOL(hAPP(X2907,X2906))
| hBOOL(hAPP(X2907,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2909),esk36_2(X2906,X2907)))
| ~ hBOOL(hAPP(X2907,X2909))
| ~ hBOOL(hAPP(X2907,X2906))
| hBOOL(hAPP(X2907,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X2907,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk36_2(X2906,X2907)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X2907,X2906))
| hBOOL(hAPP(X2907,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_536])])])])]) ).
fof(i_0_797,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),X2823),X2822)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_798,plain,
! [X2824,X2825] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2825),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2824),X2825)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_799,plain,
! [X2589,X2590,X2591,X2592] :
( ~ hBOOL(hAPP(hAPP(c_member(X2592),X2591),X2590))
| hBOOL(hAPP(hAPP(c_member(X2592),X2591),c_Set_Oinsert(X2592,X2589,X2590))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_800,plain,
! [X2550,X2551,X2552,X2553] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2553),X2552),X2551))
| hBOOL(hAPP(hAPP(c_member(X2553),X2552),c_Set_Oinsert(X2553,X2550,X2551))) )
& ( X2552 != X2550
| hBOOL(hAPP(hAPP(c_member(X2553),X2552),c_Set_Oinsert(X2553,X2550,X2551))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_537])])]) ).
fof(i_0_801,plain,
! [X2772,X2773,X2774] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2774),X2773))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2773),X2772))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2774)),X2772)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_802,plain,
! [X2741] :
( ~ c_Finite__Set_Ofinite(X2741,c_Orderings_Otop__class_Otop(tc_fun(X2741,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(X2741,c_Orderings_Otop__class_Otop(tc_fun(X2741,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_803,plain,
! [X2779,X2780] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2780)),hAPP(c_Nat_OSuc,X2779)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2780),X2779)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_804,plain,
! [X2762,X2763] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2763)),hAPP(c_Nat_OSuc,X2762)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2763),X2762)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2763),X2762))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2763)),hAPP(c_Nat_OSuc,X2762))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_805,plain,
! [X2744,X2745] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2745,X2744),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2745,X2744),tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2744,c_Orderings_Otop__class_Otop(tc_fun(X2744,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Finite__Set_Ofinite(X2745,c_Orderings_Otop__class_Otop(tc_fun(X2745,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_806,plain,
! [X1775,X1776,X1777,X1778] :
( ~ class_Orderings_Opreorder(X1778)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1778),X1777),X1776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1778),X1776),X1775))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1778),X1777),X1775)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_807,plain,
! [X1779,X1780,X1781,X1782] :
( ~ class_Orderings_Oorder(X1782)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1782),X1781),X1780))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1782),X1779),X1781))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1782),X1779),X1780)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_808,plain,
! [X2682,X2683,X2684] :
( ( X2683 = c_Groups_Ozero__class_Ozero(X2684)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2684),X2683),X2682) != c_Groups_Ozero__class_Ozero(X2684)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2684,c_Groups_Ozero__class_Ozero(X2684)),X2682))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2684,c_Groups_Ozero__class_Ozero(X2684)),X2683))
| ~ class_Groups_Oordered__comm__monoid__add(X2684) )
& ( X2682 = c_Groups_Ozero__class_Ozero(X2684)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2684),X2683),X2682) != c_Groups_Ozero__class_Ozero(X2684)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2684,c_Groups_Ozero__class_Ozero(X2684)),X2682))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2684,c_Groups_Ozero__class_Ozero(X2684)),X2683))
| ~ class_Groups_Oordered__comm__monoid__add(X2684) )
& ( X2683 != c_Groups_Ozero__class_Ozero(X2684)
| X2682 != c_Groups_Ozero__class_Ozero(X2684)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2684),X2683),X2682) = c_Groups_Ozero__class_Ozero(X2684)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2684,c_Groups_Ozero__class_Ozero(X2684)),X2682))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2684,c_Groups_Ozero__class_Ozero(X2684)),X2683))
| ~ class_Groups_Oordered__comm__monoid__add(X2684) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_809,plain,
! [X2631,X2632] : c_Sum__Type_OPlus(X2632,X2631,c_Orderings_Otop__class_Otop(tc_fun(X2632,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2631,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2632,X2631),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_810,plain,
! [X2173,X2174,X2175] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2175),X2174))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2175),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2174),X2173))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_811,plain,
! [X2167,X2168,X2169] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2169),X2168))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2169),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2168),X2167))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_812,plain,
! [X2170,X2171,X2172] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2172),X2171))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2172),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2170),X2171))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_813,plain,
! [X2164,X2165,X2166] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2166),X2165))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2166),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2164),X2165))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_814,plain,
! [X2807,X2808,X2810,X2811,X2812] :
( ( X2808 = hAPP(c_Nat_OSuc,esk33_2(X2807,X2808))
| X2808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2808),hAPP(c_Nat_OSuc,X2807))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk33_2(X2807,X2808)),X2807))
| X2808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2808),hAPP(c_Nat_OSuc,X2807))) )
& ( 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))) )
& ( X2811 != hAPP(c_Nat_OSuc,X2812)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2812),X2810))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2811),hAPP(c_Nat_OSuc,X2810))) ) ),
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_815,plain,
! [X2856,X2857,X2858,X2859] :
( ~ class_Rings_Ocomm__semiring__1(X2859)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2859),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2859),X2858),X2857)),X2856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2859),X2858),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2859),X2857),X2856)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_816,plain,
! [X2378,X2379,X2380,X2381] :
( ~ class_Groups_Oab__semigroup__add(X2381)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2381),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2381),X2380),X2379)),X2378) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2381),X2380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2381),X2379),X2378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_817,plain,
! [X2860,X2861,X2862,X2863] :
( ~ class_Rings_Ocomm__semiring__1(X2863)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2863),X2862),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2863),X2861),X2860)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2863),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2863),X2862),X2861)),X2860) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_818,plain,
! [X2582,X2583,X2584,X2585] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2585,X2584,X2583),X2582))
| X2584 = X2582
| hBOOL(hAPP(X2583,X2582)) )
& ( X2584 != X2582
| hBOOL(hAPP(c_Set_Oinsert(X2585,X2584,X2583),X2582)) )
& ( ~ hBOOL(hAPP(X2583,X2582))
| hBOOL(hAPP(c_Set_Oinsert(X2585,X2584,X2583),X2582)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_819,plain,
! [X2738] :
( ~ class_Rings_Olinordered__semidom(X2738)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2738),c_Groups_Ozero__class_Ozero(X2738)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2738),c_Groups_Oone__class_Oone(X2738)),c_Groups_Oone__class_Oone(X2738)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_820,plain,
! [X2792,X2793] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2793)),hAPP(c_Nat_OSuc,X2792)))
| 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),X2792))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2793)),hAPP(c_Nat_OSuc,X2792))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_821,plain,
! [X2087,X2088,X2089,X2090] :
( ~ class_Orderings_Opreorder(X2090)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2090,X2089),X2088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2090),X2088),X2087))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2090),X2089),X2087)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_822,plain,
! [X2095,X2096,X2097,X2098] :
( ~ class_Orderings_Opreorder(X2098)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2098),X2097),X2096))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2098,X2096),X2095))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2098),X2097),X2095)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_823,plain,
! [X2083,X2084,X2085,X2086] :
( ~ class_Orderings_Oorder(X2086)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2086,X2085),X2084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2086),X2083),X2085))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2086),X2083),X2084)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_824,plain,
! [X2091,X2092,X2093,X2094] :
( ~ class_Orderings_Oorder(X2094)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2094),X2093),X2092))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2094,X2091),X2093))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2094),X2091),X2092)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_825,plain,
! [X2527,X2528] :
( ( c_Finite__Set_Ofinite(X2528,c_Orderings_Otop__class_Otop(tc_fun(X2528,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2528,X2527),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2528,X2527),tc_HOL_Obool))) )
& ( c_Finite__Set_Ofinite(X2527,c_Orderings_Otop__class_Otop(tc_fun(X2527,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2528,X2527),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2528,X2527),tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2528,c_Orderings_Otop__class_Otop(tc_fun(X2528,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2527,c_Orderings_Otop__class_Otop(tc_fun(X2527,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_sum(X2528,X2527),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2528,X2527),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_826,plain,
! [X2525,X2526] :
( ~ c_Finite__Set_Ofinite(X2526,c_Orderings_Otop__class_Otop(tc_fun(X2526,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2525,c_Orderings_Otop__class_Otop(tc_fun(X2525,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_prod(X2526,X2525),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2526,X2525),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_827,plain,
! [X2153,X2154,X2155,X2156] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2156),X2155))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2154),X2155) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2156),X2153)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2154),X2153)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_828,plain,
! [X2572,X2573,X2574] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2574,tc_HOL_Obool),X2573),c_Set_Oinsert(X2574,X2572,X2573))),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_829,plain,
! [X2593,X2594,X2595,X2596] :
( ( c_Set_Oinsert(X2596,X2595,X2594) != c_Set_Oinsert(X2596,X2595,X2593)
| X2594 = X2593
| hBOOL(hAPP(hAPP(c_member(X2596),X2595),X2593))
| hBOOL(hAPP(hAPP(c_member(X2596),X2595),X2594)) )
& ( X2594 != X2593
| c_Set_Oinsert(X2596,X2595,X2594) = c_Set_Oinsert(X2596,X2595,X2593)
| hBOOL(hAPP(hAPP(c_member(X2596),X2595),X2593))
| hBOOL(hAPP(hAPP(c_member(X2596),X2595),X2594)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])])]) ).
fof(i_0_830,plain,
! [X2777,X2778] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2778)),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__lessD])]) ).
fof(i_0_831,plain,
! [X2788,X2789] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),X2788))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2788)),X2789)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2788)),X2789))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2789),X2788)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])]) ).
fof(i_0_832,plain,
! [X2748,X2749] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2749),X2748))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2749)),hAPP(c_Nat_OSuc,X2748))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_833,plain,
! [X2046,X2047,X2048] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2048),X2047))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2048),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2047),X2046))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_834,plain,
! [X2040,X2041,X2042] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2042),X2041))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2041),X2040))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_835,plain,
! [X2043,X2044,X2045] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2045),X2044))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2043),X2044))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_836,plain,
! [X2037,X2038,X2039] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2039),X2038))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2039),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2037),X2038))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_837,plain,
! [X2532,X2533] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2533,X2532),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2533,X2532),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2532,c_Orderings_Otop__class_Otop(tc_fun(X2532,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_838,plain,
! [X2758,X2759] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),X2758))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2758),hAPP(c_Nat_OSuc,X2759))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2758),hAPP(c_Nat_OSuc,X2759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2759),X2758)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])]) ).
fof(i_0_839,plain,
! [X2060,X2061,X2062] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2062),X2061)),X2060) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2062),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2061),X2060)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_840,plain,
! [X2844,X2845] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2845)),X2844))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2845),X2844)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_841,plain,
! [X2836,X2837] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2837)),X2836))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2837),X2836)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2837),X2836))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2837)),X2836)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_842,plain,
! [X2832,X2833] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2833),X2832))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2833)),X2832)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2833)),X2832))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2833),X2832)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_843,plain,
! [X2349,X2350,X2351,X2352] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2352,tc_HOL_Obool),X2351),X2350))
| ~ hBOOL(hAPP(X2351,X2349))
| hBOOL(hAPP(X2350,X2349)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_844,plain,
! [X2353,X2354,X2355,X2356] :
( ~ hBOOL(hAPP(X2356,X2355))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2354,tc_HOL_Obool),X2356),X2353))
| hBOOL(hAPP(X2353,X2355)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_845,plain,
! [X1970,X1971,X1972,X1973] :
( ~ class_Orderings_Opreorder(X1973)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1973,X1972),X1971))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1973,X1971),X1970))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1973,X1972),X1970)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_846,plain,
! [X1963,X1964,X1965,X1966] :
( ~ class_Orderings_Oorder(X1966)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1966,X1965),X1964))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1966,X1963),X1965))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1966,X1963),X1964)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_847,plain,
! [X2770,X2771] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2771),X2770))
| hAPP(c_Nat_OSuc,X2771) = X2770
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2771)),X2770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_848,plain,
! [X1756,X1757,X1758] :
( ~ class_Orderings_Oorder(X1758)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1758),X1757),X1756))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1758),X1756),X1757)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])]) ).
fof(i_0_849,plain,
! [X1726,X1727,X1728] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1728),X1727),X1726))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1728),X1726),X1727))
| X1727 = X1726
| ~ class_Orderings_Olinorder(X1728) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1728),X1726),X1727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1728),X1727),X1726))
| ~ class_Orderings_Olinorder(X1728) )
& ( X1727 != X1726
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1728),X1727),X1726))
| ~ class_Orderings_Olinorder(X1728) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])])]) ).
fof(i_0_850,plain,
! [X1783,X1784,X1785] :
( ~ class_Orderings_Opreorder(X1785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1785),X1784),X1783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1785),X1783),X1784)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])]) ).
fof(i_0_851,plain,
! [X1753,X1754,X1755] :
( ~ class_Orderings_Opreorder(X1755)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1755),X1754),X1753))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1755),X1753),X1754)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])]) ).
fof(i_0_852,plain,
! [X1744,X1745,X1746] :
( ~ class_Orderings_Opreorder(X1746)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1746),X1745),X1744))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1746),X1744),X1745)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])]) ).
fof(i_0_853,plain,
! [X1741,X1742,X1743] :
( ~ class_Orderings_Opreorder(X1743)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1743),X1742),X1741))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1743),X1741),X1742)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])]) ).
