%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT162+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 : n018.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 144.41s 116.04s
% Output : CNFRefutation 233.52s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1063)
% 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)))))
=> ( ! [X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),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____)),X52))),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,
! [X20,X7,X10,X1,X34,X2,X28,X5] :
( c_Finite__Set_Ofolding__image__simple(X5,X28,X2,X34,X1,X10)
=> ( c_Finite__Set_Ofinite(X28,X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X28),X20),X7))
=> hAPP(X10,c_Set_Oinsert(X28,X20,X7)) = hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X10,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
fof(fact_pigeonhole,axiom,
! [X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X5,c_Set_Oimage(X28,X5,X2,X7))),c_Finite__Set_Ocard(X28,X7)))
=> ~ c_Fun_Oinj__on(X28,X5,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).
fof(fact_notin__Lin__iff,axiom,
! [X23,X20,X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),c_Arrow__Order__Mirabelle_OLin))
=> ( X20 != X23
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X23)),X32))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X20)),X32)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X21,X22,X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X22),X21)),X32))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_PiE,axiom,
! [X20,X6,X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X28)),X2),c_FuncSet_OPi(X5,X28,X7,X6)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X28),hAPP(X2,X20)),hAPP(X6,X20)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_in__measures_I1_J,axiom,
! [X23,X20,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).
fof(fact_subset__insert,axiom,
! [X6,X7,X20,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),c_Set_Oinsert(X5,X20,X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [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_b____),v_a____)),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_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X50] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X50))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X50),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_less__fun__def,axiom,
! [X1,X2,X5,X28] :
( class_Orderings_Oord(X28)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X28)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X28),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X28),X1),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_add__leE,axiom,
! [X13,X56,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X56)),X13))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56),X13)) ) ),
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,
~ ! [X25] : ~ 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,X25,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,
! [X8,X24] :
( ~ hBOOL(hAPP(X24,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X24,X8))
=> ? [X61] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),X8))
& ! [X65] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65),X61))
=> ~ hBOOL(hAPP(X24,X65)) )
& hBOOL(hAPP(X24,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,
! [X21,X6,X22,X5] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X22),X6))
=> X22 = X21 )
=> hBOOL(hAPP(hAPP(c_member(X5),X22),c_Set_Oinsert(X5,X21,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
fof(fact_insert__ident,axiom,
! [X6,X7,X20,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X6))
=> ( c_Set_Oinsert(X5,X20,X7) = c_Set_Oinsert(X5,X20,X6)
<=> X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(fact_not__less__eq__eq,axiom,
! [X8,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8)),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X8,X14] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_xt1_I9_J,axiom,
! [X30,X29,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X30))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X20))
| X20 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_order__less__asym,axiom,
! [X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X29,X30,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_card_Oinsert,axiom,
! [X20,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X5,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert) ).
fof(fact_less__le__not__le,axiom,
! [X23,X20,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X23),X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_card__insert__if,axiom,
! [X20,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)) = c_Finite__Set_Ocard(X5,X7) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X5,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X14,X8] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X14))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,X14)))
<=> X8 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [X17,X13] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X17))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),hAPP(c_Nat_OSuc,X17)))
=> X17 = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucE,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X13)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
=> X17 = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> X20 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_linorder__not__less,axiom,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X23),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_leD,axiom,
! [X16,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__le,axiom,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_card__insert__disjoint,axiom,
! [X20,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X5,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_le__SucE,axiom,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),hAPP(c_Nat_OSuc,X13)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
=> X17 = hAPP(c_Nat_OSuc,X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X13] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X13)),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
<=> X20 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_not__one__less__zero,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X15,X16,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X16 != X15
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__cases,axiom,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ( X16 != X15
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( X16 != X15
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X20,X23,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X20))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> X20 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_not__leE,axiom,
! [X16,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__one__le__zero,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X15,X16] :
( X16 != X15
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_equalityE,axiom,
! [X5,X6,X7] :
( X7 = X6
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_order__less__irrefl,axiom,
! [X16,X5] :
( class_Orderings_Opreorder(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_linorder__le__cases,axiom,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_not__less0,axiom,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__nat__zero__code,axiom,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_less__zeroE,axiom,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__irrefl__nat,axiom,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(help_c__fequal__1,axiom,
! [X23,X20] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X20),X23))
| X20 = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_card__infinite,axiom,
! [X7,X5] :
( ~ c_Finite__Set_Ofinite(X5,X7)
=> c_Finite__Set_Ocard(X5,X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__infinite) ).
fof(conj_0,conjecture,
hBOOL(hAPP(hAPP(c_member(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',conj_0) ).
fof(fact__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_G_Aa_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_096,axiom,
? [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)))))
& ! [X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),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____)),X52))),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,
! [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))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X8))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PiProf) ).
fof(fact_n_I2_J,axiom,
! [X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),v_n____))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),X52))),v_Lab____)),v_Lba____)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n_I2_J) ).
fof(fact_pred__subset__eq2,axiom,
! [X11,X12,X28,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X28,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_fun(X28,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X28,tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_fun(X28,tc_HOL_Obool)),X5,c_COMBC(X28,tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X28,tc_prod(X5,X28)),tc_fun(X28,tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X28),tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool),X28,c_member(tc_prod(X5,X28)))),c_Product__Type_OPair(X5,X28)))),X12)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_fun(X28,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X28,tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_fun(X28,tc_HOL_Obool)),X5,c_COMBC(X28,tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X28,tc_prod(X5,X28)),tc_fun(X28,tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X28),tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool),X28,c_member(tc_prod(X5,X28)))),c_Product__Type_OPair(X5,X28)))),X11)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact__C2_C,axiom,
! [X64,X24,X55,X38,X21,X22] :
( X22 != X21
=> ( X38 != X55
=> ( X22 != X55
=> ( X21 != X38
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X24),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(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),X22),X21)),hAPP(X24,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),X38),X55)),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),X22),X21)),hAPP(v_F,X24)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X38),X55)),hAPP(v_F,X64))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C2_C) ).
fof(fact__C1_C,axiom,
! [X64,X24,X55,X38,X21,X22] :
( X22 != X21
=> ( X38 != X55
=> ( X22 != X55
=> ( X21 != X38
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X24),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(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),X22),X21)),hAPP(X24,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),X38),X55)),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),X22),X21)),hAPP(v_F,X24)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X38),X55)),hAPP(v_F,X64))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_pairwise__neutrality,axiom,
! [X64,X24,X55,X38,X21,X22] :
( X22 != X21
=> ( X38 != X55
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X24),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(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),X22),X21)),hAPP(X24,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),X38),X55)),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),X22),X21)),hAPP(v_F,X24)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X38),X55)),hAPP(v_F,X64))) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
fof(fact_pred__equals__eq2,axiom,
! [X11,X12,X28,X5] :
( hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_fun(X28,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X28,tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_fun(X28,tc_HOL_Obool)),X5,c_COMBC(X28,tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X28,tc_prod(X5,X28)),tc_fun(X28,tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X28),tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool),X28,c_member(tc_prod(X5,X28)))),c_Product__Type_OPair(X5,X28)))),X12) = hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_fun(X28,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X28,tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_fun(X28,tc_HOL_Obool)),X5,c_COMBC(X28,tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X28,tc_prod(X5,X28)),tc_fun(X28,tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X28),tc_fun(tc_fun(tc_prod(X5,X28),tc_HOL_Obool),tc_HOL_Obool),X28,c_member(tc_prod(X5,X28)))),c_Product__Type_OPair(X5,X28)))),X11)
<=> X12 = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_Pi__mono,axiom,
! [X48,X6,X28,X7,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),hAPP(X6,X3)),hAPP(X48,X3))) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X28),tc_HOL_Obool),c_FuncSet_OPi(X5,X28,X7,X6)),c_FuncSet_OPi(X5,X28,X7,X48))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_Pi__I,axiom,
! [X6,X2,X28,X7,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> hBOOL(hAPP(hAPP(c_member(X28),hAPP(X2,X3)),hAPP(X6,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X28)),X2),c_FuncSet_OPi(X5,X28,X7,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_IIA__def,axiom,
! [X10] :
( c_Arrow__Order__Mirabelle_OIIA(X10)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X41] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X41),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(X41,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(X10,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(X10,X41))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact__C4_C,axiom,
! [X64,X24,X4,X21,X22] :
( X22 != X21
=> ( X21 != X4
=> ( X22 != 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))),X24),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(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),X22),X21)),hAPP(X24,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),X21),X4)),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),X22),X21)),hAPP(v_F,X24)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X4)),hAPP(v_F,X64))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C4_C) ).
fof(fact_dictatorI,axiom,
! [X9,X10] :
( 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))),X10),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,X9)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X67),X68)),hAPP(X10,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X10,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_in__lex__prod,axiom,
! [X53,X54,X55,X38,X21,X22,X28,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X28),tc_prod(X5,X28))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X28),tc_prod(X5,X28)),hAPP(hAPP(c_Product__Type_OPair(X5,X28),X22),X21)),hAPP(hAPP(c_Product__Type_OPair(X5,X28),X38),X55))),c_Wellfounded_Olex__prod(X5,X28,X54,X53)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X22),X38)),X54))
| ( X22 = X38
& hBOOL(hAPP(hAPP(c_member(tc_prod(X28,X28)),hAPP(hAPP(c_Product__Type_OPair(X28,X28),X21),X55)),X53)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact__C3_C,axiom,
! [X64,X24,X21,X22] :
( X22 != X21
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X24),c_Arrow__Order__Mirabelle_OProf))
=> ( hBOOL(hAPP(hAPP(c_member(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),X22),X21)),hAPP(X24,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),X21),X22)),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),X22),X21)),hAPP(v_F,X24)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),hAPP(v_F,X64))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__C3_C) ).
fof(fact_subset__image__iff,axiom,
! [X7,X2,X28,X6,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),c_Set_Oimage(X28,X5,X2,X7)))
<=> ? [X82] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),X82),X7))
& X6 = c_Set_Oimage(X28,X5,X2,X82) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_same__fstI,axiom,
! [X5,X12,X23,X45,X28,X20,X24] :
( hBOOL(hAPP(X24,X20))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28,X28)),hAPP(hAPP(c_Product__Type_OPair(X28,X28),X45),X23)),hAPP(X12,X20)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X28),tc_prod(X5,X28))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X28),tc_prod(X5,X28)),hAPP(hAPP(c_Product__Type_OPair(X5,X28),X20),X45)),hAPP(hAPP(c_Product__Type_OPair(X5,X28),X20),X23))),c_Recdef_Osame__fst(X5,X28,X24,X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X5,X28] :
( class_Orderings_Oord(X28)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X28),X2),X1))
<=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,hAPP(X2,X3)),hAPP(X1,X3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
! [X6,X7,X10,X1,X34,X2,X28,X5] :
( c_Finite__Set_Ofolding__image__simple__idem(X5,X28,X2,X34,X1,X10)
=> ( c_Finite__Set_Ofinite(X28,X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),X6),X7))
=> hAPP(hAPP(X2,hAPP(X10,X6)),hAPP(X10,X7)) = hAPP(X10,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [X20,X7,X10,X1,X34,X2,X28,X5] :
( c_Finite__Set_Ofolding__image__simple__idem(X5,X28,X2,X34,X1,X10)
=> ( c_Finite__Set_Ofinite(X28,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X28),X20),X7))
=> hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X10,X7)) = hAPP(X10,X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
! [X20,X7,X10,X1,X34,X2,X28,X5] :
( c_Finite__Set_Ofolding__image__simple__idem(X5,X28,X2,X34,X1,X10)
=> ( c_Finite__Set_Ofinite(X28,X7)
=> hAPP(X10,c_Set_Oinsert(X28,X20,X7)) = hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X10,X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [X20,X10,X1,X34,X2,X28,X5] :
( c_Finite__Set_Ofolding__image__simple__idem(X5,X28,X2,X34,X1,X10)
=> hAPP(hAPP(X2,X20),X20) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_card__bij__eq,axiom,
! [X1,X6,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),c_Set_Oimage(X5,X28,X2,X7)),X6))
=> ( c_Fun_Oinj__on(X28,X5,X1,X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X28,X5,X1,X6)),X7))
=> ( c_Finite__Set_Ofinite(X5,X7)
=> ( c_Finite__Set_Ofinite(X28,X6)
=> c_Finite__Set_Ocard(X5,X7) = c_Finite__Set_Ocard(X28,X6) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(fact_unanimity__def,axiom,
! [X10] :
( c_Arrow__Order__Mirabelle_Ounanimity(X10)
<=> ! [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(X10,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_card__bij,axiom,
! [X1,X6,X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X28)),X2),c_FuncSet_OPi(X5,X28,X7,hAPP(c_COMBK(tc_fun(X28,tc_HOL_Obool),X5),X6))))
=> ( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X28,X5)),X1),c_FuncSet_OPi(X28,X5,X6,hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X28),X7))))
=> ( c_Fun_Oinj__on(X28,X5,X1,X6)
=> ( c_Finite__Set_Ofinite(X5,X7)
=> ( c_Finite__Set_Ofinite(X28,X6)
=> c_Finite__Set_Ocard(X5,X7) = c_Finite__Set_Ocard(X28,X6) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij) ).
fof(fact_pred__subset__eq,axiom,
! [X11,X12,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X12)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X12),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_in__above,axiom,
! [X23,X20,X32,X21,X22] :
( X22 != X21
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),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),X20),X23)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X32),X22),X21)))
<=> ( X20 != X23
& ( X20 = X21
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X22),X23)),X32)) )
& ( X20 != X21
=> ( ( X23 = X21
=> ( X20 = X22
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X22)),X32)) ) )
& ( X23 != X21
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X23)),X32)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_in__below,axiom,
! [X23,X20,X32,X21,X22] :
( X22 != X21
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),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),X20),X23)),c_Arrow__Order__Mirabelle_Obelow(X32,X22,X21)))
<=> ( X20 != X23
& ( X23 = X22
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X21)),X32)) )
& ( X23 != X22
=> ( ( X20 = X22
=> ( X23 = X21
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X23)),X32)) ) )
& ( X20 != X22
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X23)),X32)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_inv__into__into,axiom,
! [X7,X2,X28,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X20),c_Set_Oimage(X28,X5,X2,X7)))
=> hBOOL(hAPP(hAPP(c_member(X28),hAPP(c_Hilbert__Choice_Oinv__into(X28,X5,X7,X2),X20)),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).
fof(fact_inj__image__subset__iff,axiom,
! [X6,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),c_Set_Oimage(X5,X28,X2,X7)),c_Set_Oimage(X5,X28,X2,X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_in__finite__psubset,axiom,
! [X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X5,tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X7),X6)),c_Wellfounded_Ofinite__psubset(X5)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
& c_Finite__Set_Ofinite(X5,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_funcset__image,axiom,
! [X6,X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X28)),X2),c_FuncSet_OPi(X5,X28,X7,hAPP(c_COMBK(tc_fun(X28,tc_HOL_Obool),X5),X6))))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),c_Set_Oimage(X5,X28,X2,X7)),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__image) ).
fof(fact_inv__into__injective,axiom,
! [X23,X20,X2,X7,X28,X5] :
( hAPP(c_Hilbert__Choice_Oinv__into(X5,X28,X7,X2),X20) = hAPP(c_Hilbert__Choice_Oinv__into(X5,X28,X7,X2),X23)
=> ( hBOOL(hAPP(hAPP(c_member(X28),X20),c_Set_Oimage(X5,X28,X2,X7)))
=> ( hBOOL(hAPP(hAPP(c_member(X28),X23),c_Set_Oimage(X5,X28,X2,X7)))
=> X20 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).
fof(fact_Ints__odd__less__0,axiom,
! [X22,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X22),c_Int_Oring__1__class_OInts(X5)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),X22)),X22)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X22),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_range__ex1__eq,axiom,
! [X21,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X28),X21),c_Set_Oimage(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
<=> ? [X3] :
( X21 = hAPP(X2,X3)
& ! [X80] :
( X21 = hAPP(X2,X80)
=> X80 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_card__image__le,axiom,
! [X2,X28,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X28,c_Set_Oimage(X5,X28,X2,X7))),c_Finite__Set_Ocard(X5,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).
fof(fact_inj__on__strict__subset,axiom,
! [X7,X6,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X6)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X28,tc_HOL_Obool)),c_Set_Oimage(X5,X28,X2,X7)),c_Set_Oimage(X5,X28,X2,X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_endo__inj__surj,axiom,
! [X2,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X5,X5,X2,X7)),X7))
=> ( c_Fun_Oinj__on(X5,X5,X2,X7)
=> c_Set_Oimage(X5,X5,X2,X7) = X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_in__measures_I2_J,axiom,
! [X42,X2,X23,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_List_Omeasures(X5,c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat),X2,X42))))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X23)))
| ( hAPP(X2,X20) = hAPP(X2,X23)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_List_Omeasures(X5,X42))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).
fof(fact_card__inj__on__le,axiom,
! [X6,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),c_Set_Oimage(X5,X28,X2,X7)),X6))
=> ( c_Finite__Set_Ofinite(X28,X6)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X7)),c_Finite__Set_Ocard(X28,X6))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_image__iff,axiom,
! [X7,X2,X28,X34,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X34),c_Set_Oimage(X28,X5,X2,X7)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X28),X3),X7))
& X34 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_measures__lesseq,axiom,
! [X42,X5,X23,X20,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X20)),hAPP(X2,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_List_Omeasures(X5,X42)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_List_Omeasures(X5,c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat),X2,X42)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__lesseq) ).
fof(fact_card__inj,axiom,
! [X6,X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X28)),X2),c_FuncSet_OPi(X5,X28,X7,hAPP(c_COMBK(tc_fun(X28,tc_HOL_Obool),X5),X6))))
=> ( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( c_Finite__Set_Ofinite(X28,X6)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X7)),c_Finite__Set_Ocard(X28,X6))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj) ).
fof(fact_Pi__anti__mono,axiom,
! [X6,X28,X7,X66,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X66),X7))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X28),tc_HOL_Obool),c_FuncSet_OPi(X5,X28,X7,X6)),c_FuncSet_OPi(X5,X28,X66,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_finite__range__imageI,axiom,
! [X2,X40,X1,X28,X5] :
( c_Finite__Set_Ofinite(X5,c_Set_Oimage(X28,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))))
=> c_Finite__Set_Ofinite(X40,c_Set_Oimage(X28,X40,hAPP(c_COMBB(X5,X40,X28,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_const__Lin__Prof,axiom,
! [X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),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),X32)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_funcset__mem,axiom,
! [X20,X6,X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X28)),X2),c_FuncSet_OPi(X5,X28,X7,hAPP(c_COMBK(tc_fun(X28,tc_HOL_Obool),X5),X6))))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> hBOOL(hAPP(hAPP(c_member(X28),hAPP(X2,X20)),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_image__mono,axiom,
! [X2,X28,X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),c_Set_Oimage(X5,X28,X2,X7)),c_Set_Oimage(X5,X28,X2,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_mlex__leq,axiom,
! [X12,X5,X23,X20,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X20)),hAPP(X2,X23)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),X12))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_Wellfounded_Omlex__prod(X5,X2,X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_in__rel__def,axiom,
! [X23,X20,X12,X28,X5] :
( c_FunDef_Oin__rel(X5,X28,X12,X20,X23)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X28)),hAPP(hAPP(c_Product__Type_OPair(X5,X28),X20),X23)),X12)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_f__inv__into__f,axiom,
! [X7,X2,X28,X23,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X23),c_Set_Oimage(X28,X5,X2,X7)))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X28,X5,X7,X2),X23)) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_surj__iff__all,axiom,
! [X2,X5,X28] :
( c_Set_Oimage(X28,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X28,X5,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)),X2),X3)) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff__all) ).
fof(fact_inj__on__inv__into,axiom,
! [X7,X2,X28,X6,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),c_Set_Oimage(X28,X5,X2,X7)))
=> c_Fun_Oinj__on(X5,X28,c_Hilbert__Choice_Oinv__into(X28,X5,X7,X2),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).
fof(fact_in__mkbot,axiom,
! [X34,X32,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X23)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X32),X34)))
<=> ( X23 != X34
& ( X20 = X34
=> X20 != X23 )
& ( X20 != X34
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X23)),X32)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X34,X32,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X23)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X32),X34)))
<=> ( X20 != X34
& ( X23 = X34
=> X20 != X23 )
& ( X23 != X34
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X23)),X32)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(help_c__COMBS__1,axiom,
! [X12,X70,X24,X5,X40,X28] : hAPP(c_COMBS(X28,X40,X5,X24,X70),X12) = hAPP(hAPP(X24,X12),hAPP(X70,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_Pi__mem,axiom,
! [X20,X6,X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X28)),X2),c_FuncSet_OPi(X5,X28,X7,X6)))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> hBOOL(hAPP(hAPP(c_member(X28),hAPP(X2,X20)),hAPP(X6,X20))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_inj__image__mem__iff,axiom,
! [X7,X22,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X28),hAPP(X2,X22)),c_Set_Oimage(X5,X28,X2,X7)))
<=> hBOOL(hAPP(hAPP(c_member(X5),X22),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_image__surj__f__inv__f,axiom,
! [X7,X2,X5,X28] :
( c_Set_Oimage(X28,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
=> c_Set_Oimage(X28,X5,X2,c_Set_Oimage(X5,X28,c_Hilbert__Choice_Oinv__into(X28,X5,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)),X2),X7)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).
fof(fact_image__inv__into__cancel,axiom,
! [X81,X66,X7,X2,X5,X28] :
( c_Set_Oimage(X28,X5,X2,X7) = X66
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X81),X66))
=> c_Set_Oimage(X28,X5,X2,c_Set_Oimage(X5,X28,c_Hilbert__Choice_Oinv__into(X28,X5,X7,X2),X81)) = X81 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_inj__on__def,axiom,
! [X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X7))
=> ! [X41] :
( hBOOL(hAPP(hAPP(c_member(X5),X41),X7))
=> ( hAPP(X2,X3) = hAPP(X2,X41)
=> X3 = X41 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_above__Lin,axiom,
! [X32,X23,X20] :
( X20 != X23
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),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,X32),X20),X23)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_range__composition,axiom,
! [X1,X2,X40,X5,X28] : c_Set_Oimage(X28,X5,hAPP(c_COMBB(X40,X5,X28,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) = c_Set_Oimage(X40,X5,X2,c_Set_Oimage(X28,X40,X1,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__composition) ).
fof(fact_measures__less,axiom,
! [X42,X5,X23,X20,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_List_Omeasures(X5,c_List_Olist_OCons(tc_fun(X5,tc_Nat_Onat),X2,X42)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__less) ).
fof(fact_finite__surj__inj,axiom,
! [X2,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),c_Set_Oimage(X5,X5,X2,X7)))
=> c_Fun_Oinj__on(X5,X5,X2,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_dictator__def,axiom,
! [X9,X10] :
( c_Arrow__Order__Mirabelle_Odictator(X10,X9)
<=> ! [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(X10,X3) = hAPP(X3,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_inj__fun,axiom,
! [X40,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X5,tc_fun(X40,X28),hAPP(c_COMBB(X28,tc_fun(X40,X28),X5,c_COMBK(X28,X40)),X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__fun) ).
fof(fact_funcset__id,axiom,
! [X7,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X5)),c_COMBI(X5)),c_FuncSet_OPi(X5,X5,X7,hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X7)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_image__image,axiom,
! [X7,X1,X40,X2,X5,X28] : c_Set_Oimage(X28,X5,X2,c_Set_Oimage(X40,X28,X1,X7)) = c_Set_Oimage(X40,X5,hAPP(c_COMBB(X28,X5,X40,X2),X1),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_below__Lin,axiom,
! [X32,X23,X20] :
( X20 != X23
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),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(X32,X20,X23)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_in__measure,axiom,
! [X2,X23,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_Wellfounded_Omeasure(X5,X2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_inv__into__image__cancel,axiom,
! [X11,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X11),X7))
=> c_Set_Oimage(X28,X5,c_Hilbert__Choice_Oinv__into(X5,X28,X7,X2),c_Set_Oimage(X5,X28,X2,X11)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).
fof(fact_finite__surj,axiom,
! [X2,X6,X28,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28,tc_HOL_Obool),X6),c_Set_Oimage(X5,X28,X2,X7)))
=> c_Finite__Set_Ofinite(X28,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(fact_mktop__Lin,axiom,
! [X20,X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),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,X32),X20)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_mkbot__Lin,axiom,
! [X20,X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),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,X32),X20)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_inv__image__comp,axiom,
! [X84,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> c_Set_Oimage(X28,X5,c_Hilbert__Choice_Oinv__into(X5,X28,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),c_Set_Oimage(X5,X28,X2,X84)) = X84 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__comp) ).
fof(fact_image__inv__f__f,axiom,
! [X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> c_Set_Oimage(X28,X5,c_Hilbert__Choice_Oinv__into(X5,X28,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),c_Set_Oimage(X5,X28,X2,X7)) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__f__f) ).
fof(fact_surj__f__inv__f,axiom,
! [X23,X2,X5,X28] :
( c_Set_Oimage(X28,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
=> hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X28,X5,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)),X2),X23)) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).
fof(fact_mlex__less,axiom,
! [X12,X5,X23,X20,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X20)),hAPP(X2,X23)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_Wellfounded_Omlex__prod(X5,X2,X12))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_surj__imp__inj__inv,axiom,
! [X2,X5,X28] :
( c_Set_Oimage(X28,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
=> c_Fun_Oinj__on(X5,X28,c_Hilbert__Choice_Oinv__into(X28,X5,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).
fof(fact_rangeI,axiom,
! [X28,X20,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X20)),c_Set_Oimage(X28,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_inj__imp__surj__inv,axiom,
! [X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> c_Set_Oimage(X28,X5,c_Hilbert__Choice_Oinv__into(X5,X28,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).
fof(fact_imageI,axiom,
! [X2,X28,X7,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> hBOOL(hAPP(hAPP(c_member(X28),hAPP(X2,X20)),c_Set_Oimage(X5,X28,X2,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact_list_Osimps_I5_J,axiom,
! [X39,X22,X46,X47,X28,X5] : c_List_Olist_Olist__case(X5,X28,X47,X46,c_List_Olist_OCons(X28,X22,X39)) = hAPP(hAPP(X46,X22),X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).