fof(i_0_854,plain,
! [X2322,X2323] :
( ~ class_Rings_Olinordered__semidom(X2323)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2323),X2322),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2323),X2322),c_Groups_Oone__class_Oone(X2323)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_855,plain,
! [X2842,X2843] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2842),hAPP(c_Nat_OSuc,X2843)))
| X2842 = X2843
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2843),X2842)) )
& ( X2842 != X2843
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2842),hAPP(c_Nat_OSuc,X2843)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2843),X2842)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_856,plain,
! [X2798,X2799] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2799)),X2798))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2799),X2798)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_857,plain,
! [X2541,X2542,X2543] :
( ~ c_Finite__Set_Ofinite(X2543,X2542)
| hBOOL(hAPP(hAPP(c_member(X2543),X2541),X2542))
| c_Finite__Set_Ocard(X2543,c_Set_Oinsert(X2543,X2541,X2542)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X2543,X2542)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])]) ).
fof(i_0_858,plain,
! [X2135,X2136,X2137] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,X2136),X2135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2137),X2136),X2135))
| ~ class_Orderings_Opreorder(X2137) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,X2135),X2136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2137),X2136),X2135))
| ~ class_Orderings_Opreorder(X2137) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,X2136),X2135))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,X2135),X2136))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2137),X2136),X2135))
| ~ class_Orderings_Opreorder(X2137) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])])]) ).
fof(i_0_859,plain,
! [X2871,X2872,X2873] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2873),X2871),X2872))
| c_Finite__Set_Ocard(X2873,c_Set_Oinsert(X2873,X2871,X2872)) = c_Finite__Set_Ocard(X2873,X2872)
| ~ c_Finite__Set_Ofinite(X2873,X2872) )
& ( hBOOL(hAPP(hAPP(c_member(X2873),X2871),X2872))
| c_Finite__Set_Ocard(X2873,c_Set_Oinsert(X2873,X2871,X2872)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2873,X2872))
| ~ c_Finite__Set_Ofinite(X2873,X2872) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])])]) ).
fof(i_0_860,plain,
! [X2578,X2579,X2580,X2581] : c_Set_Oinsert(X2581,X2580,c_Set_Oinsert(X2581,X2579,X2578)) = c_Set_Oinsert(X2581,X2579,c_Set_Oinsert(X2581,X2580,X2578)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_861,plain,
! [X2601,X2602,X2603] : hBOOL(hAPP(hAPP(c_member(X2603),X2602),c_Set_Oinsert(X2603,X2602,X2601))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_862,plain,
! [X2775,X2776] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2776),hAPP(c_Nat_OSuc,X2775)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2776),X2775))
| X2776 = X2775 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).
fof(i_0_863,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)))
| X2766 = X2767 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])]) ).
fof(i_0_864,plain,
! [X2764,X2765] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2765),hAPP(c_Nat_OSuc,X2764)))
| X2765 = X2764
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2765),X2764)) )
& ( X2765 != X2764
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2765),hAPP(c_Nat_OSuc,X2764)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2765),X2764)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])])]) ).
fof(i_0_865,plain,
! [X2760,X2761] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2761),hAPP(c_Nat_OSuc,X2760)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2761),X2760))
| 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),X2761),hAPP(c_Nat_OSuc,X2760))) )
& ( X2761 != X2760
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2761),hAPP(c_Nat_OSuc,X2760))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_866,plain,
! [X2840,X2841] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2841),X2840))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2841)),X2840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_867,plain,
! [X2864,X2865,X2866,X2867] :
( ~ class_Rings_Ocomm__semiring__1(X2867)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2867),X2866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2867),X2865),X2864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2867),X2865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2867),X2866),X2864)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_868,plain,
! [X2031,X2032,X2033] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2033),X2032))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2032),X2031))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2033),X2031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_869,plain,
! [X2518,X2519,X2520] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2520,tc_HOL_Obool),X2519),X2518))
| ~ c_Finite__Set_Ofinite(X2520,X2518)
| c_Finite__Set_Ofinite(X2520,X2519) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_870,plain,
! [X2521,X2522,X2523] :
( ~ c_Finite__Set_Ofinite(X2523,X2522)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2523,tc_HOL_Obool),X2521),X2522))
| c_Finite__Set_Ofinite(X2523,X2521) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_871,plain,
! [X2108,X2109,X2110] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2110),X2109),X2108))
| X2109 = X2108
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2110,X2109),X2108))
| ~ class_Orderings_Olinorder(X2110) )
& ( X2109 != X2108
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2110),X2109),X2108))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2110,X2109),X2108))
| ~ class_Orderings_Olinorder(X2110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])])]) ).
fof(i_0_872,plain,
! [X2147,X2148,X2149] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2149),X2148),X2147))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2149,X2147),X2148))
| ~ class_Orderings_Olinorder(X2149) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2149,X2147),X2148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2149),X2148),X2147))
| ~ class_Orderings_Olinorder(X2149) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])])]) ).
fof(i_0_873,plain,
! [X2114,X2115,X2116] :
( ~ class_Orderings_Olinorder(X2116)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2116,X2115),X2114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2116),X2114),X2115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])]) ).
fof(i_0_874,plain,
! [X2144,X2145,X2146] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2146,X2145),X2144))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2146),X2144),X2145))
| ~ class_Orderings_Olinorder(X2146) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2146),X2144),X2145))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2146,X2145),X2144))
| ~ class_Orderings_Olinorder(X2146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).
fof(i_0_875,plain,
! [X2826,X2827,X2829,X2830,X2831] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2827),X2826))
| X2826 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2827),esk35_2(X2826,X2827))) )
& ( X2829 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2830),X2831))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2830),X2829)) ) ),
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_876,plain,
! [X2834,X2835] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2835),hAPP(c_Nat_OSuc,X2834)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2835),X2834)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2835),X2834))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2835),hAPP(c_Nat_OSuc,X2834))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_877,plain,
! [X2874,X2875,X2876] :
( ~ c_Finite__Set_Ofinite(X2876,X2875)
| hBOOL(hAPP(hAPP(c_member(X2876),X2874),X2875))
| c_Finite__Set_Ocard(X2876,c_Set_Oinsert(X2876,X2874,X2875)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2876,X2875)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])]) ).
fof(i_0_878,plain,
! [X2768,X2769] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2769),X2768))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2769),hAPP(c_Nat_OSuc,X2768))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_879,plain,
! [X2902,X2903] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2903),X2902),X2902) != c_Groups_Ozero__class_Ozero(X2903)
| X2902 = c_Groups_Ozero__class_Ozero(X2903)
| ~ hBOOL(hAPP(hAPP(c_member(X2903),X2902),c_Int_Oring__1__class_OInts(X2903)))
| ~ class_Int_Oring__char__0(X2903) )
& ( X2902 != c_Groups_Ozero__class_Ozero(X2903)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2903),X2902),X2902) = c_Groups_Ozero__class_Ozero(X2903)
| ~ hBOOL(hAPP(hAPP(c_member(X2903),X2902),c_Int_Oring__1__class_OInts(X2903)))
| ~ class_Int_Oring__char__0(X2903) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).
fof(i_0_880,plain,
! [X3155,X3156,X3157,X3158] : c_Nat_Onat_Onat__case(X3158,X3157,X3156,hAPP(c_Nat_OSuc,X3155)) = hAPP(X3156,X3155),
inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).
fof(i_0_881,plain,
! [X2796,X2797] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2797),hAPP(c_Nat_OSuc,X2796)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2797),X2796))
| X2797 = hAPP(c_Nat_OSuc,X2796) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).
fof(i_0_882,plain,
! [X2790,X2791] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2791),hAPP(c_Nat_OSuc,X2790)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2791),X2790))
| 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),hAPP(c_Nat_OSuc,X2790))) )
& ( X2791 != hAPP(c_Nat_OSuc,X2790)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2791),hAPP(c_Nat_OSuc,X2790))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_883,plain,
! [X2267,X2268] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2268,tc_HOL_Obool),X2267),c_Orderings_Otop__class_Otop(tc_fun(X2268,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_884,plain,
! [X1675,X1676,X1677] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1676),X1677))
| hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| X1677 = X1676
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1677),X1676)) )
& ( ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| X1677 = X1676
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1677),X1676)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1676),X1677))
| hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1677),X1676)) )
& ( ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1677),X1676)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1676),X1677))
| hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| X1677 = X1676
| ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677)) )
& ( ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| X1677 = X1676
| ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1676),X1677))
| hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677)) )
& ( ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677))
| ~ hBOOL(hAPP(hAPP(X1675,X1676),X1677)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_885,plain,
! [X2063,X2064,X2065] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2064),X2063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2064),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2065),X2063)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_886,plain,
! [X2004,X2005,X2006] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2006,X2005),X2004))
| X2005 != X2004
| ~ class_Orderings_Oorder(X2006) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2006,X2004),X2005))
| X2005 != X2004
| ~ class_Orderings_Oorder(X2006) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2006,X2005),X2004))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2006,X2004),X2005))
| X2005 = X2004
| ~ class_Orderings_Oorder(X2006) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_887,plain,
! [X1993,X1994,X1995] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1995,X1993),X1994))
| X1993 = X1994
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1995,X1994),X1993))
| ~ class_Orderings_Oorder(X1995) )
& ( X1993 != X1994
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1995,X1993),X1994))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1995,X1994),X1993))
| ~ class_Orderings_Oorder(X1995) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_888,plain,
! [X1974,X1975,X1976] :
( ~ class_Orderings_Oorder(X1976)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1976,X1975),X1974))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1976,X1974),X1975))
| X1975 = X1974 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_889,plain,
! [X1967,X1968,X1969] :
( ~ class_Orderings_Oorder(X1969)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1969,X1968),X1967))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1969,X1967),X1968))
| X1967 = X1968 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_890,plain,
! [X2739,X2740] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2740,X2739)))
| c_Finite__Set_Ofinite(X2740,X2739) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
fof(i_0_891,plain,
! [X2787] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2787)),X2787)),
inference(variable_rename,[status(thm)],[i_0_559]) ).
fof(i_0_892,plain,
! [X2838,X2839] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2839),X2838))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2839),hAPP(c_Nat_OSuc,X2838))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_893,plain,
! [X2530,X2531] :
( ~ c_Finite__Set_Ofinite(X2531,c_Orderings_Otop__class_Otop(tc_fun(X2531,tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2531,X2530) != c_Finite__Set_Ocard(X2531,c_Orderings_Otop__class_Otop(tc_fun(X2531,tc_HOL_Obool)))
| X2530 = c_Orderings_Otop__class_Otop(tc_fun(X2531,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_894,plain,
! [X2138,X2139,X2140] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2140,X2139),X2138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2140),X2139),X2138))
| ~ class_Orderings_Oorder(X2140) )
& ( X2139 != X2138
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2140),X2139),X2138))
| ~ class_Orderings_Oorder(X2140) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2140,X2139),X2138))
| X2139 = X2138
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2140),X2139),X2138))
| ~ class_Orderings_Oorder(X2140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_895,plain,
! [X2132,X2133,X2134] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2134,X2133),X2132))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2134),X2133),X2132))
| X2133 = X2132
| ~ class_Orderings_Oorder(X2134) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2134),X2133),X2132))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2134,X2133),X2132))
| ~ class_Orderings_Oorder(X2134) )
& ( X2133 != X2132
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2134,X2133),X2132))
| ~ class_Orderings_Oorder(X2134) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_896,plain,
! [X2111,X2112,X2113] :
( ~ class_Orderings_Opreorder(X2113)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2113),X2112),X2111))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2113,X2112),X2111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_897,plain,
! [X2076,X2077] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2077),X2076))),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_898,plain,
! [X2078,X2079] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2079),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2078),X2079))),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_899,plain,
! [X3084,X3085] : c_Set_Oimage(X3085,X3085,c_COMBI(X3085),X3084) = X3084,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_900,plain,
! [X1885,X1886] : c_Fun_Oinj__on(X1886,X1886,c_COMBI(X1886),X1885),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_901,plain,
! [X2120,X2121,X2122] :
( ~ class_Orderings_Oorder(X2122)
| X2121 = X2120
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2122,X2121),X2120))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2122),X2121),X2120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_902,plain,
! [X2105,X2106,X2107] :
( ~ class_Orderings_Oorder(X2107)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2107,X2106),X2105))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2107),X2106),X2105))
| X2106 = X2105 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_903,plain,
! [X2102,X2103,X2104] :
( ~ class_Orderings_Oorder(X2104)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2104,X2103),X2102))
| X2103 = X2102
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2104),X2103),X2102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_904,plain,
! [X2099,X2100,X2101] :
( ~ class_Orderings_Oorder(X2101)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2101,X2100),X2099))
| X2099 = X2100
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2101),X2100),X2099)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_905,plain,
! [X2123,X2124,X2125] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2124),X2123))
| X2124 = X2123
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2125),X2124),X2123))
| ~ class_Orderings_Olinorder(X2125) )
& ( X2124 != X2123
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2124),X2123))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2125),X2124),X2123))
| ~ class_Orderings_Olinorder(X2125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])])]) ).