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__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_range__eqI,axiom,
! [X28,X5,X20,X2,X21] :
( X21 = hAPP(X2,X20)
=> hBOOL(hAPP(hAPP(c_member(X5),X21),c_Set_Oimage(X28,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_image__eqI,axiom,
! [X5,X7,X28,X20,X2,X21] :
( X21 = hAPP(X2,X20)
=> ( hBOOL(hAPP(hAPP(c_member(X28),X20),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X21),c_Set_Oimage(X28,X5,X2,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X28,X2,X21,X7,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( X21 = hAPP(X2,X20)
=> hBOOL(hAPP(hAPP(c_member(X28),X21),c_Set_Oimage(X5,X28,X2,X7))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__image__eq__iff,axiom,
! [X6,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Set_Oimage(X5,X28,X2,X7) = c_Set_Oimage(X5,X28,X2,X6)
<=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_add__less__cancel__right,axiom,
! [X21,X4,X22,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X4)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__right,axiom,
! [X29,X35,X30,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X35)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__left,axiom,
! [X21,X22,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X21)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__imp__less__left,axiom,
! [X29,X30,X35,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X29)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_list_Osimps_I4_J,axiom,
! [X46,X47,X28,X5] : c_List_Olist_Olist__case(X5,X28,X47,X46,c_List_Olist_ONil(X28)) = X47,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_finite__imageD,axiom,
! [X7,X2,X28,X5] :
( c_Finite__Set_Ofinite(X5,c_Set_Oimage(X28,X5,X2,X7))
=> ( c_Fun_Oinj__on(X28,X5,X2,X7)
=> c_Finite__Set_Ofinite(X28,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_psubset__trans,axiom,
! [X48,X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X6),X48))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X48)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_add__le__imp__le__right,axiom,
! [X29,X35,X30,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X35)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X21,X4,X22,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X4)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X29,X30,X35,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X29)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X21,X22,X4,X5] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X22)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X21)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_insert__subset,axiom,
! [X6,X7,X20,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5,X20,X7)),X6))
<=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(fact_inv__f__f,axiom,
! [X20,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> hAPP(c_Hilbert__Choice_Oinv__into(X5,X28,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),hAPP(X2,X20)) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__f) ).
fof(fact_inv__f__eq,axiom,
! [X23,X20,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hAPP(X2,X20) = X23
=> hAPP(c_Hilbert__Choice_Oinv__into(X5,X28,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),X23) = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__eq) ).
fof(fact_pred__equals__eq,axiom,
! [X11,X12,X5] :
( hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X12) = hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X11)
<=> X12 = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X8,X14,X60] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X8)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_inv__into__f__f,axiom,
! [X20,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> hAPP(c_Hilbert__Choice_Oinv__into(X5,X28,X7,X2),hAPP(X2,X20)) = X20 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__f) ).
fof(fact_inv__into__f__eq,axiom,
! [X23,X20,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( hAPP(X2,X20) = X23
=> hAPP(c_Hilbert__Choice_Oinv__into(X5,X28,X7,X2),X23) = X20 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [X2,X28,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( c_Finite__Set_Ocard(X28,c_Set_Oimage(X5,X28,X2,X7)) = c_Finite__Set_Ocard(X5,X7)
=> c_Fun_Oinj__on(X5,X28,X2,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X28,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( c_Fun_Oinj__on(X5,X28,X2,X7)
<=> c_Finite__Set_Ocard(X28,c_Set_Oimage(X5,X28,X2,X7)) = c_Finite__Set_Ocard(X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_insert__mono,axiom,
! [X22,X71,X48,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X48),X71))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oinsert(X5,X22,X48)),c_Set_Oinsert(X5,X22,X71))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).
fof(help_c__COMBB__1,axiom,
! [X12,X70,X24,X40,X5,X28] : hAPP(hAPP(c_COMBB(X28,X5,X40,X24),X70),X12) = hAPP(X24,hAPP(X70,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__strict__mono,axiom,
! [X69,X35,X29,X30,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X69))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X69))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_list_Osize_I2_J,axiom,
! [X39,X22,X78,X5] : c_List_Olist_Olist__size(X5,X78,c_List_Olist_OCons(X5,X22,X39)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X78,X22)),c_List_Olist_Olist__size(X5,X78,X39))),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,
! [X8,X14,X60] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X14)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X8)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_add__le__less__mono,axiom,
! [X69,X35,X29,X30,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),X29))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X35),X69))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X69))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X69,X35,X29,X30,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X35),X69))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X69))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_subset__psubset__trans,axiom,
! [X48,X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X6),X48))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X48)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X48,X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),X48))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X48)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_insert__image,axiom,
! [X2,X28,X7,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Set_Oinsert(X28,hAPP(X2,X20),c_Set_Oimage(X5,X28,X2,X7)) = c_Set_Oimage(X5,X28,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).
fof(fact_card__psubset,axiom,
! [X7,X6,X5] :
( c_Finite__Set_Ofinite(X5,X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X5,X7)),c_Finite__Set_Ocard(X5,X6)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(fact_third__alt,axiom,
! [X29,X30] :
( X30 != X29
=> ? [X31] : c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X30,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X29,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X31,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,X35,X29,X30,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),X29))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X35),X69))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X69))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X22,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X22)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X22),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X22,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X22)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X22),c_Groups_Ozero__class_Ozero(X5))) ) ),
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,
! [X6,X22,X2,X5,X28] : c_Set_Oimage(X28,X5,X2,c_Set_Oinsert(X28,X22,X6)) = c_Set_Oinsert(X5,hAPP(X2,X22),c_Set_Oimage(X28,X5,X2,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [X2,X5] :
( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Set_Oimage(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))
=> c_Fun_Oinj__on(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_subset__inj__on,axiom,
! [X7,X6,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> c_Fun_Oinj__on(X5,X28,X2,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_card__image,axiom,
! [X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> c_Finite__Set_Ocard(X28,c_Set_Oimage(X5,X28,X2,X7)) = c_Finite__Set_Ocard(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_add__neg__neg,axiom,
! [X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_Ints__add,axiom,
! [X21,X22,X5] :
( class_Rings_Oring__1(X5)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X22),c_Int_Oring__1__class_OInts(X5)))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X21),c_Int_Oring__1__class_OInts(X5)))
=> hBOOL(hAPP(hAPP(c_member(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X21)),c_Int_Oring__1__class_OInts(X5))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__add) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [X2,X5] :
( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> c_Set_Oimage(X5,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_add__strict__right__mono,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X35))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X29))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X22,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X22)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X22),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_add__nonpos__neg,axiom,
! [X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
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,
! [X6,X7,X28,X5] :
( c_Finite__Set_Ofinite(tc_sum(X5,X28),c_Sum__Type_OPlus(X5,X28,X7,X6))
<=> ( c_Finite__Set_Ofinite(X5,X7)
& c_Finite__Set_Ofinite(X28,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X6,X7,X28,X5] :
( c_Finite__Set_Ofinite(tc_sum(X5,X28),c_Sum__Type_OPlus(X5,X28,X7,X6))
=> c_Finite__Set_Ofinite(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [X6,X7,X28,X5] :
( c_Finite__Set_Ofinite(tc_sum(X5,X28),c_Sum__Type_OPlus(X5,X28,X7,X6))
=> c_Finite__Set_Ofinite(X28,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_add__right__mono,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X35))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X29))) ) ),
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,
! [X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_predicate2D,axiom,
! [X23,X20,X70,X24,X28,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X28,tc_HOL_Obool)),X24),X70))
=> ( hBOOL(hAPP(hAPP(X24,X20),X23))
=> hBOOL(hAPP(hAPP(X70,X20),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X70,X28,X5,X23,X20,X24] :
( hBOOL(hAPP(hAPP(X24,X20),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X28,tc_HOL_Obool)),X24),X70))
=> hBOOL(hAPP(hAPP(X70,X20),X23)) ) ),
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,
! [X23,X20,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X7))
=> ( hAPP(X2,X20) = hAPP(X2,X23)
<=> X20 = X23 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__onD,axiom,
! [X23,X20,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( hAPP(X2,X20) = hAPP(X2,X23)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X7))
=> X20 = X23 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_inj__on__contraD,axiom,
! [X23,X20,X7,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,X7)
=> ( X20 != X23
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X23),X7))
=> hAPP(X2,X20) != hAPP(X2,X23) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_add__leD1,axiom,
! [X13,X56,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X56)),X13))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X13,X56,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X56)),X13))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__pos__pos,axiom,
! [X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X29))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_ex__nat__less__eq,axiom,
! [X24,X8] :
( ? [X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X8))
& hBOOL(hAPP(X24,X52)) )
<=> ? [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),X8)))
& hBOOL(hAPP(X24,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,
! [X4,X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_psubset__card__mono,axiom,
! [X7,X6,X5] :
( c_Finite__Set_Ofinite(X5,X6)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X5,X7)),c_Finite__Set_Ocard(X5,X6))) ) ),
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,X35,X29,X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X69)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),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,
! [X24,X8] :
( ! [X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X52),X8))
=> hBOOL(hAPP(X24,X52)) )
<=> ! [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),X8)))
=> hBOOL(hAPP(X24,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_subset__trans,axiom,
! [X48,X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),X48))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X48)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_add__nonneg__pos,axiom,
! [X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X29))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X29))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_card__Plus__conv__if,axiom,
! [X6,X28,X7,X5] :
( ( ( c_Finite__Set_Ofinite(X5,X7)
& c_Finite__Set_Ofinite(X28,X6) )
=> c_Finite__Set_Ocard(tc_sum(X5,X28),c_Sum__Type_OPlus(X5,X28,X7,X6)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X5,X7)),c_Finite__Set_Ocard(X28,X6)) )
& ( ~ ( c_Finite__Set_Ofinite(X5,X7)
& c_Finite__Set_Ofinite(X28,X6) )
=> c_Finite__Set_Ocard(tc_sum(X5,X28),c_Sum__Type_OPlus(X5,X28,X7,X6)) = 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,
! [X6,X28,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( c_Finite__Set_Ofinite(X28,X6)
=> c_Finite__Set_Ocard(tc_sum(X5,X28),c_Sum__Type_OPlus(X5,X28,X7,X6)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X5,X7)),c_Finite__Set_Ocard(X28,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_pos__add__strict,axiom,
! [X35,X29,X30,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X35))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_card__insert__le,axiom,
! [X20,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X7)),c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__le) ).
fof(fact_Ints__odd__nonzero,axiom,
! [X22,X5] :
( class_Int_Oring__char__0(X5)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X22),c_Int_Oring__1__class_OInts(X5)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),X22)),X22) != c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X22,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X22)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_add__gr__0,axiom,
! [X8,X14] :
( 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),X14),X8)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_card__seteq,axiom,
! [X7,X6,X5] :
( c_Finite__Set_Ofinite(X5,X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X6)),c_Finite__Set_Ocard(X5,X7)))
=> X7 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_subset__insertI2,axiom,
! [X21,X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),c_Set_Oinsert(X5,X21,X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(fact_add__strict__increasing2,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X35))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),X35))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X29))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_splice_Osimps_I3_J,axiom,
! [X49,X15,X33,X16,X5] : c_List_Osplice(X5,c_List_Olist_OCons(X5,X16,X33),c_List_Olist_OCons(X5,X15,X49)) = c_List_Olist_OCons(X5,X16,c_List_Olist_OCons(X5,X15,c_List_Osplice(X5,X33,X49))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).
fof(fact_psubset__eq,axiom,
! [X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
& X7 != X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
| X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__imp__subset,axiom,
! [X6,X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X7),X6))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_insert__iff,axiom,
! [X7,X21,X22,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X22),c_Set_Oinsert(X5,X21,X7)))
<=> ( X22 = X21
| hBOOL(hAPP(hAPP(c_member(X5),X22),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
fof(fact_insertE,axiom,
! [X7,X21,X22,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X22),c_Set_Oinsert(X5,X21,X7)))
=> ( X22 != X21
=> hBOOL(hAPP(hAPP(c_member(X5),X22),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X22,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X22)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_Pi__UNIV,axiom,
! [X7,X28,X5] : c_FuncSet_OPi(X5,X28,X7,hAPP(c_COMBK(tc_fun(X28,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X28),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
fof(fact_add__increasing,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),X35))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X30,X29,X35,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X35))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_finite__Plus,axiom,
! [X6,X28,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( c_Finite__Set_Ofinite(X28,X6)
=> c_Finite__Set_Ofinite(tc_sum(X5,X28),c_Sum__Type_OPlus(X5,X28,X7,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(help_c__COMBC__1,axiom,
! [X12,X70,X24,X5,X40,X28] : hAPP(hAPP(hAPP(c_COMBC(X28,X40,X5),X24),X70),X12) = hAPP(hAPP(X24,X12),X70),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_set__eq__subset,axiom,
! [X5,X6,X7] :
( X7 = X6
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),X7)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),X7))
=> X7 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_set__rev__mp,axiom,
! [X6,X7,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> hBOOL(hAPP(hAPP(c_member(X5),X20),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_set__mp,axiom,
! [X20,X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X20),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_in__mono,axiom,
! [X20,X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X20),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_subsetD,axiom,
! [X4,X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X7))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_le__funD,axiom,
! [X20,X1,X2,X5,X28] :
( class_Orderings_Oord(X28)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X28),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,hAPP(X2,X20)),hAPP(X1,X20))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X20,X1,X2,X5,X28] :
( class_Orderings_Oord(X28)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X28),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X28,hAPP(X2,X20)),hAPP(X1,X20))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_finite__imageI,axiom,
! [X79,X28,X10,X5] :
( c_Finite__Set_Ofinite(X5,X10)
=> c_Finite__Set_Ofinite(X28,c_Set_Oimage(X5,X28,X79,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_card__mono,axiom,
! [X7,X6,X5] :
( c_Finite__Set_Ofinite(X5,X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X7)),c_Finite__Set_Ocard(X5,X6))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X35,X29,X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_inj__eq,axiom,
! [X23,X20,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hAPP(X2,X20) = hAPP(X2,X23)
<=> X20 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [X23,X20,X2,X28,X5] :
( c_Fun_Oinj__on(X5,X28,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hAPP(X2,X20) = hAPP(X2,X23)
=> X20 = X23 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injD) ).
fof(fact_less__add__Suc1,axiom,
! [X17,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),X17)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X17,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),X17),X59)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_insertI2,axiom,
! [X21,X6,X22,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X22),X6))
=> hBOOL(hAPP(hAPP(c_member(X5),X22),c_Set_Oinsert(X5,X21,X6))) ),
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,
! [X5] :
( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,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(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_Suc__less__eq,axiom,
! [X8,X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X14)),hAPP(c_Nat_OSuc,X8)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__less__SucD,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17)),hAPP(c_Nat_OSuc,X13)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [X28,X5] :
( c_Finite__Set_Ofinite(tc_fun(X5,X28),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X28),tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X28,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_order__less__trans,axiom,
! [X36,X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X36,X16,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X36),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X36),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X23,X20,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X20))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X23))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X23) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X20 = c_Groups_Ozero__class_Ozero(X5)
& X23 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [X28,X5] : c_Sum__Type_OPlus(X5,X28,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X28),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X36,X15,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X36))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X17,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),X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X15,X36,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X36))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X17,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),X17),X58))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X8,X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X8)))
<=> ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X76] :
( X14 = hAPP(c_Nat_OSuc,X76)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X76),X8)) ) ) ),
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,
! [X35,X29,X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X35)) ),
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,
! [X35,X29,X30,X5] :
( class_Groups_Oab__semigroup__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X35)) ),
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,X35,X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X69)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)),X69) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_insert__code,axiom,
! [X20,X7,X23,X5] :
( hBOOL(hAPP(c_Set_Oinsert(X5,X23,X7),X20))
<=> ( X23 = X20
| hBOOL(hAPP(X7,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_zero__less__two,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Oone__class_Oone(X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_Suc__le__mono,axiom,
! [X14,X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8)),hAPP(c_Nat_OSuc,X14)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_order__le__less__trans,axiom,
! [X36,X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X36,X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I8_J,axiom,
! [X36,X16,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X36),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X36),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X36,X16,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X36),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X36),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X28,X5] :
( c_Finite__Set_Ofinite(tc_sum(X5,X28),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X28),tc_HOL_Obool)))
<=> ( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
& c_Finite__Set_Ofinite(X28,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X28,X5] :
( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Finite__Set_Ofinite(X28,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(tc_prod(X5,X28),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X28),tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_less__add__eq__less,axiom,
! [X13,X17,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),X17),X57) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X56),X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_subset__insertI,axiom,
! [X22,X6,X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),c_Set_Oinsert(X5,X22,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(fact_Suc__lessD,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17)),X13))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__mono,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17)),hAPP(c_Nat_OSuc,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_trans__le__add1,axiom,
! [X17,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),X17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X36,X15,X16] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X36))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add2,axiom,
! [X17,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),X17),X58))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X15,X36,X16] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16),X36))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X36))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X28,X5] :
( c_Finite__Set_Ofinite(tc_fun(X5,X28),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X28),tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(X28,c_Orderings_Otop__class_Otop(tc_fun(X28,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_nat__add__assoc,axiom,
! [X56,X13,X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X13)),X56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),X56)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_less__eq__Suc__le,axiom,
! [X14,X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X14))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8)),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X8,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X14)),X8))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X17)),X13))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_predicate1D,axiom,
! [X20,X70,X24,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X24),X70))
=> ( hBOOL(hAPP(X24,X20))
=> hBOOL(hAPP(X70,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X70,X5,X20,X24] :
( hBOOL(hAPP(X24,X20))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X24),X70))
=> hBOOL(hAPP(X70,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_order__trans,axiom,
! [X36,X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X36))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X36,X16,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X36),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X36),X16)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_Suc__lessI,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
=> ( hAPP(c_Nat_OSuc,X17) != X13
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17)),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__add__one,axiom,
! [X30,X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),c_Groups_Oone__class_Oone(X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_le__less__Suc__eq,axiom,
! [X8,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,X14)))
<=> X8 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__leD,axiom,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X17)),X13))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_insert__commute,axiom,
! [X7,X23,X20,X5] : c_Set_Oinsert(X5,X20,c_Set_Oinsert(X5,X23,X7)) = c_Set_Oinsert(X5,X23,c_Set_Oinsert(X5,X20,X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
fof(fact_insertI1,axiom,
! [X6,X22,X5] : hBOOL(hAPP(hAPP(c_member(X5),X22),c_Set_Oinsert(X5,X22,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
fof(fact_less__Suc__eq,axiom,
! [X8,X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X8)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8))
| X14 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__leI,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X17)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X69,X35,X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X69)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),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,
! [X6,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ( c_Finite__Set_Ofinite(X5,X6)
=> c_Finite__Set_Ofinite(X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [X7,X6,X5] :
( c_Finite__Set_Ofinite(X5,X6)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> c_Finite__Set_Ofinite(X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_less__iff__Suc__add,axiom,
! [X8,X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8))
<=> ? [X61] : X8 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X61)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__Suc__eq__le,axiom,
! [X8,X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),hAPP(c_Nat_OSuc,X8)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_less__SucI,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [X22,X5] :
( class_Int_Oring__char__0(X5)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X22),c_Int_Oring__1__class_OInts(X5)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X22) = c_Groups_Ozero__class_Ozero(X5)
<=> X22 = c_Groups_Ozero__class_Ozero(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_le__Suc__eq,axiom,
! [X8,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),hAPP(c_Nat_OSuc,X8)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8))
| X14 = hAPP(c_Nat_OSuc,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_subset__UNIV,axiom,
! [X7,X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_nat__less__cases,axiom,
! [X24,X8,X14] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8))
=> hBOOL(hAPP(hAPP(X24,X8),X14)) )
=> ( ( X14 = X8
=> hBOOL(hAPP(hAPP(X24,X8),X14)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X14))
=> hBOOL(hAPP(hAPP(X24,X8),X14)) )
=> hBOOL(hAPP(hAPP(X24,X8),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_nat__add__left__commute,axiom,
! [X36,X15,X16] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),X36)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_order__eq__iff,axiom,
! [X23,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( X20 = X23
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X23),X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X20,X23,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X23),X20))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
<=> X20 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X15,X16,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16))
=> X16 = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X16,X15,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
=> X16 = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_card__ge__0__finite,axiom,
! [X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X5,X7)))
=> c_Finite__Set_Ofinite(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_le__imp__less__Suc,axiom,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X7,X5] :
( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X5,X7) = c_Finite__Set_Ocard(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> X7 = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_order__less__le,axiom,
! [X23,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
& X20 != X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__le__less,axiom,
! [X23,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
| X20 = X23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__imp__le,axiom,
! [X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_le__add1,axiom,
! [X17,X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),X17))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X17,X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_image__ident,axiom,
! [X83,X5] : c_Set_Oimage(X5,X5,c_COMBI(X5),X83) = X83,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_inj__on__id2,axiom,
! [X7,X5] : c_Fun_Oinj__on(X5,X5,c_COMBI(X5),X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(fact_order__neq__le__trans,axiom,
! [X29,X30,X5] :
( class_Orderings_Oorder(X5)
=> ( X30 != X29
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),X29))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X15,X16,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
| X16 = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [X29,X30,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X30),X29))
=> ( X30 != X29
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [X30,X29,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),X30))
=> ( X30 != X29
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X30)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_xt1_I12_J,axiom,
! [X29,X30,X5] :
( class_Orderings_Oorder(X5)
=> ( X30 != X29
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X29),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X30)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_less__Suc0,axiom,
! [X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X8 = 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,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13),X17))
=> X17 = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_eq__mem,axiom,
! [X23,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X20),hAPP(c_fequal,X23)))
<=> X20 = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__SucI,axiom,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),hAPP(c_Nat_OSuc,X13))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X15,X16] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_nat__less__le,axiom,
! [X8,X14] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8))
& X14 != X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X8,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8))
| X14 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_less__imp__le__nat,axiom,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X13,X17] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
| X17 = X13 )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_insert__absorb,axiom,
! [X7,X22,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X22),X7))
=> c_Set_Oinsert(X5,X22,X7) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_linorder__neq__iff,axiom,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( X20 != X23
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X20)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
| X16 = X15
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_splice_Osimps_I2_J,axiom,
! [X43,X44,X5] : c_List_Osplice(X5,c_List_Olist_OCons(X5,X44,X43),c_List_Olist_ONil(X5)) = c_List_Olist_OCons(X5,X44,X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).