fof(i_0_906,plain,
! [X2117,X2118,X2119] :
( ~ class_Orderings_Oorder(X2119)
| X2118 = X2117
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2119,X2117),X2118))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2119),X2117),X2118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_907,plain,
! [X2813] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2813),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X2813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2813 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2813),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_908,plain,
! [X2806] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2806),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_909,plain,
! [X2029,X2030] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2030),X2029))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2029),X2030))
| X2030 = X2029 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_910,plain,
! [X1718,X1719,X1720] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1720),X1719),hAPP(c_fequal,X1718)))
| X1719 = X1718 )
& ( X1719 != X1718
| hBOOL(hAPP(hAPP(c_member(X1720),X1719),hAPP(c_fequal,X1718))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_911,plain,
! [X2794,X2795] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2795),X2794))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2795),hAPP(c_Nat_OSuc,X2794))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_912,plain,
! [X2712] :
( ~ class_Rings_Olinordered__semidom(X2712)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2712),c_Groups_Oone__class_Oone(X2712)),c_Groups_Ozero__class_Ozero(X2712))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])]) ).
fof(i_0_913,plain,
! [X2195,X2196] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2196),X2195))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2196),X2195)) )
& ( X2196 != X2195
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2196),X2195)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2196),X2195))
| X2196 = X2195
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2196),X2195)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_914,plain,
! [X2193,X2194] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2194),X2193))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2194),X2193))
| X2194 = X2193 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2194),X2193))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2194),X2193)) )
& ( X2194 != X2193
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2194),X2193)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_915,plain,
! [X2191,X2192] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2192),X2191))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2192),X2191)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_916,plain,
! [X2189,X2190] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2190),X2189))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2190),X2189)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_917,plain,
! [X2185,X2186] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2186),X2185))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2186),X2185)) )
& ( X2186 != X2185
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2186),X2185)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_918,plain,
! [X2586,X2587,X2588] :
( ~ hBOOL(hAPP(hAPP(c_member(X2588),X2587),X2586))
| c_Set_Oinsert(X2588,X2587,X2586) = X2586 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_919,plain,
! [X1723,X1724,X1725] :
( ( X1724 = X1723
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1725),X1724),X1723))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1725),X1723),X1724))
| ~ class_Orderings_Olinorder(X1725) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1725),X1724),X1723))
| X1724 != X1723
| ~ class_Orderings_Olinorder(X1725) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1725),X1723),X1724))
| X1724 != X1723
| ~ class_Orderings_Olinorder(X1725) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_920,plain,
! [X2375,X2376,X2377] :
( ~ class_Rings_Olinordered__idom(X2377)
| X2376 = X2375
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2377),X2376),X2375))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2377),X2375),X2376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])]) ).
fof(i_0_921,plain,
! [X1786,X1787,X1788] :
( ~ class_Orderings_Olinorder(X1788)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1788),X1787),X1786))
| X1787 = X1786
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1788),X1786),X1787)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_922,plain,
! [X1735,X1736,X1737] :
( ~ class_Orderings_Olinorder(X1737)
| X1736 = X1735
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1737),X1736),X1735))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1737),X1735),X1736)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])]) ).
fof(i_0_923,plain,
! [X1732,X1733,X1734] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1734),X1732),X1733))
| X1732 = X1733
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1734),X1733),X1732))
| ~ class_Orderings_Olinorder(X1734) )
& ( X1732 != X1733
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1734),X1732),X1733))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1734),X1733),X1732))
| ~ class_Orderings_Olinorder(X1734) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])])]) ).
fof(i_0_924,plain,
! [X1729,X1730,X1731] :
( ~ class_Orderings_Olinorder(X1731)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1731),X1730),X1729))
| X1730 = X1729
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1731),X1729),X1730)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_925,plain,
! [X1916,X1917,X1918] : c_List_Osplice(X1918,c_List_Olist_OCons(X1918,X1917,X1916),c_List_Olist_ONil(X1918)) = c_List_Olist_OCons(X1918,X1917,X1916),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).
fof(i_0_926,plain,
! [X2529] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X2529),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2529),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2529,c_Orderings_Otop__class_Otop(tc_fun(X2529,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2529,c_Orderings_Otop__class_Otop(tc_fun(X2529,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X2529),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2529),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_927,plain,
! [X2187,X2188] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2188),X2187))
| X2188 = X2187
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2188),X2187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_928,plain,
! [X2575,X2576,X2577] : c_Set_Oinsert(X2577,X2576,c_Set_Oinsert(X2577,X2576,X2575)) = c_Set_Oinsert(X2577,X2576,X2575),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
fof(i_0_929,plain,
! [X1712,X1713] : hBOOL(hAPP(hAPP(c_member(X1713),X1712),c_Orderings_Otop__class_Otop(tc_fun(X1713,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_930,plain,
! [X1658,X1659] : hBOOL(hAPP(hAPP(c_member(X1659),X1658),c_Orderings_Otop__class_Otop(tc_fun(X1659,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_931,plain,
! [X2561,X2562,X2563] :
( ( ~ c_Finite__Set_Ofinite(X2563,c_Set_Oinsert(X2563,X2562,X2561))
| c_Finite__Set_Ofinite(X2563,X2561) )
& ( ~ c_Finite__Set_Ofinite(X2563,X2561)
| c_Finite__Set_Ofinite(X2563,c_Set_Oinsert(X2563,X2562,X2561)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).
fof(i_0_932,plain,
! [X1672,X1673,X1674] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1674),X1673),X1672))
| hBOOL(hAPP(X1672,X1673)) )
& ( ~ hBOOL(hAPP(X1672,X1673))
| hBOOL(hAPP(hAPP(c_member(X1674),X1673),X1672)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_933,plain,
! [X2141,X2142,X2143] :
( ~ class_Orderings_Olinorder(X2143)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2143,X2142),X2141))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2143),X2141),X2142)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_934,plain,
! [X2126,X2127,X2128] :
( ~ class_Orderings_Olinorder(X2128)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2128,X2127),X2126))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2128),X2126),X2127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])]) ).
fof(i_0_935,plain,
! [X2129,X2130,X2131] :
( ~ class_Orderings_Olinorder(X2131)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2131),X2130),X2129))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2131,X2129),X2130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_936,plain,
! [X2783,X2784] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2784)),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]) ).
fof(i_0_937,plain,
! [X2710] :
( ~ class_Rings_Olinordered__semidom(X2710)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2710,c_Groups_Oone__class_Oone(X2710)),c_Groups_Ozero__class_Ozero(X2710))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_938,plain,
! [X2070,X2071,X2073,X2074,X2075] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2071),X2070))
| X2070 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2071),esk11_2(X2070,X2071)) )
& ( X2073 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2074),X2075)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2074),X2073)) ) ),
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_939,plain,
! [X1685,X1686] :
( ( X1686 = X1685
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1686),X1685))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1685),X1686)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1686),X1685))
| X1686 != X1685 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1685),X1686))
| X1686 != X1685 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_940,plain,
! [X1683,X1684] :
( X1684 = X1683
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1684),X1683))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1683),X1684)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_941,plain,
! [X2814,X2816,X2817] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2814))
| X2814 = hAPP(c_Nat_OSuc,esk34_1(X2814)) )
& ( X2816 != hAPP(c_Nat_OSuc,X2817)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2816)) ) ),
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_942,plain,
! [X1750,X1751,X1752] :
( ~ class_Orderings_Oorder(X1752)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1752),X1751),X1750))
| X1750 != X1751 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_943,plain,
! [X1747,X1748,X1749] :
( ~ class_Orderings_Oorder(X1749)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1749),X1748),X1747))
| X1748 != X1747 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_944,plain,
! [X1738,X1739,X1740] :
( ~ class_Orderings_Oorder(X1740)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1740),X1739),X1738))
| X1739 != X1738 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_945,plain,
! [X2357,X2358,X2359] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2357,tc_HOL_Obool),X2359),X2358))
| X2359 != X2358 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2357,tc_HOL_Obool),X2358),X2359))
| X2359 != X2358 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])])]) ).
fof(i_0_946,plain,
! [X2367,X2368,X2369] :
( X2369 != X2368
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2367,tc_HOL_Obool),X2369),X2368)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_947,plain,
! [X2364,X2365,X2366] :
( X2366 != X2365
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2364,tc_HOL_Obool),X2365),X2366)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_948,plain,
! [X1721,X1722] :
( ~ class_Orderings_Opreorder(X1722)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1722),X1721),X1721)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])]) ).
fof(i_0_949,plain,
! [X2373,X2374] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2374,tc_HOL_Obool),X2373),X2373)),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_950,plain,
! [X2656] :
( ( X2656 = 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)),X2656)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2656))
| X2656 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_951,plain,
! [X2398,X2399,X2400,X2401] :
( ~ class_Groups_Ocancel__semigroup__add(X2401)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2401),X2400),X2399) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2401),X2398),X2399)
| X2400 = X2398 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_952,plain,
! [X2386,X2387,X2388,X2389] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2389),X2388),X2387) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2389),X2386),X2387)
| X2388 = X2386
| ~ class_Groups_Ocancel__semigroup__add(X2389) )
& ( X2388 != X2386
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2389),X2388),X2387) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2389),X2386),X2387)
| ~ class_Groups_Ocancel__semigroup__add(X2389) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_953,plain,
! [X2394,X2395,X2396,X2397] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X2397)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2397),X2396),X2395) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2397),X2396),X2394)
| X2395 = X2394 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_954,plain,
! [X2390,X2391,X2392,X2393] :
( ~ class_Groups_Ocancel__semigroup__add(X2393)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2393),X2392),X2391) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2393),X2392),X2390)
| X2391 = X2390 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_955,plain,
! [X2382,X2383,X2384,X2385] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2385),X2384),X2383) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2385),X2384),X2382)
| X2383 = X2382
| ~ class_Groups_Ocancel__semigroup__add(X2385) )
& ( X2383 != X2382
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2385),X2384),X2383) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2385),X2384),X2382)
| ~ class_Groups_Ocancel__semigroup__add(X2385) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_956,plain,
! [X1789,X1790,X1791,X1792,X1793] :
( ( X1792 = X1790
| c_List_Olist_OCons(X1793,X1792,X1791) != c_List_Olist_OCons(X1793,X1790,X1789) )
& ( X1791 = X1789
| c_List_Olist_OCons(X1793,X1792,X1791) != c_List_Olist_OCons(X1793,X1790,X1789) )
& ( X1792 != X1790
| X1791 != X1789
| c_List_Olist_OCons(X1793,X1792,X1791) = c_List_Olist_OCons(X1793,X1790,X1789) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).
fof(i_0_957,plain,
! [X2007,X2008,X2009] :
( ~ class_Orderings_Olinorder(X2009)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2009,X2008),X2007))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2009,X2007),X2008)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_958,plain,
! [X1955,X1956,X1957] :
( ~ class_Orderings_Olinorder(X1957)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1957,X1956),X1955))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1957,X1955),X1956)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).
fof(i_0_959,plain,
! [X2781,X2782] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2782),hAPP(c_Nat_OSuc,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__right]) ).
fof(i_0_960,plain,
! [X2785,X2786] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2786)),X2785) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2786),hAPP(c_Nat_OSuc,X2785)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_961,plain,
! [X2657] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2657),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_573]) ).
fof(i_0_962,plain,
! [X2655] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2655),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_574]) ).
fof(i_0_963,plain,
! [X2645] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2645),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_575]) ).
fof(i_0_964,plain,
! [X2887] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2887)),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_965,plain,
! [X2658,X2659] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2659),X2658))
| X2658 != 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_966,plain,
! [X2066,X2067] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2067),X2066))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2066),X2067)) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_967,plain,
! [X2751] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2751))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_968,plain,
! [X1680,X1681] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1681),X1680))
| X1680 != X1681 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_969,plain,
! [X1678,X1679] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1679),X1678))
| X1679 != X1678 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_970,plain,
! [X2713] :
( ~ class_Rings_Olinordered__semidom(X2713)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2713),c_Groups_Ozero__class_Ozero(X2713)),c_Groups_Oone__class_Oone(X2713))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_971,plain,
! [X2895] :
( ~ class_Rings_Oring__1(X2895)
| hBOOL(hAPP(hAPP(c_member(X2895),c_Groups_Ozero__class_Ozero(X2895)),c_Int_Oring__1__class_OInts(X2895))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).
fof(i_0_972,plain,
! [X2899] :
( ~ class_Rings_Oring__1(X2899)
| hBOOL(hAPP(hAPP(c_member(X2899),c_Groups_Oone__class_Oone(X2899)),c_Int_Oring__1__class_OInts(X2899))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).
fof(i_0_973,plain,
! [X1682] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1682),X1682)),
inference(variable_rename,[status(thm)],[i_0_576]) ).
fof(i_0_974,plain,
! [X1657] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1657),X1657)),
inference(variable_rename,[status(thm)],[i_0_577]) ).
fof(i_0_975,plain,
! [X2054,X2055,X2056] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2056),X2055) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2054),X2055)
| X2056 = X2054 )
& ( X2056 != X2054
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2056),X2055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2054),X2055) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_976,plain,
! [X2057,X2058,X2059] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2059),X2058) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2059),X2057)
| X2058 = X2057 )
& ( X2058 != X2057
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2059),X2058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2059),X2057) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_977,plain,
! [X2558,X2559,X2560] :
( ~ c_Finite__Set_Ofinite(X2560,X2559)
| c_Finite__Set_Ofinite(X2560,c_Set_Oinsert(X2560,X2558,X2559)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).