fof(fact_finite__option__UNIV,axiom,
! [X5] :
( c_Finite__Set_Ofinite(tc_Option_Ooption(X5),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X5),tc_HOL_Obool)))
<=> c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_le__neq__implies__less,axiom,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
=> ( X17 != X13
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_insert__absorb2,axiom,
! [X7,X20,X5] : c_Set_Oinsert(X5,X20,c_Set_Oinsert(X5,X20,X7)) = c_Set_Oinsert(X5,X20,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [X20,X5] : hBOOL(hAPP(hAPP(c_member(X5),X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_UNIV__I,axiom,
! [X20,X5] : hBOOL(hAPP(hAPP(c_member(X5),X20),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_finite__insert,axiom,
! [X7,X22,X5] :
( c_Finite__Set_Ofinite(X5,c_Set_Oinsert(X5,X22,X7))
<=> c_Finite__Set_Ofinite(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).
fof(fact_mem__def,axiom,
! [X7,X20,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
<=> hBOOL(hAPP(X7,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_linorder__le__less__linear,axiom,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_add__Suc,axiom,
! [X13,X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17)),X13) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_le__iff__add,axiom,
! [X8,X14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8))
<=> ? [X61] : X8 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X61) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_nat__neq__iff,axiom,
! [X8,X14] :
( X14 != X8
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_gr0__conv__Suc,axiom,
! [X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8))
<=> ? [X52] : X8 = hAPP(c_Nat_OSuc,X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X15,X16,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> X15 != X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X15,X16,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> X16 != X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X15,X16,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> X16 != X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_equalityD1,axiom,
! [X5,X6,X7] :
( X7 = X6
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X5,X6,X7] :
( X7 = X6
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_subset__refl,axiom,
! [X7,X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X7)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_neq0__conv,axiom,
! [X8] :
( X8 != 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)),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_add__right__imp__eq,axiom,
! [X35,X30,X29,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X29),X30) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X30)
=> X29 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X4,X22,X21,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X22) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X22)
<=> X21 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Ocancel__ab__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)
=> X29 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X35,X29,X30,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X29) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35)
=> X29 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X4,X21,X22,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X21) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X4)
<=> X21 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_list_Oinject,axiom,
! [X37,X38,X39,X22,X5] :
( c_List_Olist_OCons(X5,X22,X39) = c_List_Olist_OCons(X5,X38,X37)
<=> ( X22 = X38
& X39 = X37 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).
fof(fact_linorder__linear,axiom,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_add__Suc__right,axiom,
! [X13,X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X13)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_add__Suc__shift,axiom,
! [X13,X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17)),X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X13)),
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,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
=> X13 != 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,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zero__less__Suc,axiom,
! [X13] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_less__not__refl3,axiom,
! [X18,X19] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X19),X18))
=> X19 != X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X17,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X17))
=> X17 != X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_zero__less__one,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_Ints__0,axiom,
! [X5] :
( class_Rings_Oring__1(X5)
=> hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Ozero__class_Ozero(X5)),c_Int_Oring__1__class_OInts(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(fact_Ints__1,axiom,
! [X5] :
( class_Rings_Oring__1(X5)
=> hBOOL(hAPP(hAPP(c_member(X5),c_Groups_Oone__class_Oone(X5)),c_Int_Oring__1__class_OInts(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(fact_nat__add__right__cancel,axiom,
! [X8,X60,X14] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X60) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8),X60)
<=> X14 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X8,X14,X60] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X14) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X8)
<=> X14 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_finite_OinsertI,axiom,
! [X22,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> c_Finite__Set_Ofinite(X5,c_Set_Oinsert(X5,X22,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_lessI,axiom,
! [X13] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),hAPP(c_Nat_OSuc,X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_top1I,axiom,
! [X20,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_le__0__eq,axiom,
! [X8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X8 = 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,
! [X8,X14] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X8) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X14 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X8 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X8 = 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,
! [X8,X14] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X8)
<=> ( ( X14 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X8 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X8 = 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,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
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,
! [X35,X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X35),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_gr0I,axiom,
! [X13] :
( X13 != 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)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_top__greatest,axiom,
! [X16,X5] :
( class_Orderings_Otop(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),c_Orderings_Otop__class_Otop(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_double__eq__0__iff,axiom,
! [X22,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X22) = c_Groups_Ozero__class_Ozero(X5)
<=> X22 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X22,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X22)
<=> X22 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__iff,axiom,
! [X22,X21,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X21 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X21),X22)
<=> X22 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_order__eq__refl,axiom,
! [X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( X16 = X15
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(help_c__COMBK__1,axiom,
! [X88,X87,X28,X5] : hAPP(hAPP(c_COMBK(X5,X28),X87),X88) = X87,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_list_Osimps_I3_J,axiom,
! [X26,X27,X5] : c_List_Olist_OCons(X5,X27,X26) != c_List_Olist_ONil(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).
fof(fact_list_Osimps_I2_J,axiom,
! [X26,X27,X5] : c_List_Olist_ONil(X5) != c_List_Olist_OCons(X5,X27,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_nat__add__commute,axiom,
! [X13,X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_order__refl,axiom,
! [X16,X5] :
( class_Orderings_Opreorder(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_not__Cons__self2,axiom,
! [X33,X16,X5] : c_List_Olist_OCons(X5,X16,X33) != X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_not__Cons__self,axiom,
! [X16,X5,X33] : X33 != c_List_Olist_OCons(X5,X16,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(fact_top__apply,axiom,
! [X20,X28,X5] :
( class_Orderings_Otop(X5)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X28,X5)),X20) = c_Orderings_Otop__class_Otop(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_add__is__0,axiom,
! [X8,X14] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X8) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X8 = 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,
! [X13,X17] :
( X17 = X13
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(help_c__fequal__2,axiom,
! [X23,X20] :
( X20 != X23
| hBOOL(hAPP(hAPP(c_fequal,X20),X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_add__eq__self__zero,axiom,
! [X13,X17] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X13) = X17
=> X13 = 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,
! [X13] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_finite__UNIV,axiom,
! [X5] :
( class_Finite__Set_Ofinite(X5)
=> c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,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,
! [X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X30) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0__left,axiom,
! [X30,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X30) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X30,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X30) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X30,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),c_Groups_Ozero__class_Ozero(X5)) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__right,axiom,
! [X30,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),c_Groups_Ozero__class_Ozero(X5)) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X30,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X30),c_Groups_Ozero__class_Ozero(X5)) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X13] : hAPP(c_Nat_OSuc,X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_list_Osize_I1_J,axiom,
! [X78,X5] : c_List_Olist_Olist__size(X5,X78,c_List_Olist_ONil(X5)) = 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,
! [X13] : hAPP(c_Nat_OSuc,X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),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,
! [X49,X5] : c_List_Osplice(X5,c_List_Olist_ONil(X5),X49) = X49,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
fof(fact_splice__Nil2,axiom,
! [X33,X5] : c_List_Osplice(X5,X33,c_List_Olist_ONil(X5)) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X13] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X8] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X17] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17,
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_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(fact_Suc__inject,axiom,
! [X15,X16] :
( hAPP(c_Nat_OSuc,X16) = hAPP(c_Nat_OSuc,X15)
=> X16 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
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__neq__Zero,axiom,
! [X17] : hAPP(c_Nat_OSuc,X17) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X73] : hAPP(c_Nat_OSuc,X73) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__not__Zero,axiom,
! [X17] : hAPP(c_Nat_OSuc,X17) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_Zero__neq__Suc,axiom,
! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X72] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X72),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__not__Suc,axiom,
! [X17] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_finite,axiom,
! [X7,X5] :
( class_Finite__Set_Ofinite(X5)
=> c_Finite__Set_Ofinite(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_finite__code,axiom,
! [X7,X5] :
( class_Finite__Set_Ofinite(X5)
=> c_Finite__Set_Ofinite(X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_Suc__n__not__n,axiom,
! [X13] : hAPP(c_Nat_OSuc,X13) != X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X13] : X13 != hAPP(c_Nat_OSuc,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(help_c__COMBI__1,axiom,
! [X87,X5] : hAPP(c_COMBI(X5),X87) = X87,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(fact_distinct_Osimps_I1_J,axiom,
! [X5] : c_List_Odistinct(X5,c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(fact_one__neq__zero,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Oone__class_Oone(X5) != c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_zero__neq__one,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Ozero__class_Ozero(X5) != c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
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,
! [X13] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).
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__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__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_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__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__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__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__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_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__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_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/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_518,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)))))
=> ( ! [X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X52),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____)),X52))),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_519,plain,
! [X20,X7,X10,X1,X34,X2,X28,X5] :
( c_Finite__Set_Ofolding__image__simple(X5,X28,X2,X34,X1,X10)
=> ( c_Finite__Set_Ofinite(X28,X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X28),X20),X7))
=> hAPP(X10,c_Set_Oinsert(X28,X20,X7)) = hAPP(hAPP(X2,hAPP(X1,X20)),hAPP(X10,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(i_0_520,plain,
! [X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X5,c_Set_Oimage(X28,X5,X2,X7))),c_Finite__Set_Ocard(X28,X7)))
=> ~ c_Fun_Oinj__on(X28,X5,X2,X7) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).
fof(i_0_521,plain,
! [X23,X20,X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),c_Arrow__Order__Mirabelle_OLin))
=> ( X20 != X23
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X20),X23)),X32))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X20)),X32)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_522,plain,
! [X21,X22,X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X22),X21)),X32))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),X32)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_523,plain,
! [X20,X6,X7,X2,X28,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X28)),X2),c_FuncSet_OPi(X5,X28,X7,X6)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X28),hAPP(X2,X20)),hAPP(X6,X20)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_524,plain,
! [X23,X20,X5] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X20),X23)),c_List_Omeasures(X5,c_List_Olist_ONil(tc_fun(X5,tc_Nat_Onat))))),
inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J]) ).
fof(i_0_525,plain,
! [X6,X7,X20,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),c_Set_Oinsert(X5,X20,X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6)) ) ),
inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).
fof(i_0_526,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_b____),v_a____)),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_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_527,plain,
~ ! [X50] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X50))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X50),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_528,plain,
! [X1,X2,X5,X28] :
( class_Orderings_Oord(X28)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X28)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X28),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X28),X1),X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_529,plain,
! [X13,X56,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17),X56)),X13))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56),X13)) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_530,plain,
~ ! [X25] : ~ 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,X25,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_531,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_532,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_533,plain,
! [X8,X24] :
( ~ hBOOL(hAPP(X24,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(X24,X8))
=> ? [X61] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),X8))
& ! [X65] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65),X61))
=> ~ hBOOL(hAPP(X24,X65)) )
& hBOOL(hAPP(X24,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_534,plain,
! [X21,X6,X22,X5] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X5),X22),X6))
=> X22 = X21 )
=> hBOOL(hAPP(hAPP(c_member(X5),X22),c_Set_Oinsert(X5,X21,X6))) ),
inference(fof_simplification,[status(thm)],[fact_insertCI]) ).
fof(i_0_535,plain,
! [X6,X7,X20,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X6))
=> ( c_Set_Oinsert(X5,X20,X7) = c_Set_Oinsert(X5,X20,X6)
<=> X7 = X6 ) ) ),
inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).
fof(i_0_536,plain,
! [X8,X14] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14),X8))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8)),X14)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_537,plain,
! [X8,X14] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X14),X8))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,X14))) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_538,plain,
! [X30,X29,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X30))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29)) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_539,plain,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X20))
| X20 = X23 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_540,plain,
! [X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_541,plain,
! [X29,X30,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X30),X29))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X29),X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_542,plain,
! [X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_543,plain,
! [X15,X16,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_544,plain,
! [X20,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X5,X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).
fof(i_0_545,plain,
! [X23,X20,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X23),X20)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_546,plain,
! [X20,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)) = c_Finite__Set_Ocard(X5,X7) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X5,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).
fof(i_0_547,plain,
! [X14,X8] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X14))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,X14)))
<=> X8 = X14 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_548,plain,
! [X17,X13] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X17))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),hAPP(c_Nat_OSuc,X17)))
=> X17 = X13 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_549,plain,
! [X13,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),hAPP(c_Nat_OSuc,X13)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X13))
=> X17 = X13 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_550,plain,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> X20 = X23 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_551,plain,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X23),X20)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_552,plain,
! [X16,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15)) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_553,plain,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X20)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_554,plain,
! [X20,X7,X5] :
( c_Finite__Set_Ofinite(X5,X7)
=> ( ~ hBOOL(hAPP(hAPP(c_member(X5),X20),X7))
=> c_Finite__Set_Ocard(X5,c_Set_Oinsert(X5,X20,X7)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X5,X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).