fof(i_0_978,plain,
! [X2750] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2750),hAPP(c_Nat_OSuc,X2750))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_979,plain,
! [X1696,X1697] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1697,tc_HOL_Obool)),X1696)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_980,plain,
! [X2648] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2648),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X2648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2648 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2648),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_981,plain,
! [X2820,X2821] :
( ( X2821 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2821 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2821),X2820) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2820 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2821 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2821),X2820) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2821 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2821),X2820) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2820 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2821),X2820) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2821 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2820 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2821),X2820) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2821 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2820 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2821),X2820) = 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_982,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(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2818) )
& ( 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(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2818) )
& ( X2819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2818 = 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),X2819),X2818) )
& ( X2818 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2818 = 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),X2819),X2818) )
& ( X2819 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2818 != 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),X2819),X2818) )
& ( X2819 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2818 != 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),X2819),X2818) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_983,plain,
! [X1615,X1616] :
( hAPP(X1616,esk1_2(X1615,X1616)) != hAPP(X1615,esk1_2(X1615,X1616))
| X1616 = X1615 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_984,plain,
! [X2711] :
( ~ class_Rings_Olinordered__semidom(X2711)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2711,c_Groups_Ozero__class_Ozero(X2711)),c_Groups_Oone__class_Oone(X2711))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_985,plain,
! [X3198,X3199] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X3199),X3198))
| X3199 = X3198 ),
inference(variable_rename,[status(thm)],[i_0_578]) ).
fof(i_0_986,plain,
! [X2886] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X2886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X2886)),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_987,plain,
! [X2868,X2869,X2870] :
( ~ class_Rings_Ocomm__semiring__1(X2870)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2870),X2869),X2868) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2870),X2868),X2869) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_988,plain,
! [X2660] :
( X2660 = 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)),X2660)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_989,plain,
! [X2183,X2184] :
( ~ class_Orderings_Otop(X2184)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2184,X2183),c_Orderings_Otop__class_Otop(X2184))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_990,plain,
! [X2877,X2878] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2878),X2877),X2877) != c_Groups_Ozero__class_Ozero(X2878)
| X2877 = c_Groups_Ozero__class_Ozero(X2878)
| ~ class_Groups_Olinordered__ab__group__add(X2878) )
& ( X2877 != c_Groups_Ozero__class_Ozero(X2878)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2878),X2877),X2877) = c_Groups_Ozero__class_Ozero(X2878)
| ~ class_Groups_Olinordered__ab__group__add(X2878) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_991,plain,
! [X2667,X2668] :
( ( c_Groups_Ozero__class_Ozero(X2668) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2668),X2667),X2667)
| X2667 = c_Groups_Ozero__class_Ozero(X2668)
| ~ class_Groups_Olinordered__ab__group__add(X2668) )
& ( X2667 != c_Groups_Ozero__class_Ozero(X2668)
| c_Groups_Ozero__class_Ozero(X2668) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2668),X2667),X2667)
| ~ class_Groups_Olinordered__ab__group__add(X2668) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_992,plain,
! [X2879,X2880,X2881] :
( ( X2880 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2881),X2880),X2879)
| X2879 = c_Groups_Ozero__class_Ozero(X2881)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2881) )
& ( X2879 != c_Groups_Ozero__class_Ozero(X2881)
| X2880 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2881),X2880),X2879)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2881) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_993,plain,
! [X2001,X2002,X2003] :
( ~ class_Orderings_Opreorder(X2003)
| X2002 != X2001
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2003,X2002),X2001)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_994,plain,
! [X3176,X3177,X3178,X3179] : hAPP(hAPP(c_COMBK(X3179,X3178),X3177),X3176) = X3177,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_995,plain,
! [X1706,X1707,X1708] : c_List_Olist_OCons(X1708,X1707,X1706) != c_List_Olist_ONil(X1708),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).
fof(i_0_996,plain,
! [X1703,X1704,X1705] : c_List_Olist_ONil(X1705) != c_List_Olist_OCons(X1705,X1704,X1703),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
fof(i_0_997,plain,
! [X2068,X2069] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2069),X2068) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2068),X2069),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_998,plain,
! [X1953,X1954] :
( ~ class_Orderings_Opreorder(X1954)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1954,X1953),X1953)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_999,plain,
! [X2647] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2647)),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_1000,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_le0]) ).
fof(i_0_1001,plain,
! [X1794,X1795,X1796] : c_List_Olist_OCons(X1796,X1795,X1794) != X1794,
inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).
fof(i_0_1002,plain,
! [X1797,X1798,X1799] : X1799 != c_List_Olist_OCons(X1798,X1797,X1799),
inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).
fof(i_0_1003,plain,
! [X1709,X1710,X1711] :
( ~ class_Orderings_Otop(X1711)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1710,X1711)),X1709) = c_Orderings_Otop__class_Otop(X1711) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_1004,plain,
! [X2651,X2652] :
( ( X2652 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2652),X2651) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2652),X2651) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2652 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2651 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2652),X2651) = 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_1005,plain,
! [X2049,X2050] :
( X2050 != X2049
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2050),X2049)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1006,plain,
! [X3200,X3201] :
( X3201 != X3200
| hBOOL(hAPP(hAPP(c_fequal,X3201),X3200)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1007,plain,
! [X2653,X2654] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2654),X2653) != X2654
| X2653 = 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_1008,plain,
! [X2080] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2080),X2080)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1009,plain,
! [X2524] :
( ~ class_Finite__Set_Ofinite(X2524)
| c_Finite__Set_Ofinite(X2524,c_Orderings_Otop__class_Otop(tc_fun(X2524,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_1010,plain,
! [X2746,X2747] :
( ~ class_Rings_Ocomm__semiring__1(X2747)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2747),c_Groups_Ozero__class_Ozero(X2747)),X2746) = X2746 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_1011,plain,
! [X2665,X2666] :
( ~ class_Groups_Ocomm__monoid__add(X2666)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2666),c_Groups_Ozero__class_Ozero(X2666)),X2665) = X2665 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_1012,plain,
! [X2663,X2664] :
( ~ class_Groups_Omonoid__add(X2664)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2664),c_Groups_Ozero__class_Ozero(X2664)),X2663) = X2663 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_1013,plain,
! [X2882,X2883] :
( ~ class_Rings_Ocomm__semiring__1(X2883)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2883),X2882),c_Groups_Ozero__class_Ozero(X2883)) = X2882 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_1014,plain,
! [X2671,X2672] :
( ~ class_Groups_Ocomm__monoid__add(X2672)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2672),X2671),c_Groups_Ozero__class_Ozero(X2672)) = X2671 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_1015,plain,
! [X2669,X2670] :
( ~ class_Groups_Omonoid__add(X2670)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2670),X2669),c_Groups_Ozero__class_Ozero(X2670)) = X2669 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_1016,plain,
! [X2884] : hAPP(c_Nat_OSuc,X2884) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2884),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1017,plain,
! [X2900,X2901] : c_List_Olist_Olist__size(X2901,X2900,c_List_Olist_ONil(X2901)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J]) ).
fof(i_0_1018,plain,
! [X2885] : hAPP(c_Nat_OSuc,X2885) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2885),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1019,plain,
! [X1930,X1931] : c_List_Osplice(X1931,c_List_Olist_ONil(X1931),X1930) = X1930,
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).
fof(i_0_1020,plain,
! [X1928,X1929] : c_List_Osplice(X1929,X1928,c_List_Olist_ONil(X1929)) = X1928,
inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).
fof(i_0_1021,plain,
! [X2649] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2649) = X2649,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_1022,plain,
! [X2846] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2846) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2846)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(i_0_1023,plain,
! [X2650] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2650),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2650,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_1024,plain,
! [X3169,X3170] :
( ~ class_Finite__Set_Ofinite(X3170)
| ~ class_Finite__Set_Ofinite(X3169)
| class_Finite__Set_Ofinite(tc_sum(X3170,X3169)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_1025,plain,
! [X3161,X3162] :
( ~ class_Finite__Set_Ofinite(X3162)
| ~ class_Finite__Set_Ofinite(X3161)
| class_Finite__Set_Ofinite(tc_fun(X3162,X3161)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_1026,plain,
! [X3172,X3173] :
( ~ class_Finite__Set_Ofinite(X3173)
| ~ class_Finite__Set_Ofinite(X3172)
| class_Finite__Set_Ofinite(tc_prod(X3173,X3172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_1027,plain,
! [X2804,X2805] :
( hAPP(c_Nat_OSuc,X2805) != hAPP(c_Nat_OSuc,X2804)
| X2805 = X2804 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1028,plain,
! [X2802,X2803] :
( ( hAPP(c_Nat_OSuc,X2803) != hAPP(c_Nat_OSuc,X2802)
| X2803 = X2802 )
& ( X2803 != X2802
| hAPP(c_Nat_OSuc,X2803) = hAPP(c_Nat_OSuc,X2802) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1029,plain,
! [X3167,X3168] :
( ~ class_Orderings_Oord(X3168)
| class_Orderings_Oord(tc_fun(X3167,X3168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1030,plain,
! [X3163,X3164] :
( ~ class_Orderings_Oorder(X3164)
| class_Orderings_Oorder(tc_fun(X3163,X3164)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1031,plain,
! [X3159,X3160] :
( ~ class_Orderings_Opreorder(X3160)
| class_Orderings_Opreorder(tc_fun(X3159,X3160)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1032,plain,
! [X3165,X3166] :
( ~ class_Orderings_Otop(X3166)
| class_Orderings_Otop(tc_fun(X3165,X3166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_1033,plain,
! [X2716,X2717] :
( c_Finite__Set_Ofinite(X2717,X2716)
| c_Finite__Set_Ocard(X2717,X2716) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_579])]) ).
fof(i_0_1034,plain,
! [X2755] : hAPP(c_Nat_OSuc,X2755) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1035,plain,
! [X2754] : hAPP(c_Nat_OSuc,X2754) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1036,plain,
! [X2752] : hAPP(c_Nat_OSuc,X2752) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1037,plain,
! [X2757] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2757),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1038,plain,
! [X2756] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2756),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1039,plain,
! [X2753] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2753),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1040,plain,
! [X2516,X2517] :
( ~ class_Finite__Set_Ofinite(X2517)
| c_Finite__Set_Ofinite(X2517,X2516) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_1041,plain,
! [X2514,X2515] :
( ~ class_Finite__Set_Ofinite(X2515)
| c_Finite__Set_Ofinite(X2515,X2514) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(i_0_1042,plain,
! [X2801] : hAPP(c_Nat_OSuc,X2801) != X2801,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1043,plain,
! [X2800] : X2800 != hAPP(c_Nat_OSuc,X2800),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1044,plain,
! [X3174,X3175] : hAPP(c_COMBI(X3175),X3174) = X3174,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1045,plain,
! [X1702] : c_List_Odistinct(X1702,c_List_Olist_ONil(X1702)),
inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).
fof(i_0_1046,plain,
! [X2662] :
( ~ class_Rings_Ozero__neq__one(X2662)
| c_Groups_Ozero__class_Ozero(X2662) != c_Groups_Oone__class_Oone(X2662) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_1047,plain,
! [X2661] :
( ~ class_Rings_Ozero__neq__one(X2661)
| c_Groups_Oone__class_Oone(X2661) != c_Groups_Ozero__class_Ozero(X2661) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_1048,plain,
! [X3171] :
( ~ class_Finite__Set_Ofinite(X3171)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X3171)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_1049,plain,
! [X2888] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X2888) = X2888,
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,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_1052,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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),esk18_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_1053,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk12_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_581]),
[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),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_1055,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_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_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),esk18_0)) ),
inference(split_conjunct,[status(thm)],[i_0_580]),
[final] ).
cnf(i_0_1057,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1))),v_Lab____)),v_Lba____))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk12_0)) ),
inference(split_conjunct,[status(thm)],[i_0_581]),
[final] ).
cnf(i_0_1058,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),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_1059,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_1060,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_1061,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk17_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,esk17_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_1062,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk17_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,esk17_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_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),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,esk16_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,esk16_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_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)))
| 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,esk14_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,esk14_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_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),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,esk14_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,esk14_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_1066,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_588]),
[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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk17_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,esk17_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_1068,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk17_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,esk17_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_1069,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk16_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,esk16_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_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,esk14_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,esk14_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_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,esk14_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,esk14_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_1072,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,esk31_5(X3,X2,X1,X4,X5))),hAPP(X3,esk31_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1073,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,esk32_5(X3,X2,X1,X4,X5))),hAPP(X3,esk32_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[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),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,esk22_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,esk22_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_591]),
[final] ).
cnf(i_0_1075,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk22_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,esk22_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_591]),
[final] ).
cnf(i_0_1076,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk15_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,esk15_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_592]),
[final] ).
cnf(i_0_1077,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),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,esk15_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,esk15_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_592]),
[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(X4,esk22_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,esk22_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_591]),
[final] ).
cnf(i_0_1079,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk22_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,esk22_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_591]),
[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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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,esk15_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,esk15_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_592]),
[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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk15_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,esk15_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_592]),
[final] ).
cnf(i_0_1082,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),esk20_2(X1,X2)),esk21_2(X1,X2))),hAPP(X2,esk19_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_593]),
[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),esk20_2(X1,X2)),esk21_2(X1,X2))),hAPP(esk19_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_593]),
[final] ).
cnf(i_0_1084,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk19_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_593]),
[final] ).
cnf(i_0_1085,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk20_2(X1,X2) != esk21_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_593]),
[final] ).
cnf(i_0_1086,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_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),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,esk13_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,esk13_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_595]),
[final] ).
cnf(i_0_1088,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),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,esk13_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,esk13_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_595]),
[final] ).
cnf(i_0_1089,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_596]),
[final] ).
cnf(i_0_1090,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_594]),
[final] ).
cnf(i_0_1091,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk31_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_589]),
[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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk13_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,esk13_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_595]),
[final] ).
cnf(i_0_1093,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk13_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,esk13_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_595]),
[final] ).
cnf(i_0_1094,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk43_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_597]),
[final] ).
cnf(i_0_1095,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk32_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_590]),
[final] ).
cnf(i_0_1096,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_598]),
[final] ).
cnf(i_0_1097,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_1098,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_594]),
[final] ).
cnf(i_0_1099,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_594]),
[final] ).
cnf(i_0_1100,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,esk10_4(X3,X2,X4,X1))),hAPP(X3,esk10_4(X3,X2,X4,X1))))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1101,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_600]),
[final] ).
cnf(i_0_1102,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk27_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1103,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(hAPP(c_Arrow__Order__Mirabelle_Omkbot,hAPP(v_P____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk46_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1104,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_603]),
[final] ).
cnf(i_0_1105,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_604]),
[final] ).
cnf(i_0_1106,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_605]),
[final] ).
cnf(i_0_1107,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_606]),
[final] ).
cnf(i_0_1108,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_607]),
[final] ).
cnf(i_0_1109,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_608]),
[final] ).
cnf(i_0_1110,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_609]),
[final] ).
cnf(i_0_1111,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_610]),
[final] ).
cnf(i_0_1112,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk46_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1113,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_1114,negated_conjecture,
( hAPP(v_h____,esk46_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1115,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_611]),
[final] ).
cnf(i_0_1116,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_612]),
[final] ).
cnf(i_0_1117,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_612]),
[final] ).
cnf(i_0_1118,negated_conjecture,
( hAPP(v_h____,esk46_0) = v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1119,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_613]),
[final] ).
cnf(i_0_1120,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_606]),
[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))
| 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_606]),
[final] ).
cnf(i_0_1122,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_606]),
[final] ).
cnf(i_0_1123,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_606]),
[final] ).
cnf(i_0_1124,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_607]),
[final] ).
cnf(i_0_1125,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_607]),
[final] ).
cnf(i_0_1126,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_607]),
[final] ).
cnf(i_0_1127,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_607]),
[final] ).
cnf(i_0_1128,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_604]),
[final] ).
cnf(i_0_1129,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk43_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_597]),
[final] ).
cnf(i_0_1130,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_614]),
[final] ).
cnf(i_0_1131,plain,
( X1 = hAPP(X2,esk45_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_615]),
[final] ).
cnf(i_0_1132,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_616]),
[final] ).
cnf(i_0_1133,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_617]),
[final] ).
cnf(i_0_1134,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_618]),
[final] ).
cnf(i_0_1135,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,X4)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_List_Omeasures(X1,c_List_Olist_OCons(tc_fun(X1,tc_Nat_Onat),X5,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1136,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| hAPP(v_h____,esk46_0) != v_n____
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_c____),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1137,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_611]),
[final] ).
cnf(i_0_1138,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk42_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_620]),
[final] ).
cnf(i_0_1139,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_606]),
[final] ).
cnf(i_0_1140,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_606]),
[final] ).
cnf(i_0_1141,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_606]),
[final] ).
cnf(i_0_1142,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat),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)),c_List_Omeasures(X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1143,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_622]),
[final] ).
cnf(i_0_1144,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_623]),
[final] ).
cnf(i_0_1145,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_624]),
[final] ).
cnf(i_0_1146,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_612]),
[final] ).
cnf(i_0_1147,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)))))
| esk45_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_615]),
[final] ).
cnf(i_0_1148,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_625]),
[final] ).
cnf(i_0_1149,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_606]),
[final] ).
cnf(i_0_1150,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_606]),
[final] ).
cnf(i_0_1151,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_606]),
[final] ).
cnf(i_0_1152,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_606]),
[final] ).
cnf(i_0_1153,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_606]),
[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),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_607]),
[final] ).
cnf(i_0_1155,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_626]),
[final] ).
cnf(i_0_1156,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_607]),
[final] ).
cnf(i_0_1157,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_607]),
[final] ).
cnf(i_0_1158,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),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_627]),
[final] ).
cnf(i_0_1159,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),esk25_1(X1)),esk26_1(X1))),hAPP(X1,esk23_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),esk25_1(X1)),esk26_1(X1))),hAPP(X1,esk24_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1160,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1161,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_628]),
[final] ).
cnf(i_0_1162,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_607]),
[final] ).
cnf(i_0_1163,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_607]),
[final] ).
cnf(i_0_1164,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_607]),
[final] ).
cnf(i_0_1165,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_607]),
[final] ).
cnf(i_0_1166,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_607]),
[final] ).
cnf(i_0_1167,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat),X1,X5))))
| 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_List_Omeasures(X4,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1168,negated_conjecture,
( hAPP(v_h____,esk46_0) = v_n____
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1169,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_629]),
[final] ).
cnf(i_0_1170,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_630]),
[final] ).
cnf(i_0_1171,plain,
( X1 = hAPP(X2,esk44_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_615]),
[final] ).
cnf(i_0_1172,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| 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_List_Omeasures(X4,c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat),X1,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1173,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_614]),
[final] ).
cnf(i_0_1174,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_631]),
[final] ).
cnf(i_0_1175,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_606]),
[final] ).
cnf(i_0_1176,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X1)),esk26_1(X1))),hAPP(esk24_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),esk25_1(X1)),esk26_1(X1))),hAPP(esk23_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1177,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X1)),esk26_1(X1))),hAPP(esk23_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),esk25_1(X1)),esk26_1(X1))),hAPP(esk24_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1178,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_631]),
[final] ).
cnf(i_0_1179,plain,
( X3 = esk44_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_615]),
[final] ).
cnf(i_0_1180,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_632]),
[final] ).
cnf(i_0_1181,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_622]),
[final] ).
cnf(i_0_1182,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_607]),
[final] ).
cnf(i_0_1183,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),esk41_3(X1,X3,X2))) != esk41_3(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_633]),
[final] ).
cnf(i_0_1184,plain,
( c_Nitpick_Orefl_H(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk2_2(X2,X1)),esk2_2(X2,X1))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_634]),
[final] ).
cnf(i_0_1185,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(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_P____,esk46_0)),v_c____),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)))
| hAPP(v_h____,esk46_0) != v_n____ ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1186,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_635]),
[final] ).
cnf(i_0_1187,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),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_636]),
[final] ).
cnf(i_0_1188,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_637]),
[final] ).
cnf(i_0_1189,plain,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_638]),
[final] ).
cnf(i_0_1190,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_639]),
[final] ).
cnf(i_0_1191,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_640]),
[final] ).
cnf(i_0_1192,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_641]),
[final] ).
cnf(i_0_1193,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_642]),
[final] ).
cnf(i_0_1194,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_637]),
[final] ).
cnf(i_0_1195,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_636]),
[final] ).
cnf(i_0_1196,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_637]),
[final] ).
cnf(i_0_1197,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_636]),
[final] ).
cnf(i_0_1198,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_643]),
[final] ).
cnf(i_0_1199,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk6_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1200,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk5_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1201,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(hAPP(c_Arrow__Order__Mirabelle_Omktop,hAPP(v_P____,esk46_0)),v_e____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_d____)),hAPP(v_P____,esk46_0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____)) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1202,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk25_1(X1)),esk26_1(X1))),hAPP(X1,esk23_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),esk25_1(X1)),esk26_1(X1))),hAPP(X1,esk24_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1203,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_645]),
[final] ).
cnf(i_0_1204,negated_conjecture,
( hAPP(v_h____,esk46_0) = v_n____
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0)),v_e____)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,esk46_0)),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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____,esk46_0))) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1205,plain,
( X1 = hAPP(X2,esk42_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_620]),
[final] ).
cnf(i_0_1206,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_606]),
[final] ).
cnf(i_0_1207,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_646]),
[final] ).
cnf(i_0_1208,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat),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_619]),
[final] ).
cnf(i_0_1209,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_List_Omeasures(X4,c_List_Olist_OCons(tc_fun(X4,tc_Nat_Onat),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_647]),
[final] ).
cnf(i_0_1210,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_648]),
[final] ).
cnf(i_0_1211,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_649]),
[final] ).
cnf(i_0_1212,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_607]),
[final] ).
cnf(i_0_1213,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_List_Omeasures(X1,c_List_Olist_ONil(tc_fun(X1,tc_Nat_Onat))))),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1214,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_651]),
[final] ).
cnf(i_0_1215,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_652]),
[final] ).
cnf(i_0_1216,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_653]),
[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)),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_654]),
[final] ).
cnf(i_0_1218,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_655]),
[final] ).
cnf(i_0_1219,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_656]),
[final] ).
cnf(i_0_1220,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_657]),
[final] ).
cnf(i_0_1221,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_658]),
[final] ).
cnf(i_0_1222,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_659]),
[final] ).
cnf(i_0_1223,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_641]),
[final] ).
cnf(i_0_1224,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_597]),
[final] ).
cnf(i_0_1225,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_660]),
[final] ).
cnf(i_0_1226,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_661]),
[final] ).
cnf(i_0_1227,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),esk29_1(X1)),esk30_1(X1))),hAPP(X1,esk28_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1228,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_633]),
[final] ).
cnf(i_0_1229,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_662]),
[final] ).
cnf(i_0_1230,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_663]),
[final] ).
cnf(i_0_1231,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_636]),
[final] ).
cnf(i_0_1232,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_637]),
[final] ).
cnf(i_0_1233,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_637]),
[final] ).
cnf(i_0_1234,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_636]),
[final] ).
cnf(i_0_1235,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_655]),
[final] ).
cnf(i_0_1236,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_664]),
[final] ).
cnf(i_0_1237,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))),esk7_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_649]),
[final] ).
cnf(i_0_1238,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_665]),
[final] ).
cnf(i_0_1239,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_666]),
[final] ).
cnf(i_0_1240,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_667]),
[final] ).
cnf(i_0_1241,plain,
c_List_Olist_Olist__case(X1,X2,X3,X4,c_List_Olist_OCons(X2,X5,X6)) = hAPP(hAPP(X4,X5),X6),
inference(split_conjunct,[status(thm)],[i_0_668]),
[final] ).
cnf(i_0_1242,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1243,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_670]),
[final] ).
cnf(i_0_1244,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_671]),
[final] ).
cnf(i_0_1245,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_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1246,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk23_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1247,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))),esk28_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1248,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_672]),
[final] ).
cnf(i_0_1249,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_620]),
[final] ).
cnf(i_0_1250,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_673]),
[final] ).
cnf(i_0_1251,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_1252,plain,
( hAPP(X1,esk5_4(X2,X1,X3,X4)) = hAPP(X1,esk6_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1253,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_674]),
[final] ).
cnf(i_0_1254,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_675]),
[final] ).
cnf(i_0_1255,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_676]),
[final] ).
cnf(i_0_1256,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_677]),
[final] ).
cnf(i_0_1257,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_678]),
[final] ).
cnf(i_0_1258,plain,
c_List_Olist_Olist__case(X1,X2,X3,X4,c_List_Olist_ONil(X2)) = X3,
inference(split_conjunct,[status(thm)],[i_0_679]),
[final] ).
cnf(i_0_1259,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_680]),
[final] ).
cnf(i_0_1260,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_681]),
[final] ).
cnf(i_0_1261,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_682]),
[final] ).
cnf(i_0_1262,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_683]),
[final] ).
cnf(i_0_1263,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_684]),
[final] ).
cnf(i_0_1264,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_685]),
[final] ).
cnf(i_0_1265,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk29_1(X1)),esk30_1(X1))),hAPP(esk28_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1266,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_686]),
[final] ).
cnf(i_0_1267,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_687]),
[final] ).
cnf(i_0_1268,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_688]),
[final] ).
cnf(i_0_1269,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_689]),
[final] ).
cnf(i_0_1270,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_690]),
[final] ).
cnf(i_0_1271,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_691]),
[final] ).
cnf(i_0_1272,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_692]),
[final] ).
cnf(i_0_1273,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_693]),
[final] ).
cnf(i_0_1274,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_694]),
[final] ).
cnf(i_0_1275,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_695]),
[final] ).
cnf(i_0_1276,plain,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_696]),
[final] ).
cnf(i_0_1277,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_634]),
[final] ).
cnf(i_0_1278,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_697]),
[final] ).
cnf(i_0_1279,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_686]),
[final] ).
cnf(i_0_1280,plain,
c_List_Olist_Olist__size(X1,X2,c_List_Olist_OCons(X1,X3,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2,X3)),c_List_Olist_Olist__size(X1,X2,X4))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_698]),
[final] ).
cnf(i_0_1281,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_636]),
[final] ).
cnf(i_0_1282,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_637]),
[final] ).
cnf(i_0_1283,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_699]),
[final] ).
cnf(i_0_1284,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_686]),
[final] ).
cnf(i_0_1285,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk5_4(X1,X2,X3,X4) != esk6_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1286,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_700]),
[final] ).
cnf(i_0_1287,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_701]),
[final] ).
cnf(i_0_1288,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_702]),
[final] ).
cnf(i_0_1289,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_703]),
[final] ).
cnf(i_0_1290,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_1291,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_704]),
[final] ).
cnf(i_0_1292,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_705]),
[final] ).
cnf(i_0_1293,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_706]),
[final] ).