fof(i_0_555,plain,
! [X13,X17] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),hAPP(c_Nat_OSuc,X13)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17),X13))
=> X17 = hAPP(c_Nat_OSuc,X13) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_556,plain,
! [X13] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X13)),X13)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_557,plain,
! [X23,X20,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X23))
<=> X20 = X23 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_558,plain,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_559,plain,
! [X15,X16,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X16 != X15
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_560,plain,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> ( X16 != X15
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_561,plain,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( X16 != X15
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X15),X16)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_562,plain,
! [X20,X23,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X23),X20))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X23))
<=> X20 = X23 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_563,plain,
! [X16,X15,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_564,plain,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_565,plain,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_566,plain,
! [X15,X16] :
( X16 != X15
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),X15))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_567,plain,
! [X5,X6,X7] :
( X7 = X6
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X7),X6))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X6),X7)) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_568,plain,
! [X16,X5] :
( class_Orderings_Opreorder(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X16),X16)) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_569,plain,
! [X15,X16,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X16),X15))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X15),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_570,plain,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_571,plain,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_572,plain,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_573,plain,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X13)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_574,plain,
! [X13] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X13)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_575,plain,
! [X23,X20] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X20),X23))
| X20 = X23 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_576,plain,
! [X7,X5] :
( ~ c_Finite__Set_Ofinite(X5,X7)
=> c_Finite__Set_Ocard(X5,X7) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
fof(i_0_577,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_578,plain,
! [X2326] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk17_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2326),esk17_0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X2326))),v_Lab____)),v_Lba____)))) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk17_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_518])])])]) ).
fof(i_0_579,plain,
! [X2213] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk11_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,X2213),esk11_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____)),X2213))),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),esk11_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_580,plain,
! [X1648] : hBOOL(hAPP(hAPP(c_member(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____)),X1648))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
inference(variable_rename,[status(thm)],[fact_PiProf]) ).
fof(i_0_581,plain,
! [X1950] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1950),v_n____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),X1950))),v_Lab____)),v_Lba____)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n_I2_J])]) ).
fof(i_0_582,plain,
! [X2261,X2262,X2263,X2264] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2264,tc_fun(X2263,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2264,tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_fun(X2263,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2263,tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_fun(X2263,tc_HOL_Obool)),X2264,c_COMBC(X2263,tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2263,tc_prod(X2264,X2263)),tc_fun(X2263,tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),X2264,c_COMBB(tc_prod(X2264,X2263),tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool),X2263,c_member(tc_prod(X2264,X2263)))),c_Product__Type_OPair(X2264,X2263)))),X2262)),hAPP(hAPP(c_COMBC(X2264,tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_fun(X2263,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2263,tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_fun(X2263,tc_HOL_Obool)),X2264,c_COMBC(X2263,tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2263,tc_prod(X2264,X2263)),tc_fun(X2263,tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),X2264,c_COMBB(tc_prod(X2264,X2263),tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool),X2263,c_member(tc_prod(X2264,X2263)))),c_Product__Type_OPair(X2264,X2263)))),X2261)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),X2262),X2261)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),X2262),X2261))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2264,tc_fun(X2263,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2264,tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_fun(X2263,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2263,tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_fun(X2263,tc_HOL_Obool)),X2264,c_COMBC(X2263,tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2263,tc_prod(X2264,X2263)),tc_fun(X2263,tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),X2264,c_COMBB(tc_prod(X2264,X2263),tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool),X2263,c_member(tc_prod(X2264,X2263)))),c_Product__Type_OPair(X2264,X2263)))),X2262)),hAPP(hAPP(c_COMBC(X2264,tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_fun(X2263,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2263,tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_fun(X2263,tc_HOL_Obool)),X2264,c_COMBC(X2263,tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2263,tc_prod(X2264,X2263)),tc_fun(X2263,tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool)),X2264,c_COMBB(tc_prod(X2264,X2263),tc_fun(tc_fun(tc_prod(X2264,X2263),tc_HOL_Obool),tc_HOL_Obool),X2263,c_member(tc_prod(X2264,X2263)))),c_Product__Type_OPair(X2264,X2263)))),X2261))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_583,plain,
! [X2239,X2240,X2241,X2242,X2243,X2244] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),hAPP(v_F,X2240)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2242),X2241)),hAPP(v_F,X2239)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),hAPP(X2240,esk16_6(X2239,X2240,X2241,X2242,X2243,X2244))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2242),X2241)),hAPP(X2239,esk16_6(X2239,X2240,X2241,X2242,X2243,X2244))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2239),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2240),c_Arrow__Order__Mirabelle_OProf))
| X2243 = X2242
| X2244 = X2241
| X2242 = X2241
| X2244 = X2243 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2242),X2241)),hAPP(v_F,X2239)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),hAPP(v_F,X2240)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),hAPP(X2240,esk16_6(X2239,X2240,X2241,X2242,X2243,X2244))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2242),X2241)),hAPP(X2239,esk16_6(X2239,X2240,X2241,X2242,X2243,X2244))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2239),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2240),c_Arrow__Order__Mirabelle_OProf))
| X2243 = X2242
| X2244 = X2241
| X2242 = X2241
| X2244 = X2243 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),hAPP(v_F,X2240)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2242),X2241)),hAPP(v_F,X2239)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),hAPP(X2240,esk16_6(X2239,X2240,X2241,X2242,X2243,X2244))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2242),X2241)),hAPP(X2239,esk16_6(X2239,X2240,X2241,X2242,X2243,X2244))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2239),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2240),c_Arrow__Order__Mirabelle_OProf))
| X2243 = X2242
| X2244 = X2241
| X2242 = X2241
| X2244 = X2243 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2242),X2241)),hAPP(v_F,X2239)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),hAPP(v_F,X2240)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2244),X2243)),hAPP(X2240,esk16_6(X2239,X2240,X2241,X2242,X2243,X2244))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2242),X2241)),hAPP(X2239,esk16_6(X2239,X2240,X2241,X2242,X2243,X2244))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2239),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2240),c_Arrow__Order__Mirabelle_OProf))
| X2243 = X2242
| X2244 = X2241
| X2242 = X2241
| X2244 = X2243 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).
fof(i_0_584,plain,
! [X2232,X2233,X2234,X2235,X2236,X2237] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2236)),hAPP(X2233,esk15_6(X2232,X2233,X2234,X2235,X2236,X2237))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2235),X2234)),hAPP(X2232,esk15_6(X2232,X2233,X2234,X2235,X2236,X2237))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2236)),hAPP(v_F,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),X2235),X2234)),hAPP(v_F,X2232)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2232),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2233),c_Arrow__Order__Mirabelle_OProf))
| X2236 = X2235
| X2237 = X2234
| X2235 = X2234
| X2237 = X2236 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2236)),hAPP(X2233,esk15_6(X2232,X2233,X2234,X2235,X2236,X2237))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2235),X2234)),hAPP(X2232,esk15_6(X2232,X2233,X2234,X2235,X2236,X2237))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2237),X2236)),hAPP(v_F,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),X2235),X2234)),hAPP(v_F,X2232)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2232),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2233),c_Arrow__Order__Mirabelle_OProf))
| X2236 = X2235
| X2237 = X2234
| X2235 = X2234
| X2237 = X2236 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C1_C])])])]) ).
fof(i_0_585,plain,
! [X2219,X2220,X2221,X2222,X2223,X2224] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2224),X2223)),hAPP(v_F,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),X2222),X2221)),hAPP(v_F,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),X2224),X2223)),hAPP(X2220,esk13_6(X2219,X2220,X2221,X2222,X2223,X2224))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2222),X2221)),hAPP(X2219,esk13_6(X2219,X2220,X2221,X2222,X2223,X2224))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2219),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2220),c_Arrow__Order__Mirabelle_OProf))
| X2222 = X2221
| X2224 = X2223 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2222),X2221)),hAPP(v_F,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),X2224),X2223)),hAPP(v_F,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),X2224),X2223)),hAPP(X2220,esk13_6(X2219,X2220,X2221,X2222,X2223,X2224))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2222),X2221)),hAPP(X2219,esk13_6(X2219,X2220,X2221,X2222,X2223,X2224))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2219),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2220),c_Arrow__Order__Mirabelle_OProf))
| X2222 = X2221
| X2224 = 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),X2224),X2223)),hAPP(v_F,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),X2222),X2221)),hAPP(v_F,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),X2224),X2223)),hAPP(X2220,esk13_6(X2219,X2220,X2221,X2222,X2223,X2224))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2222),X2221)),hAPP(X2219,esk13_6(X2219,X2220,X2221,X2222,X2223,X2224))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2219),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2220),c_Arrow__Order__Mirabelle_OProf))
| X2222 = X2221
| X2224 = X2223 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2222),X2221)),hAPP(v_F,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),X2224),X2223)),hAPP(v_F,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),X2224),X2223)),hAPP(X2220,esk13_6(X2219,X2220,X2221,X2222,X2223,X2224))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2222),X2221)),hAPP(X2219,esk13_6(X2219,X2220,X2221,X2222,X2223,X2224))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2219),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2220),c_Arrow__Order__Mirabelle_OProf))
| X2222 = X2221
| X2224 = X2223 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pairwise__neutrality])])])]) ).
fof(i_0_586,plain,
! [X1722,X1723,X1724,X1725] :
( ( hAPP(hAPP(c_COMBC(X1725,tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1724,tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),X1725,c_COMBC(X1724,tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1724,tc_prod(X1725,X1724)),tc_fun(X1724,tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),X1725,c_COMBB(tc_prod(X1725,X1724),tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool),X1724,c_member(tc_prod(X1725,X1724)))),c_Product__Type_OPair(X1725,X1724)))),X1723) != hAPP(hAPP(c_COMBC(X1725,tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1724,tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),X1725,c_COMBC(X1724,tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1724,tc_prod(X1725,X1724)),tc_fun(X1724,tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),X1725,c_COMBB(tc_prod(X1725,X1724),tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool),X1724,c_member(tc_prod(X1725,X1724)))),c_Product__Type_OPair(X1725,X1724)))),X1722)
| X1723 = X1722 )
& ( X1723 != X1722
| hAPP(hAPP(c_COMBC(X1725,tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1724,tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),X1725,c_COMBC(X1724,tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1724,tc_prod(X1725,X1724)),tc_fun(X1724,tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),X1725,c_COMBB(tc_prod(X1725,X1724),tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool),X1724,c_member(tc_prod(X1725,X1724)))),c_Product__Type_OPair(X1725,X1724)))),X1723) = hAPP(hAPP(c_COMBC(X1725,tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1724,tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_fun(X1724,tc_HOL_Obool)),X1725,c_COMBC(X1724,tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1724,tc_prod(X1725,X1724)),tc_fun(X1724,tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool)),X1725,c_COMBB(tc_prod(X1725,X1724),tc_fun(tc_fun(tc_prod(X1725,X1724),tc_HOL_Obool),tc_HOL_Obool),X1724,c_member(tc_prod(X1725,X1724)))),c_Product__Type_OPair(X1725,X1724)))),X1722) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_587,plain,
! [X2510,X2511,X2512,X2513,X2514] :
( ( hBOOL(hAPP(hAPP(c_member(X2514),esk30_5(X2510,X2511,X2512,X2513,X2514)),X2513))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2514,X2512),tc_HOL_Obool),c_FuncSet_OPi(X2514,X2512,X2513,X2511)),c_FuncSet_OPi(X2514,X2512,X2513,X2510))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2512,tc_HOL_Obool),hAPP(X2511,esk30_5(X2510,X2511,X2512,X2513,X2514))),hAPP(X2510,esk30_5(X2510,X2511,X2512,X2513,X2514))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2514,X2512),tc_HOL_Obool),c_FuncSet_OPi(X2514,X2512,X2513,X2511)),c_FuncSet_OPi(X2514,X2512,X2513,X2510))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_588,plain,
! [X2516,X2517,X2518,X2519,X2520] :
( ( hBOOL(hAPP(hAPP(c_member(X2520),esk31_5(X2516,X2517,X2518,X2519,X2520)),X2519))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2520,X2518)),X2517),c_FuncSet_OPi(X2520,X2518,X2519,X2516))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2518),hAPP(X2517,esk31_5(X2516,X2517,X2518,X2519,X2520))),hAPP(X2516,esk31_5(X2516,X2517,X2518,X2519,X2520))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2520,X2518)),X2517),c_FuncSet_OPi(X2520,X2518,X2519,X2516))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_589,plain,
! [X2492,X2493,X2494,X2495,X2496,X2498,X2503,X2504] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2492,X2493)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2492,X2494)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2493,esk25_5(X2492,X2493,X2494,X2495,X2496))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2494,esk25_5(X2492,X2493,X2494,X2495,X2496))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2494),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2493),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2492) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2492,X2494)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2492,X2493)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2493,esk25_5(X2492,X2493,X2494,X2495,X2496))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2494,esk25_5(X2492,X2493,X2494,X2495,X2496))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2494),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2493),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2492) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2492,X2493)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2492,X2494)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2493,esk25_5(X2492,X2493,X2494,X2495,X2496))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2494,esk25_5(X2492,X2493,X2494,X2495,X2496))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2494),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2493),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2492) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2492,X2494)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2492,X2493)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2493,esk25_5(X2492,X2493,X2494,X2495,X2496))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2495),X2496)),hAPP(X2494,esk25_5(X2492,X2493,X2494,X2495,X2496))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2494),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2493),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2492) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk26_1(X2498)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2498) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk27_1(X2498)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2498) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X2498)),esk29_1(X2498))),hAPP(esk26_1(X2498),X2503)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X2498)),esk29_1(X2498))),hAPP(esk27_1(X2498),X2503)))
| c_Arrow__Order__Mirabelle_OIIA(X2498) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X2498)),esk29_1(X2498))),hAPP(esk27_1(X2498),X2504)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X2498)),esk29_1(X2498))),hAPP(esk26_1(X2498),X2504)))
| c_Arrow__Order__Mirabelle_OIIA(X2498) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X2498)),esk29_1(X2498))),hAPP(X2498,esk26_1(X2498))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X2498)),esk29_1(X2498))),hAPP(X2498,esk27_1(X2498))))
| c_Arrow__Order__Mirabelle_OIIA(X2498) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X2498)),esk29_1(X2498))),hAPP(X2498,esk26_1(X2498))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X2498)),esk29_1(X2498))),hAPP(X2498,esk27_1(X2498))))
| c_Arrow__Order__Mirabelle_OIIA(X2498) ) ),
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_590,plain,
! [X2226,X2227,X2228,X2229,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),X2230),X2229)),hAPP(v_F,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),X2229),X2228)),hAPP(v_F,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),X2230),X2229)),hAPP(X2227,esk14_5(X2226,X2227,X2228,X2229,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),X2229),X2228)),hAPP(X2226,esk14_5(X2226,X2227,X2228,X2229,X2230))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2226),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2227),c_Arrow__Order__Mirabelle_OProf))
| X2230 = X2228
| X2229 = X2228
| X2230 = 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),X2229),X2228)),hAPP(v_F,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),X2230),X2229)),hAPP(v_F,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),X2230),X2229)),hAPP(X2227,esk14_5(X2226,X2227,X2228,X2229,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),X2229),X2228)),hAPP(X2226,esk14_5(X2226,X2227,X2228,X2229,X2230))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2226),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2227),c_Arrow__Order__Mirabelle_OProf))
| X2230 = X2228
| X2229 = X2228
| X2230 = 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),X2230),X2229)),hAPP(v_F,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),X2229),X2228)),hAPP(v_F,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),X2230),X2229)),hAPP(X2227,esk14_5(X2226,X2227,X2228,X2229,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),X2229),X2228)),hAPP(X2226,esk14_5(X2226,X2227,X2228,X2229,X2230))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2226),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2227),c_Arrow__Order__Mirabelle_OProf))
| X2230 = X2228
| X2229 = X2228
| X2230 = 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),X2229),X2228)),hAPP(v_F,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),X2230),X2229)),hAPP(v_F,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),X2230),X2229)),hAPP(X2227,esk14_5(X2226,X2227,X2228,X2229,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),X2229),X2228)),hAPP(X2226,esk14_5(X2226,X2227,X2228,X2229,X2230))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2226),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2227),c_Arrow__Order__Mirabelle_OProf))
| X2230 = X2228
| X2229 = X2228
| X2230 = X2229 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C4_C])])])]) ).
fof(i_0_591,plain,
! [X2327,X2328] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk18_2(X2327,X2328)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2328,X2327)
| ~ 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))),X2328),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( esk19_2(X2327,X2328) != esk20_2(X2327,X2328)
| c_Arrow__Order__Mirabelle_Odictator(X2328,X2327)
| ~ 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))),X2328),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk19_2(X2327,X2328)),esk20_2(X2327,X2328))),hAPP(esk18_2(X2327,X2328),X2327)))
| c_Arrow__Order__Mirabelle_Odictator(X2328,X2327)
| ~ 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))),X2328),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk19_2(X2327,X2328)),esk20_2(X2327,X2328))),hAPP(X2328,esk18_2(X2327,X2328))))
| c_Arrow__Order__Mirabelle_Odictator(X2328,X2327)
| ~ 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))),X2328),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_592,plain,
! [X1951,X1952,X1953,X1954,X1955,X1956,X1957,X1958] :
( ( X1956 = X1954
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1958,X1958)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1958),X1956),X1954)),X1952))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1958,X1957),tc_prod(X1958,X1957))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1958,X1957),tc_prod(X1958,X1957)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1957),X1956),X1955)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1957),X1954),X1953))),c_Wellfounded_Olex__prod(X1958,X1957,X1952,X1951))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1957,X1957)),hAPP(hAPP(c_Product__Type_OPair(X1957,X1957),X1955),X1953)),X1951))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1958,X1958)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1958),X1956),X1954)),X1952))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1958,X1957),tc_prod(X1958,X1957))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1958,X1957),tc_prod(X1958,X1957)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1957),X1956),X1955)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1957),X1954),X1953))),c_Wellfounded_Olex__prod(X1958,X1957,X1952,X1951))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1958,X1958)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1958),X1956),X1954)),X1952))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1958,X1957),tc_prod(X1958,X1957))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1958,X1957),tc_prod(X1958,X1957)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1957),X1956),X1955)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1957),X1954),X1953))),c_Wellfounded_Olex__prod(X1958,X1957,X1952,X1951))) )
& ( X1956 != X1954
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1957,X1957)),hAPP(hAPP(c_Product__Type_OPair(X1957,X1957),X1955),X1953)),X1951))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1958,X1957),tc_prod(X1958,X1957))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1958,X1957),tc_prod(X1958,X1957)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1957),X1956),X1955)),hAPP(hAPP(c_Product__Type_OPair(X1958,X1957),X1954),X1953))),c_Wellfounded_Olex__prod(X1958,X1957,X1952,X1951))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_593,plain,
! [X2214,X2215,X2216,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),X2217),X2216)),hAPP(v_F,X2215)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2216),X2217)),hAPP(v_F,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),X2217),X2216)),hAPP(X2215,esk12_4(X2214,X2215,X2216,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),X2216),X2217)),hAPP(X2214,esk12_4(X2214,X2215,X2216,X2217))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2214),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2215),c_Arrow__Order__Mirabelle_OProf))
| X2217 = 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),X2216),X2217)),hAPP(v_F,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),X2217),X2216)),hAPP(v_F,X2215)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2217),X2216)),hAPP(X2215,esk12_4(X2214,X2215,X2216,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),X2216),X2217)),hAPP(X2214,esk12_4(X2214,X2215,X2216,X2217))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2214),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2215),c_Arrow__Order__Mirabelle_OProf))
| X2217 = 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),X2217),X2216)),hAPP(v_F,X2215)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2216),X2217)),hAPP(v_F,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),X2217),X2216)),hAPP(X2215,esk12_4(X2214,X2215,X2216,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),X2216),X2217)),hAPP(X2214,esk12_4(X2214,X2215,X2216,X2217))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2214),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2215),c_Arrow__Order__Mirabelle_OProf))
| X2217 = 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),X2216),X2217)),hAPP(v_F,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),X2217),X2216)),hAPP(v_F,X2215)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2217),X2216)),hAPP(X2215,esk12_4(X2214,X2215,X2216,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),X2216),X2217)),hAPP(X2214,esk12_4(X2214,X2215,X2216,X2217))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2214),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2215),c_Arrow__Order__Mirabelle_OProf))
| X2217 = X2216 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C3_C])])])]) ).
fof(i_0_594,plain,
! [X3108,X3109,X3110,X3111,X3112,X3114,X3115,X3116,X3117,X3118,X3119] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3110,tc_HOL_Obool),esk44_5(X3108,X3109,X3110,X3111,X3112)),X3108))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3112,tc_HOL_Obool),X3111),c_Set_Oimage(X3110,X3112,X3109,X3108))) )
& ( X3111 = c_Set_Oimage(X3110,X3112,X3109,esk44_5(X3108,X3109,X3110,X3111,X3112))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3112,tc_HOL_Obool),X3111),c_Set_Oimage(X3110,X3112,X3109,X3108))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3116,tc_HOL_Obool),X3119),X3114))
| X3117 != c_Set_Oimage(X3116,X3118,X3115,X3119)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3118,tc_HOL_Obool),X3117),c_Set_Oimage(X3116,X3118,X3115,X3114))) ) ),
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_595,plain,
! [X1915,X1916,X1917,X1918,X1919,X1920,X1921] :
( ~ hBOOL(hAPP(X1921,X1920))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1919,X1919)),hAPP(hAPP(c_Product__Type_OPair(X1919,X1919),X1918),X1917)),hAPP(X1916,X1920)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1915,X1919),tc_prod(X1915,X1919))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1915,X1919),tc_prod(X1915,X1919)),hAPP(hAPP(c_Product__Type_OPair(X1915,X1919),X1920),X1918)),hAPP(hAPP(c_Product__Type_OPair(X1915,X1919),X1920),X1917))),c_Recdef_Osame__fst(X1915,X1919,X1921,X1916))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_596,plain,
! [X2031,X2032,X2033,X2034,X2035] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2033,X2034),X2032),X2031))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2034,hAPP(X2032,X2035)),hAPP(X2031,X2035)))
| ~ class_Orderings_Oord(X2034) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2034,hAPP(X2032,esk9_4(X2031,X2032,X2033,X2034))),hAPP(X2031,esk9_4(X2031,X2032,X2033,X2034))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2033,X2034),X2032),X2031))
| ~ class_Orderings_Oord(X2034) ) ),
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_597,plain,
! [X2570,X2571,X2572,X2573,X2574,X2575,X2576,X2577] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2577,X2576,X2575,X2574,X2573,X2572)
| ~ c_Finite__Set_Ofinite(X2576,X2571)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2576,tc_HOL_Obool),X2570),X2571))
| hAPP(hAPP(X2575,hAPP(X2572,X2570)),hAPP(X2572,X2571)) = hAPP(X2572,X2571) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_598,plain,
! [X2688,X2689,X2690,X2691,X2692,X2693,X2694,X2695] :
( ~ c_Finite__Set_Ofolding__image__simple(X2695,X2694,X2693,X2692,X2691,X2690)
| ~ c_Finite__Set_Ofinite(X2694,X2689)
| hBOOL(hAPP(hAPP(c_member(X2694),X2688),X2689))
| hAPP(X2690,c_Set_Oinsert(X2694,X2688,X2689)) = hAPP(hAPP(X2693,hAPP(X2691,X2688)),hAPP(X2690,X2689)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_519])]) ).
fof(i_0_599,plain,
! [X2674,X2675,X2676,X2677,X2678,X2679,X2680,X2681] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2681,X2680,X2679,X2678,X2677,X2676)
| ~ c_Finite__Set_Ofinite(X2680,X2675)
| ~ hBOOL(hAPP(hAPP(c_member(X2680),X2674),X2675))
| hAPP(hAPP(X2679,hAPP(X2677,X2674)),hAPP(X2676,X2675)) = hAPP(X2676,X2675) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_600,plain,
! [X2592,X2593,X2594,X2595,X2596,X2597,X2598,X2599] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2599,X2598,X2597,X2596,X2595,X2594)
| ~ c_Finite__Set_Ofinite(X2598,X2593)
| hAPP(X2594,c_Set_Oinsert(X2598,X2592,X2593)) = hAPP(hAPP(X2597,hAPP(X2595,X2592)),hAPP(X2594,X2593)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).
fof(i_0_601,plain,
! [X2600,X2601,X2602,X2603,X2604,X2605,X2606] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2606,X2605,X2604,X2603,X2602,X2601)
| hAPP(hAPP(X2604,X2600),X2600) = X2600 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).