cnf(i_0_1294,plain,
( X1 = X2
| c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X1,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X2,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,esk4_2(X2,X1),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))) ),
inference(split_conjunct,[status(thm)],[i_0_707]),
[final] ).
cnf(i_0_1295,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_708]),
[final] ).
cnf(i_0_1296,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_709]),
[final] ).
cnf(i_0_1297,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_710]),
[final] ).
cnf(i_0_1298,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_694]),
[final] ).
cnf(i_0_1299,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_711]),
[final] ).
cnf(i_0_1300,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_712]),
[final] ).
cnf(i_0_1301,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_713]),
[final] ).
cnf(i_0_1302,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_714]),
[final] ).
cnf(i_0_1303,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_715]),
[final] ).
cnf(i_0_1304,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_716]),
[final] ).
cnf(i_0_1305,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_717]),
[final] ).
cnf(i_0_1306,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_718]),
[final] ).
cnf(i_0_1307,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_675]),
[final] ).
cnf(i_0_1308,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_719]),
[final] ).
cnf(i_0_1309,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_677]),
[final] ).
cnf(i_0_1310,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_720]),
[final] ).
cnf(i_0_1311,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_721]),
[final] ).
cnf(i_0_1312,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_722]),
[final] ).
cnf(i_0_1313,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_723]),
[final] ).
cnf(i_0_1314,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_724]),
[final] ).
cnf(i_0_1315,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_725]),
[final] ).
cnf(i_0_1316,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk8_0)),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_1317,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_1318,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk9_0)),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_1319,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_1320,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_728]),
[final] ).
cnf(i_0_1321,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_728]),
[final] ).
cnf(i_0_1322,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_729]),
[final] ).
cnf(i_0_1323,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_730]),
[final] ).
cnf(i_0_1324,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_731]),
[final] ).
cnf(i_0_1325,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_683]),
[final] ).
cnf(i_0_1326,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_732]),
[final] ).
cnf(i_0_1327,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_685]),
[final] ).
cnf(i_0_1328,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_733]),
[final] ).
cnf(i_0_1329,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_734]),
[final] ).
cnf(i_0_1330,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_704]),
[final] ).
cnf(i_0_1331,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_735]),
[final] ).
cnf(i_0_1332,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_735]),
[final] ).
cnf(i_0_1333,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_736]),
[final] ).
cnf(i_0_1334,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_737]),
[final] ).
cnf(i_0_1335,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_738]),
[final] ).
cnf(i_0_1336,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_690]),
[final] ).
cnf(i_0_1337,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_739]),
[final] ).
cnf(i_0_1338,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_644]),
[final] ).
cnf(i_0_1339,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_740]),
[final] ).
cnf(i_0_1340,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_741]),
[final] ).
cnf(i_0_1341,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_722]),
[final] ).
cnf(i_0_1342,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_742]),
[final] ).
cnf(i_0_1343,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_742]),
[final] ).
cnf(i_0_1344,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_743]),
[final] ).
cnf(i_0_1345,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_744]),
[final] ).
cnf(i_0_1346,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_745]),
[final] ).
cnf(i_0_1347,plain,
c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_c____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_d____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,esk3_0,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(split_conjunct,[status(thm)],[i_0_746]),
[final] ).
cnf(i_0_1348,plain,
c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_c____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_d____,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,v_e____,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))),
inference(split_conjunct,[status(thm)],[fact_dist]),
[final] ).
cnf(i_0_1349,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk40_2(X1,X2)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1350,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_748]),
[final] ).
cnf(i_0_1351,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_699]),
[final] ).
cnf(i_0_1352,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_749]),
[final] ).
cnf(i_0_1353,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_750]),
[final] ).
cnf(i_0_1354,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_751]),
[final] ).
cnf(i_0_1355,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_752]),
[final] ).
cnf(i_0_1356,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk37_2(X1,X2)),X2))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_753]),
[final] ).
cnf(i_0_1357,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_709]),
[final] ).
cnf(i_0_1358,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_710]),
[final] ).
cnf(i_0_1359,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_754]),
[final] ).
cnf(i_0_1360,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_755]),
[final] ).
cnf(i_0_1361,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_756]),
[final] ).
cnf(i_0_1362,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_757]),
[final] ).
cnf(i_0_1363,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_758]),
[final] ).
cnf(i_0_1364,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_759]),
[final] ).
cnf(i_0_1365,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_760]),
[final] ).
cnf(i_0_1366,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_761]),
[final] ).
cnf(i_0_1367,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_735]),
[final] ).
cnf(i_0_1368,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_762]),
[final] ).
cnf(i_0_1369,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_763]),
[final] ).
cnf(i_0_1370,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_764]),
[final] ).
cnf(i_0_1371,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_765]),
[final] ).
cnf(i_0_1372,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_766]),
[final] ).
cnf(i_0_1373,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_767]),
[final] ).
cnf(i_0_1374,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_721]),
[final] ).
cnf(i_0_1375,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_768]),
[final] ).
cnf(i_0_1376,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_769]),
[final] ).
cnf(i_0_1377,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_770]),
[final] ).
cnf(i_0_1378,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk37_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_753]),
[final] ).
cnf(i_0_1379,plain,
c_List_Osplice(X1,c_List_Olist_OCons(X1,X2,X3),c_List_Olist_OCons(X1,X4,X5)) = c_List_Olist_OCons(X1,X2,c_List_Olist_OCons(X1,X4,c_List_Osplice(X1,X3,X5))),
inference(split_conjunct,[status(thm)],[i_0_771]),
[final] ).
cnf(i_0_1380,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_772]),
[final] ).
cnf(i_0_1381,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_1382,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_1383,plain,
( hBOOL(hAPP(X1,esk40_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1384,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk39_2(X1,X2)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1385,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_775]),
[final] ).
cnf(i_0_1386,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_1387,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_777]),
[final] ).
cnf(i_0_1388,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_778]),
[final] ).
cnf(i_0_1389,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk9_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_1390,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk8_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_1391,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_1392,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_1393,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk38_2(X1,X2)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_753]),
[final] ).
cnf(i_0_1394,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_779]),
[final] ).
cnf(i_0_1395,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_780]),
[final] ).
cnf(i_0_1396,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_781]),
[final] ).
cnf(i_0_1397,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_728]),
[final] ).
cnf(i_0_1398,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_772]),
[final] ).
cnf(i_0_1399,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_773]),
[final] ).
cnf(i_0_1400,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_782]),
[final] ).
cnf(i_0_1401,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_759]),
[final] ).
cnf(i_0_1402,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_759]),
[final] ).
cnf(i_0_1403,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_764]),
[final] ).
cnf(i_0_1404,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_783]),
[final] ).
cnf(i_0_1405,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_1406,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_785]),
[final] ).
cnf(i_0_1407,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_786]),
[final] ).
cnf(i_0_1408,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_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_788]),
[final] ).
cnf(i_0_1410,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_789]),
[final] ).
cnf(i_0_1411,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_1412,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_599]),
[final] ).
cnf(i_0_1413,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_791]),
[final] ).
cnf(i_0_1414,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_792]),
[final] ).
cnf(i_0_1415,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_793]),
[final] ).
cnf(i_0_1416,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_794]),
[final] ).
cnf(i_0_1417,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_795]),
[final] ).
cnf(i_0_1418,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk36_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_796]),
[final] ).
cnf(i_0_1419,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_797]),
[final] ).
cnf(i_0_1420,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_798]),
[final] ).
cnf(i_0_1421,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_775]),
[final] ).
cnf(i_0_1422,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_799]),
[final] ).
cnf(i_0_1423,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_800]),
[final] ).
cnf(i_0_1424,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_777]),
[final] ).
cnf(i_0_1425,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_801]),
[final] ).
cnf(i_0_1426,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_802]),
[final] ).
cnf(i_0_1427,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_1428,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_772]),
[final] ).
cnf(i_0_1429,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_803]),
[final] ).
cnf(i_0_1430,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_804]),
[final] ).
cnf(i_0_1431,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_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)),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_765]),
[final] ).
cnf(i_0_1433,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_765]),
[final] ).
cnf(i_0_1434,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_806]),
[final] ).
cnf(i_0_1435,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_807]),
[final] ).
cnf(i_0_1436,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_808]),
[final] ).
cnf(i_0_1437,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_808]),
[final] ).
cnf(i_0_1438,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_809]),
[final] ).
cnf(i_0_1439,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_810]),
[final] ).
cnf(i_0_1440,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_811]),
[final] ).
cnf(i_0_1441,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_812]),
[final] ).
cnf(i_0_1442,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_813]),
[final] ).
cnf(i_0_1443,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_814]),
[final] ).
cnf(i_0_1444,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_815]),
[final] ).
cnf(i_0_1445,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_816]),
[final] ).
cnf(i_0_1446,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_817]),
[final] ).
cnf(i_0_1447,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1448,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_808]),
[final] ).
cnf(i_0_1449,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_819]),
[final] ).
cnf(i_0_1450,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_820]),
[final] ).
cnf(i_0_1451,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_821]),
[final] ).
cnf(i_0_1452,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_822]),
[final] ).
cnf(i_0_1453,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_823]),
[final] ).
cnf(i_0_1454,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_824]),
[final] ).
cnf(i_0_1455,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_825]),
[final] ).
cnf(i_0_1456,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_826]),
[final] ).
cnf(i_0_1457,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_827]),
[final] ).
cnf(i_0_1458,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_828]),
[final] ).
cnf(i_0_1459,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_829]),
[final] ).
cnf(i_0_1460,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_830]),
[final] ).
cnf(i_0_1461,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_831]),
[final] ).
cnf(i_0_1462,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_804]),
[final] ).
cnf(i_0_1463,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_832]),
[final] ).
cnf(i_0_1464,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_833]),
[final] ).
cnf(i_0_1465,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_834]),
[final] ).
cnf(i_0_1466,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_835]),
[final] ).
cnf(i_0_1467,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_836]),
[final] ).
cnf(i_0_1468,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_825]),
[final] ).
cnf(i_0_1469,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_825]),
[final] ).
cnf(i_0_1470,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_837]),
[final] ).
cnf(i_0_1471,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_838]),
[final] ).
cnf(i_0_1472,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_839]),
[final] ).
cnf(i_0_1473,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_840]),
[final] ).
cnf(i_0_1474,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_841]),
[final] ).
cnf(i_0_1475,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_842]),
[final] ).
cnf(i_0_1476,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_843]),
[final] ).
cnf(i_0_1477,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_844]),
[final] ).
cnf(i_0_1478,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_845]),
[final] ).
cnf(i_0_1479,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_846]),
[final] ).
cnf(i_0_1480,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_847]),
[final] ).
cnf(i_0_1481,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_848]),
[final] ).
cnf(i_0_1482,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_849]),
[final] ).
cnf(i_0_1483,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_850]),
[final] ).
cnf(i_0_1484,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_851]),
[final] ).
cnf(i_0_1485,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_852]),
[final] ).
cnf(i_0_1486,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_853]),
[final] ).
cnf(i_0_1487,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_854]),
[final] ).
cnf(i_0_1488,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_855]),
[final] ).
cnf(i_0_1489,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_856]),
[final] ).
cnf(i_0_1490,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk36_2(X2,X3)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_796]),
[final] ).
cnf(i_0_1491,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_820]),
[final] ).
cnf(i_0_1492,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_857]),
[final] ).
cnf(i_0_1493,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_858]),
[final] ).
cnf(i_0_1494,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_859]),
[final] ).
cnf(i_0_1495,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_775]),
[final] ).
cnf(i_0_1496,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1497,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_860]),
[final] ).
cnf(i_0_1498,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_861]),
[final] ).
cnf(i_0_1499,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_862]),
[final] ).
cnf(i_0_1500,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_863]),
[final] ).
cnf(i_0_1501,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_864]),
[final] ).
cnf(i_0_1502,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_865]),
[final] ).
cnf(i_0_1503,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk18_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_1504,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk12_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_581]),
[final] ).
cnf(i_0_1505,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_1506,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_866]),
[final] ).
cnf(i_0_1507,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_841]),
[final] ).
cnf(i_0_1508,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_842]),
[final] ).
cnf(i_0_1509,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_867]),
[final] ).
cnf(i_0_1510,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_868]),
[final] ).
cnf(i_0_1511,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_814]),
[final] ).
cnf(i_0_1512,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_869]),
[final] ).
cnf(i_0_1513,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_870]),
[final] ).
cnf(i_0_1514,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk38_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_753]),
[final] ).
cnf(i_0_1515,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_871]),
[final] ).
cnf(i_0_1516,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_872]),
[final] ).
cnf(i_0_1517,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_873]),
[final] ).
cnf(i_0_1518,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_874]),
[final] ).
cnf(i_0_1519,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_858]),
[final] ).
cnf(i_0_1520,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk35_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1521,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_876]),
[final] ).
cnf(i_0_1522,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1523,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_1524,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_859]),
[final] ).
cnf(i_0_1525,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_877]),
[final] ).
cnf(i_0_1526,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_878]),
[final] ).
cnf(i_0_1527,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_865]),
[final] ).
cnf(i_0_1528,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_879]),
[final] ).
cnf(i_0_1529,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_880]),
[final] ).
cnf(i_0_1530,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk36_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_796]),
[final] ).
cnf(i_0_1531,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_881]),
[final] ).
cnf(i_0_1532,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_882]),
[final] ).
cnf(i_0_1533,plain,
( hBOOL(hAPP(X1,esk39_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1534,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_883]),
[final] ).
cnf(i_0_1535,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_884]),
[final] ).
cnf(i_0_1536,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_885]),
[final] ).
cnf(i_0_1537,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_886]),
[final] ).
cnf(i_0_1538,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_887]),
[final] ).
cnf(i_0_1539,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_888]),
[final] ).
cnf(i_0_1540,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_889]),
[final] ).
cnf(i_0_1541,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_814]),
[final] ).
cnf(i_0_1542,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_855]),
[final] ).
cnf(i_0_1543,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_890]),
[final] ).
cnf(i_0_1544,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_891]),
[final] ).
cnf(i_0_1545,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_892]),
[final] ).
cnf(i_0_1546,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_876]),
[final] ).
cnf(i_0_1547,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_879]),
[final] ).
cnf(i_0_1548,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_893]),
[final] ).
cnf(i_0_1549,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_875]),
[final] ).
cnf(i_0_1550,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_894]),
[final] ).
cnf(i_0_1551,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_895]),
[final] ).
cnf(i_0_1552,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_858]),
[final] ).
cnf(i_0_1553,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_896]),
[final] ).
cnf(i_0_1554,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_897]),
[final] ).
cnf(i_0_1555,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_898]),
[final] ).
cnf(i_0_1556,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_899]),
[final] ).
cnf(i_0_1557,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1558,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1559,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_894]),
[final] ).
cnf(i_0_1560,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_895]),
[final] ).
cnf(i_0_1561,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_901]),
[final] ).
cnf(i_0_1562,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_902]),
[final] ).
cnf(i_0_1563,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_903]),
[final] ).
cnf(i_0_1564,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_904]),
[final] ).
cnf(i_0_1565,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_905]),
[final] ).
cnf(i_0_1566,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_871]),
[final] ).
cnf(i_0_1567,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_906]),
[final] ).
cnf(i_0_1568,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_831]),
[final] ).
cnf(i_0_1569,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_907]),
[final] ).
cnf(i_0_1570,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1571,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_909]),
[final] ).
cnf(i_0_1572,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1573,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_911]),
[final] ).
cnf(i_0_1574,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_882]),
[final] ).
cnf(i_0_1575,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_864]),
[final] ).
cnf(i_0_1576,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_838]),
[final] ).
cnf(i_0_1577,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_912]),
[final] ).
cnf(i_0_1578,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_913]),
[final] ).
cnf(i_0_1579,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_914]),
[final] ).
cnf(i_0_1580,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_915]),
[final] ).
cnf(i_0_1581,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_916]),
[final] ).
cnf(i_0_1582,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_917]),
[final] ).
cnf(i_0_1583,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_918]),
[final] ).
cnf(i_0_1584,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_919]),
[final] ).
cnf(i_0_1585,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_920]),
[final] ).
cnf(i_0_1586,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_921]),
[final] ).
cnf(i_0_1587,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_922]),
[final] ).
cnf(i_0_1588,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_923]),
[final] ).
cnf(i_0_1589,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_924]),
[final] ).
cnf(i_0_1590,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_849]),
[final] ).
cnf(i_0_1591,plain,
c_List_Osplice(X1,c_List_Olist_OCons(X1,X2,X3),c_List_Olist_ONil(X1)) = c_List_Olist_OCons(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1592,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_926]),
[final] ).
cnf(i_0_1593,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_913]),
[final] ).
cnf(i_0_1594,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_914]),
[final] ).
cnf(i_0_1595,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_927]),
[final] ).
cnf(i_0_1596,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_928]),
[final] ).
cnf(i_0_1597,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_929]),
[final] ).
cnf(i_0_1598,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_930]),
[final] ).
cnf(i_0_1599,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_931]),
[final] ).
cnf(i_0_1600,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_926]),
[final] ).
cnf(i_0_1601,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_905]),
[final] ).
cnf(i_0_1602,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1603,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_874]),
[final] ).
cnf(i_0_1604,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_933]),
[final] ).
cnf(i_0_1605,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_934]),
[final] ).
cnf(i_0_1606,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_872]),
[final] ).
cnf(i_0_1607,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_935]),
[final] ).
cnf(i_0_1608,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_936]),
[final] ).
cnf(i_0_1609,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_937]),
[final] ).
cnf(i_0_1610,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk11_2(X2,X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1611,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1612,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_940]),
[final] ).
cnf(i_0_1613,plain,
( X1 = hAPP(c_Nat_OSuc,esk34_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_941]),
[final] ).
cnf(i_0_1614,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_894]),
[final] ).
cnf(i_0_1615,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_849]),
[final] ).
cnf(i_0_1616,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_942]),
[final] ).
cnf(i_0_1617,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_943]),
[final] ).
cnf(i_0_1618,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_944]),
[final] ).
cnf(i_0_1619,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_919]),
[final] ).
cnf(i_0_1620,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_919]),
[final] ).
cnf(i_0_1621,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_783]),
[final] ).
cnf(i_0_1622,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_783]),
[final] ).
cnf(i_0_1623,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_945]),
[final] ).
cnf(i_0_1624,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_945]),
[final] ).
cnf(i_0_1625,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_946]),
[final] ).
cnf(i_0_1626,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_773]),
[final] ).
cnf(i_0_1627,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_947]),
[final] ).
cnf(i_0_1628,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_948]),
[final] ).
cnf(i_0_1629,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_949]),
[final] ).
cnf(i_0_1630,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_950]),
[final] ).
cnf(i_0_1631,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_951]),
[final] ).
cnf(i_0_1632,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_952]),
[final] ).
cnf(i_0_1633,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_953]),
[final] ).
cnf(i_0_1634,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_954]),
[final] ).
cnf(i_0_1635,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_955]),
[final] ).
cnf(i_0_1636,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X3,X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1637,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X4,X1) != c_List_Olist_OCons(X3,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1638,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_957]),
[final] ).
cnf(i_0_1639,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_958]),
[final] ).
cnf(i_0_1640,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_959]),
[final] ).
cnf(i_0_1641,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_960]),
[final] ).
cnf(i_0_1642,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_907]),
[final] ).
cnf(i_0_1643,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_961]),
[final] ).
cnf(i_0_1644,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_962]),
[final] ).
cnf(i_0_1645,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_963]),
[final] ).
cnf(i_0_1646,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_964]),
[final] ).
cnf(i_0_1647,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1648,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1649,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_965]),
[final] ).
cnf(i_0_1650,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_966]),
[final] ).
cnf(i_0_1651,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_967]),
[final] ).
cnf(i_0_1652,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1653,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1654,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1655,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_968]),
[final] ).
cnf(i_0_1656,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_969]),
[final] ).
cnf(i_0_1657,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_938]),
[final] ).
cnf(i_0_1658,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_970]),
[final] ).
cnf(i_0_1659,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_971]),
[final] ).
cnf(i_0_1660,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_972]),
[final] ).
cnf(i_0_1661,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),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),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_974]),
[final] ).
cnf(i_0_1663,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_975]),
[final] ).
cnf(i_0_1664,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_976]),
[final] ).
cnf(i_0_1665,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_814]),
[final] ).
cnf(i_0_1666,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_931]),
[final] ).
cnf(i_0_1667,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_977]),
[final] ).
cnf(i_0_1668,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_865]),
[final] ).
cnf(i_0_1669,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_882]),
[final] ).
cnf(i_0_1670,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk7_2(X2,X1)) != hAPP(esk7_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_649]),
[final] ).
cnf(i_0_1671,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_978]),
[final] ).
cnf(i_0_1672,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_979]),
[final] ).
cnf(i_0_1673,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_980]),
[final] ).
cnf(i_0_1674,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_981]),
[final] ).
cnf(i_0_1675,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_982]),
[final] ).
cnf(i_0_1676,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_941]),
[final] ).
cnf(i_0_1677,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1678,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_984]),
[final] ).
cnf(i_0_1679,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_985]),
[final] ).
cnf(i_0_1680,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_981]),
[final] ).
cnf(i_0_1681,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_981]),
[final] ).
cnf(i_0_1682,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_982]),
[final] ).
cnf(i_0_1683,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_982]),
[final] ).
cnf(i_0_1684,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_986]),
[final] ).
cnf(i_0_1685,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_987]),
[final] ).
cnf(i_0_1686,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_988]),
[final] ).
cnf(i_0_1687,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_950]),
[final] ).
cnf(i_0_1688,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_981]),
[final] ).
cnf(i_0_1689,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_982]),
[final] ).
cnf(i_0_1690,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_989]),
[final] ).
cnf(i_0_1691,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_990]),
[final] ).
cnf(i_0_1692,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_991]),
[final] ).
cnf(i_0_1693,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_992]),
[final] ).
cnf(i_0_1694,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_981]),
[final] ).
cnf(i_0_1695,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_981]),
[final] ).
cnf(i_0_1696,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_982]),
[final] ).
cnf(i_0_1697,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_982]),
[final] ).
cnf(i_0_1698,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_886]),
[final] ).
cnf(i_0_1699,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_886]),
[final] ).
cnf(i_0_1700,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_993]),
[final] ).
cnf(i_0_1701,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_895]),
[final] ).
cnf(i_0_1702,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1703,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_995]),
[final] ).
cnf(i_0_1704,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_996]),
[final] ).
cnf(i_0_1705,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_997]),
[final] ).
cnf(i_0_1706,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1707,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_999]),
[final] ).
cnf(i_0_1708,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_1000]),
[final] ).
cnf(i_0_1709,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_980]),
[final] ).
cnf(i_0_1710,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(split_conjunct,[status(thm)],[i_0_1001]),
[final] ).
cnf(i_0_1711,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(split_conjunct,[status(thm)],[i_0_1002]),
[final] ).
cnf(i_0_1712,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_1003]),
[final] ).
cnf(i_0_1713,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_1004]),
[final] ).
cnf(i_0_1714,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_1004]),
[final] ).
cnf(i_0_1715,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1716,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_917]),
[final] ).
cnf(i_0_1717,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1005]),
[final] ).
cnf(i_0_1718,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1006]),
[final] ).
cnf(i_0_1719,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_1007]),
[final] ).
cnf(i_0_1720,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1008]),
[final] ).
cnf(i_0_1721,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_1009]),
[final] ).
cnf(i_0_1722,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_1010]),
[final] ).
cnf(i_0_1723,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_1011]),
[final] ).
cnf(i_0_1724,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_1012]),
[final] ).
cnf(i_0_1725,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_990]),
[final] ).
cnf(i_0_1726,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_991]),
[final] ).
cnf(i_0_1727,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_992]),
[final] ).
cnf(i_0_1728,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_1013]),
[final] ).
cnf(i_0_1729,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_1014]),
[final] ).
cnf(i_0_1730,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_1015]),
[final] ).
cnf(i_0_1731,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_1016]),
[final] ).
cnf(i_0_1732,plain,
c_List_Olist_Olist__size(X1,X2,c_List_Olist_ONil(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1733,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_1018]),
[final] ).
cnf(i_0_1734,plain,
c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1019]),
[final] ).
cnf(i_0_1735,plain,
c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1020]),
[final] ).
cnf(i_0_1736,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_1737,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_1004]),
[final] ).
cnf(i_0_1738,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_1739,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_1021]),
[final] ).
cnf(i_0_1740,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_1022]),
[final] ).
cnf(i_0_1741,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_1023]),
[final] ).
cnf(i_0_1742,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_1024]),
[final] ).
cnf(i_0_1743,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_1025]),
[final] ).
cnf(i_0_1744,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_1026]),
[final] ).
cnf(i_0_1745,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1027]),
[final] ).
cnf(i_0_1746,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_1747,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1748,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1749,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1750,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1751,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_608]),
[final] ).
cnf(i_0_1752,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_1033]),
[final] ).
cnf(i_0_1753,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1034]),
[final] ).
cnf(i_0_1754,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_1755,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_1756,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1757,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_1758,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_1759,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1760,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1761,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1762,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1763,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1044]),
[final] ).
cnf(i_0_1764,plain,
c_List_Odistinct(X1,c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1765,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_1046]),
[final] ).
cnf(i_0_1766,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_1047]),
[final] ).
cnf(i_0_1767,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_1768,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_1769,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_1770,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1771,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_1772,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1773,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_1774,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_1775,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_1776,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_1777,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_1778,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_1779,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_1780,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_1781,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_1782,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_1783,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_1784,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_1785,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_1786,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_1787,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_1788,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_1789,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_1790,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1791,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1792,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1793,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1794,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1795,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1796,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1797,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1798,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1799,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_1800,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1801,plain,
v_c____ != v_d____,
inference(split_conjunct,[status(thm)],[fact__096c_A_126_061_Ad_096]),
[final] ).
cnf(i_0_1802,axiom,
X1 = X1 ).
cnf(i_0_1803,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1804,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1805,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1806,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1807,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1808,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1809,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1810,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1811,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1812,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1813,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1814,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1815,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1816,axiom,
( X1 != X2
| esk21_2(X1,X3) = esk21_2(X2,X3) ) ).
cnf(i_0_1817,axiom,
( X1 != X2
| esk21_2(X3,X1) = esk21_2(X3,X2) ) ).
cnf(i_0_1818,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_1819,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_1820,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_1821,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_1822,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_1823,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_1824,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1825,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1826,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1827,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1828,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1829,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1830,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1831,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1832,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1833,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1834,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1835,axiom,
( X1 != X2
| esk45_5(X1,X3,X4,X5,X6) = esk45_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1836,axiom,
( X1 != X2
| esk45_5(X3,X1,X4,X5,X6) = esk45_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1837,axiom,
( X1 != X2
| esk45_5(X3,X4,X1,X5,X6) = esk45_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1838,axiom,
( X1 != X2
| esk45_5(X3,X4,X5,X1,X6) = esk45_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1839,axiom,
( X1 != X2
| esk45_5(X3,X4,X5,X6,X1) = esk45_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1840,axiom,
( X1 != X2
| c_List_Olist_OCons(X1,X3,X4) = c_List_Olist_OCons(X2,X3,X4) ) ).
cnf(i_0_1841,axiom,
( X1 != X2
| c_List_Olist_OCons(X3,X1,X4) = c_List_Olist_OCons(X3,X2,X4) ) ).
cnf(i_0_1842,axiom,
( X1 != X2
| c_List_Olist_OCons(X3,X4,X1) = c_List_Olist_OCons(X3,X4,X2) ) ).
cnf(i_0_1843,axiom,
( X1 != X2
| esk44_4(X1,X3,X4,X5) = esk44_4(X2,X3,X4,X5) ) ).
cnf(i_0_1844,axiom,
( X1 != X2
| esk44_4(X3,X1,X4,X5) = esk44_4(X3,X2,X4,X5) ) ).
cnf(i_0_1845,axiom,
( X1 != X2
| esk44_4(X3,X4,X1,X5) = esk44_4(X3,X4,X2,X5) ) ).
cnf(i_0_1846,axiom,
( X1 != X2
| esk44_4(X3,X4,X5,X1) = esk44_4(X3,X4,X5,X2) ) ).
cnf(i_0_1847,axiom,
( X1 != X2
| esk41_3(X1,X3,X4) = esk41_3(X2,X3,X4) ) ).
cnf(i_0_1848,axiom,
( X1 != X2
| esk41_3(X3,X1,X4) = esk41_3(X3,X2,X4) ) ).
cnf(i_0_1849,axiom,
( X1 != X2
| esk41_3(X3,X4,X1) = esk41_3(X3,X4,X2) ) ).
cnf(i_0_1850,axiom,
( X1 != X2
| esk6_4(X1,X3,X4,X5) = esk6_4(X2,X3,X4,X5) ) ).
cnf(i_0_1851,axiom,
( X1 != X2
| esk6_4(X3,X1,X4,X5) = esk6_4(X3,X2,X4,X5) ) ).
cnf(i_0_1852,axiom,
( X1 != X2
| esk6_4(X3,X4,X1,X5) = esk6_4(X3,X4,X2,X5) ) ).
cnf(i_0_1853,axiom,
( X1 != X2
| esk6_4(X3,X4,X5,X1) = esk6_4(X3,X4,X5,X2) ) ).
cnf(i_0_1854,axiom,
( X1 != X2
| esk5_4(X1,X3,X4,X5) = esk5_4(X2,X3,X4,X5) ) ).
cnf(i_0_1855,axiom,
( X1 != X2
| esk5_4(X3,X1,X4,X5) = esk5_4(X3,X2,X4,X5) ) ).
cnf(i_0_1856,axiom,
( X1 != X2
| esk5_4(X3,X4,X1,X5) = esk5_4(X3,X4,X2,X5) ) ).
cnf(i_0_1857,axiom,
( X1 != X2
| esk5_4(X3,X4,X5,X1) = esk5_4(X3,X4,X5,X2) ) ).
cnf(i_0_1858,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_1859,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X1,X3,X4,X5,X6) = c_List_Olist_Olist__case(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1860,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X3,X1,X4,X5,X6) = c_List_Olist_Olist__case(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1861,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X3,X4,X1,X5,X6) = c_List_Olist_Olist__case(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1862,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X3,X4,X5,X1,X6) = c_List_Olist_Olist__case(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1863,axiom,
( X1 != X2
| c_List_Olist_Olist__case(X3,X4,X5,X6,X1) = c_List_Olist_Olist__case(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1864,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).
cnf(i_0_1865,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).
cnf(i_0_1866,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).
cnf(i_0_1867,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_1869,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_1870,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_1871,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X1,X3)
| c_Nitpick_Orefl_H(X2,X3) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| ~ c_Nitpick_Orefl_H(X3,X1)
| c_Nitpick_Orefl_H(X3,X2) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| ~ c_List_Odistinct(X1,X3)
| c_List_Odistinct(X2,X3) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| ~ c_List_Odistinct(X3,X1)
| c_List_Odistinct(X3,X2) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1920,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_1921,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_1922,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_1923,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_1924,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_1925,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_1926,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1935,plain,
X1 = X1,
inference(equality_inference,[],[1066]) ).
cnf(i_0_1964,plain,
X1 = X1,
inference(equality_inference,[],[1269]) ).
cnf(i_0_1970,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[1428]) ).
cnf(i_0_1972,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(equality_inference,[],[1496]) ).
cnf(i_0_1977,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(equality_inference,[],[1558]) ).
cnf(i_0_1983,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1626]) ).
cnf(i_0_1984,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1627]) ).
cnf(i_0_1988,plain,
X1 = X1,
inference(equality_inference,[],[1636]) ).
cnf(i_0_1989,plain,
X1 = X1,
inference(equality_inference,[],[1637]) ).
cnf(i_0_1990,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1647]) ).
cnf(i_0_1992,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1655]) ).
cnf(i_0_1993,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1656]) ).
cnf(i_0_1995,plain,
X1 = X1,
inference(equality_inference,[],[1663]) ).
cnf(i_0_1996,plain,
X1 = X1,
inference(equality_inference,[],[1664]) ).
cnf(i_0_1998,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[1668]) ).
cnf(i_0_2000,plain,
X1 = X1,
inference(equality_inference,[],[1677]) ).
cnf(i_0_2004,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(equality_inference,[],[1717]) ).
cnf(i_0_2005,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1718]) ).
cnf(i_0_2009,plain,
X1 = X1,
inference(equality_inference,[],[1746]) ).
cnf(i_0_2013,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_1458]) ).
cnf(i_0_2053,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1629]) ).
cnf(i_0_2065,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1598]) ).
cnf(i_0_2068,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1629]) ).
cnf(i_0_2073,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2080,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2083,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1671]) ).
cnf(i_0_2086,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1671]) ).
cnf(i_0_2089,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1556]) ).
cnf(i_0_2106,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1720]) ).
cnf(i_0_2127,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1544]) ).
cnf(i_0_2130,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1544]) ).
cnf(i_0_2147,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1544]) ).
cnf(i_0_2165,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1544]) ).
cnf(i_0_2170,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1629]) ).
cnf(i_0_2181,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1557]) ).
cnf(i_0_2186,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1570]) ).
cnf(i_0_2189,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1711]) ).
cnf(i_0_2190,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1557]) ).
cnf(i_0_2193,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_1458]) ).
cnf(i_0_2217,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2257,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2283,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1598]) ).
cnf(i_0_2295,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_1458]) ).
cnf(i_0_2298,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_1458]) ).
cnf(i_0_2299,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1557]) ).
cnf(i_0_2302,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1629]) ).
cnf(i_0_2305,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2308,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2314,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1557]) ).
cnf(i_0_2324,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oinsert(X1,X3,X2))),
inference(rename_variables,[],[i_0_1458]) ).
cnf(i_0_2327,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(rename_variables,[],[i_0_1498]) ).
cnf(i_0_2330,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1544]) ).
cnf(i_0_2336,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1761]) ).
cnf(i_0_2345,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1557]) ).
cnf(i_0_2349,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2351,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2353,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2357,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2359,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2367,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1598]) ).
cnf(i_0_2368,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1711]) ).
cnf(i_0_2369,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(rename_variables,[],[i_0_1702]) ).
cnf(i_0_2374,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2377,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2380,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2383,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1671]) ).
cnf(i_0_2386,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2396,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_1741]) ).
cnf(i_0_2399,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1711]) ).
cnf(i_0_2402,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1710]) ).
cnf(i_0_2406,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1557]) ).
cnf(i_0_2407,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1763]) ).
cnf(i_0_2414,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1544]) ).
cnf(i_0_2419,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1711]) ).
cnf(i_0_2420,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2423,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1710]) ).
cnf(i_0_2424,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1770]) ).
cnf(i_0_2436,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1703]) ).
cnf(i_0_2437,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1703]) ).
cnf(i_0_2440,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1711]) ).
cnf(i_0_2443,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1710]) ).
cnf(i_0_2447,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1703]) ).
cnf(i_0_2448,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X1,X2,X3),
inference(rename_variables,[],[i_0_1704]) ).
cnf(i_0_2449,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1710]) ).
cnf(i_0_2453,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_1741]) ).
cnf(i_0_2457,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1703]) ).
cnf(i_0_2458,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1710]) ).
cnf(c_0_1800,plain,
( X1 = esk44_4(X2,X3,X4,X5)
| X2 != hAPP(X3,X1)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_Set_Oimage(X5,X4,X3,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X5,X4,X3,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
i_0_1179 ).
cnf(c_0_1801,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,X5) ),
i_0_1244 ).
cnf(c_0_1802,plain,
( X1 = esk44_4(X2,X3,X4,X5)
| X2 != hAPP(X3,X1)
| ~ c_Fun_Oinj__on(X5,X4,X3,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(csr,[status(thm)],[c_0_1800,c_0_1801]) ).
cnf(c_0_1803,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
i_0_1570 ).
cnf(c_0_1804,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
i_0_1745 ).
cnf(c_0_1805,plain,
( X1 = hAPP(c_Nat_OSuc,esk34_1(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
i_0_1613 ).
cnf(c_0_1806,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) ),
i_0_1676 ).
cnf(c_0_1807,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))) ),
i_0_1306 ).
cnf(c_0_1808,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
i_0_1759 ).
cnf(c_0_1809,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
i_0_1780 ).
cnf(c_0_1810,plain,
( X1 = esk44_4(X2,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,X1) ),
inference(spm,[status(thm)],[c_0_1802,c_0_1803]) ).
cnf(c_0_1811,plain,
( esk34_1(X1) = X2
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_1804,c_0_1805]),c_0_1806]) ).
cnf(c_0_1812,plain,
( X1 = hAPP(X2,esk44_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))) ),
i_0_1171 ).
cnf(c_0_1813,plain,
( c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_1807,c_0_1803]) ).
cnf(c_0_1814,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
i_0_1597 ).
cnf(c_0_1815,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,c_Set_Oimage(X1,X3,X4,X2))
| ~ c_Fun_Oinj__on(X1,X3,X4,X2) ),
i_0_1259 ).
cnf(c_0_1816,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(spm,[status(thm)],[c_0_1808,c_0_1809]) ).
cnf(c_0_1817,plain,
esk44_4(hAPP(c_Nat_OSuc,X1),c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = X1,
inference(er,[status(thm)],[c_0_1810]) ).
cnf(c_0_1818,plain,
( hAPP(X1,esk5_4(X2,X1,X3,X4)) = hAPP(X1,esk6_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
i_0_1252 ).
cnf(c_0_1819,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| esk5_4(X4,X3,X2,X1) != esk6_4(X4,X3,X2,X1) ),
i_0_1285 ).
cnf(c_0_1820,plain,
esk34_1(hAPP(c_Nat_OSuc,X1)) = X1,
inference(er,[status(thm)],[c_0_1811]) ).
cnf(c_0_1821,plain,
( hAPP(c_Nat_OSuc,esk44_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat)) = X1
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1812,c_0_1813]),c_0_1803]),c_0_1814])]) ).
cnf(c_0_1822,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2) ),
inference(spm,[status(thm)],[c_0_1815,c_0_1816]) ).
cnf(c_0_1823,plain,
c_Fun_Oinj__on(X1,X2,c_Nat_OSuc,X3),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1817,c_0_1818]),c_0_1817]),c_0_1819]) ).
cnf(c_0_1824,plain,
( esk44_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk34_1(X1)
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(spm,[status(thm)],[c_0_1820,c_0_1821]) ).
cnf(c_0_1825,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_1822,c_0_1823]) ).
cnf(c_0_1826,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)),
i_0_1640 ).
cnf(c_0_1827,plain,
esk44_4(X1,c_Nat_OSuc,tc_Nat_Onat,tc_Nat_Onat) = esk34_1(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1824,c_0_1825])]) ).
cnf(c_0_1828,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)) ),
i_0_1549 ).
cnf(c_0_1829,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk34_1(X2))) = 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)),X2)) ),
inference(spm,[status(thm)],[c_0_1826,c_0_1805]) ).
cnf(c_0_1830,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) ),
i_0_1665 ).
cnf(c_0_1831,plain,
hAPP(c_Nat_OSuc,esk34_1(X1)) = X1,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1821,c_0_1825])]),c_0_1827]) ).
cnf(c_0_1832,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
inference(spm,[status(thm)],[c_0_1828,c_0_1829]) ).
cnf(c_0_1833,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_1830,c_0_1831]) ).
cnf(c_0_1834,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(spm,[status(thm)],[c_0_1832,c_0_1833]) ).
cnf(c_0_1835,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
i_0_1741 ).
cnf(c_0_1836,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
i_0_1661 ).
cnf(c_0_1837,plain,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_1834,c_0_1835])]),c_0_1836]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT163+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n025.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:58:58 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 155.69/125.14 % Version : CSE_E---1.7
% 155.69/125.14 % Problem : theBenchmark.p
% 155.69/125.14 % SZS status Theorem for theBenchmark.p
% 155.69/125.14 % SZS output start CNFRefutation
% See solution above
% 235.07/204.58 % Total time : 123.565s
%------------------------------------------------------------------------------