fof(i_0_602,plain,
! [X3198,X3199,X3200,X3201,X3202,X3203] :
( ~ c_Fun_Oinj__on(X3203,X3202,X3201,X3200)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3202,tc_HOL_Obool),c_Set_Oimage(X3203,X3202,X3201,X3200)),X3199))
| ~ c_Fun_Oinj__on(X3202,X3203,X3198,X3199)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3203,tc_HOL_Obool),c_Set_Oimage(X3202,X3203,X3198,X3199)),X3200))
| ~ c_Finite__Set_Ofinite(X3203,X3200)
| ~ c_Finite__Set_Ofinite(X3202,X3199)
| c_Finite__Set_Ocard(X3203,X3200) = c_Finite__Set_Ocard(X3202,X3199) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).
fof(i_0_603,plain,
! [X2482,X2483,X2484,X2485,X2487,X2491] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2482)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2483),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),X2484),X2485)),hAPP(X2483,esk21_4(X2482,X2483,X2484,X2485))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2484),X2485)),hAPP(X2482,X2483))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk22_1(X2487)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X2487) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk23_1(X2487)),esk24_1(X2487))),hAPP(esk22_1(X2487),X2491)))
| c_Arrow__Order__Mirabelle_Ounanimity(X2487) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk23_1(X2487)),esk24_1(X2487))),hAPP(X2487,esk22_1(X2487))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2487) ) ),
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_604,plain,
! [X2522,X2523,X2524,X2525,X2526,X2527] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2527,X2526)),X2525),c_FuncSet_OPi(X2527,X2526,X2524,hAPP(c_COMBK(tc_fun(X2526,tc_HOL_Obool),X2527),X2523))))
| ~ c_Fun_Oinj__on(X2527,X2526,X2525,X2524)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2526,X2527)),X2522),c_FuncSet_OPi(X2526,X2527,X2523,hAPP(c_COMBK(tc_fun(X2527,tc_HOL_Obool),X2526),X2524))))
| ~ c_Fun_Oinj__on(X2526,X2527,X2522,X2523)
| ~ c_Finite__Set_Ofinite(X2527,X2524)
| ~ c_Finite__Set_Ofinite(X2526,X2523)
| c_Finite__Set_Ocard(X2527,X2524) = c_Finite__Set_Ocard(X2526,X2523) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij])]) ).
fof(i_0_605,plain,
! [X2305,X2306,X2307] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2307,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2307,tc_fun(X2307,tc_HOL_Obool),tc_HOL_Obool),c_member(X2307)),X2306)),hAPP(hAPP(c_COMBC(X2307,tc_fun(X2307,tc_HOL_Obool),tc_HOL_Obool),c_member(X2307)),X2305)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2307,tc_HOL_Obool),X2306),X2305)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2307,tc_HOL_Obool),X2306),X2305))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2307,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2307,tc_fun(X2307,tc_HOL_Obool),tc_HOL_Obool),c_member(X2307)),X2306)),hAPP(hAPP(c_COMBC(X2307,tc_fun(X2307,tc_HOL_Obool),tc_HOL_Obool),c_member(X2307)),X2305))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_606,plain,
! [X2971,X2972,X2973,X2974] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2974,c_Set_Oimage(X2973,X2974,X2972,X2971))),c_Finite__Set_Ocard(X2973,X2971)))
| ~ c_Fun_Oinj__on(X2973,X2974,X2972,X2971) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_520])]) ).
fof(i_0_607,plain,
! [X1726,X1727,X1728,X1729,X1730] :
( ( X1727 != X1726
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1727 != X1729
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1730),X1726)),X1728))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1726 != X1729
| X1727 = X1730
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1730)),X1728))
| X1727 = X1729
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1726 = X1729
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),X1728))
| X1727 = X1729
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1727 != X1729
| X1727 = X1729
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1726 != X1729
| X1726 = X1729
| X1727 = X1729
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),X1728))
| X1726 = X1729
| X1727 = X1729
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1726 != X1729
| X1727 != X1730
| X1727 = X1729
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),X1728))
| X1727 != X1730
| X1727 = X1729
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1726 != X1729
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1730)),X1728))
| X1727 = X1729
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),X1728))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1730)),X1728))
| X1727 = X1729
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1727 != X1729
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1730),X1726)),X1728))
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1726 != X1729
| X1726 = X1729
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1730),X1726)),X1728))
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),X1728))
| X1726 = X1729
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1730),X1726)),X1728))
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1726 != X1729
| X1727 != X1730
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1730),X1726)),X1728))
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),X1728))
| X1727 != X1730
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1730),X1726)),X1728))
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( X1726 != X1729
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1730)),X1728))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1730),X1726)),X1728))
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),X1728))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1730)),X1728))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1730),X1726)),X1728))
| X1727 = X1726
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1727),X1726)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1728),X1730),X1729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1728),c_Arrow__Order__Mirabelle_OLin))
| X1730 = X1729 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_608,plain,
! [X1819,X1820,X1821,X1822,X1823] :
( ( X1820 != X1819
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1819 != X1823
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1822)),X1821))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1820 != X1823
| X1819 = X1822
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1822),X1819)),X1821))
| X1819 = X1823
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1820 = X1823
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),X1821))
| X1819 = X1823
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1819 != X1823
| X1819 = X1823
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1820 != X1823
| X1820 = X1823
| X1819 = X1823
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),X1821))
| X1820 = X1823
| X1819 = X1823
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1820 != X1823
| X1819 != X1822
| X1819 = X1823
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),X1821))
| X1819 != X1822
| X1819 = X1823
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1820 != X1823
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1822),X1819)),X1821))
| X1819 = X1823
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),X1821))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1822),X1819)),X1821))
| X1819 = X1823
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1819 != X1823
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1822)),X1821))
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1820 != X1823
| X1820 = X1823
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1822)),X1821))
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),X1821))
| X1820 = X1823
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1822)),X1821))
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1820 != X1823
| X1819 != X1822
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1822)),X1821))
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),X1821))
| X1819 != X1822
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1822)),X1821))
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( X1820 != X1823
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1822),X1819)),X1821))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1822)),X1821))
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),X1821))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1822),X1819)),X1821))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1822)),X1821))
| X1820 = X1819
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1820),X1819)),c_Arrow__Order__Mirabelle_Obelow(X1821,X1823,X1822)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1821),c_Arrow__Order__Mirabelle_OLin))
| X1823 = X1822 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_609,plain,
! [X3028,X3029,X3030,X3031,X3032] :
( ~ hBOOL(hAPP(hAPP(c_member(X3032),X3031),c_Set_Oimage(X3030,X3032,X3029,X3028)))
| hBOOL(hAPP(hAPP(c_member(X3030),hAPP(c_Hilbert__Choice_Oinv__into(X3030,X3032,X3028,X3029),X3031)),X3028)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).
fof(i_0_610,plain,
! [X3154,X3155,X3156,X3157,X3158] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3157,tc_HOL_Obool),c_Set_Oimage(X3158,X3157,X3156,X3155)),c_Set_Oimage(X3158,X3157,X3156,X3154)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3158,tc_HOL_Obool),X3155),X3154))
| ~ c_Fun_Oinj__on(X3158,X3157,X3156,c_Orderings_Otop__class_Otop(tc_fun(X3158,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3158,tc_HOL_Obool),X3155),X3154))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3157,tc_HOL_Obool),c_Set_Oimage(X3158,X3157,X3156,X3155)),c_Set_Oimage(X3158,X3157,X3156,X3154)))
| ~ c_Fun_Oinj__on(X3158,X3157,X3156,c_Orderings_Otop__class_Otop(tc_fun(X3158,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_611,plain,
! [X2560,X2561,X2562] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2562,tc_HOL_Obool)),X2561),X2560))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2562,tc_HOL_Obool),tc_fun(X2562,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2562,tc_HOL_Obool),tc_fun(X2562,tc_HOL_Obool)),X2561),X2560)),c_Wellfounded_Ofinite__psubset(X2562))) )
& ( c_Finite__Set_Ofinite(X2562,X2560)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2562,tc_HOL_Obool),tc_fun(X2562,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2562,tc_HOL_Obool),tc_fun(X2562,tc_HOL_Obool)),X2561),X2560)),c_Wellfounded_Ofinite__psubset(X2562))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2562,tc_HOL_Obool)),X2561),X2560))
| ~ c_Finite__Set_Ofinite(X2562,X2560)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2562,tc_HOL_Obool),tc_fun(X2562,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2562,tc_HOL_Obool),tc_fun(X2562,tc_HOL_Obool)),X2561),X2560)),c_Wellfounded_Ofinite__psubset(X2562))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).
fof(i_0_612,plain,
! [X3193,X3194,X3195,X3196,X3197] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X3197,X3196)),X3195),c_FuncSet_OPi(X3197,X3196,X3194,hAPP(c_COMBK(tc_fun(X3196,tc_HOL_Obool),X3197),X3193))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3196,tc_HOL_Obool),c_Set_Oimage(X3197,X3196,X3195,X3194)),X3193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_613,plain,
! [X3022,X3023,X3024,X3025,X3026,X3027] :
( hAPP(c_Hilbert__Choice_Oinv__into(X3027,X3026,X3025,X3024),X3023) != hAPP(c_Hilbert__Choice_Oinv__into(X3027,X3026,X3025,X3024),X3022)
| ~ hBOOL(hAPP(hAPP(c_member(X3026),X3023),c_Set_Oimage(X3027,X3026,X3024,X3025)))
| ~ hBOOL(hAPP(hAPP(c_member(X3026),X3022),c_Set_Oimage(X3027,X3026,X3024,X3025)))
| X3023 = X3022 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).
fof(i_0_614,plain,
! [X2913,X2914] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2914),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2914),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2914),c_Groups_Oone__class_Oone(X2914)),X2913)),X2913)),c_Groups_Ozero__class_Ozero(X2914)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2914),X2913),c_Groups_Ozero__class_Ozero(X2914)))
| ~ hBOOL(hAPP(hAPP(c_member(X2914),X2913),c_Int_Oring__1__class_OInts(X2914)))
| ~ class_Rings_Olinordered__idom(X2914) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2914),X2913),c_Groups_Ozero__class_Ozero(X2914)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2914),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2914),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2914),c_Groups_Oone__class_Oone(X2914)),X2913)),X2913)),c_Groups_Ozero__class_Ozero(X2914)))
| ~ hBOOL(hAPP(hAPP(c_member(X2914),X2913),c_Int_Oring__1__class_OInts(X2914)))
| ~ class_Rings_Olinordered__idom(X2914) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).
fof(i_0_615,plain,
! [X2975,X2976,X2977,X2978,X2980,X2981] :
( ( X2975 = hAPP(X2976,esk36_4(X2975,X2976,X2977,X2978))
| ~ hBOOL(hAPP(hAPP(c_member(X2977),X2975),c_Set_Oimage(X2978,X2977,X2976,c_Orderings_Otop__class_Otop(tc_fun(X2978,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2978,X2977,X2976,c_Orderings_Otop__class_Otop(tc_fun(X2978,tc_HOL_Obool))) )
& ( X2975 != hAPP(X2976,X2980)
| X2980 = esk36_4(X2975,X2976,X2977,X2978)
| ~ hBOOL(hAPP(hAPP(c_member(X2977),X2975),c_Set_Oimage(X2978,X2977,X2976,c_Orderings_Otop__class_Otop(tc_fun(X2978,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2978,X2977,X2976,c_Orderings_Otop__class_Otop(tc_fun(X2978,tc_HOL_Obool))) )
& ( X2975 = hAPP(X2976,esk37_5(X2975,X2976,X2977,X2978,X2981))
| X2975 != hAPP(X2976,X2981)
| hBOOL(hAPP(hAPP(c_member(X2977),X2975),c_Set_Oimage(X2978,X2977,X2976,c_Orderings_Otop__class_Otop(tc_fun(X2978,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2978,X2977,X2976,c_Orderings_Otop__class_Otop(tc_fun(X2978,tc_HOL_Obool))) )
& ( esk37_5(X2975,X2976,X2977,X2978,X2981) != X2981
| X2975 != hAPP(X2976,X2981)
| hBOOL(hAPP(hAPP(c_member(X2977),X2975),c_Set_Oimage(X2978,X2977,X2976,c_Orderings_Otop__class_Otop(tc_fun(X2978,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X2978,X2977,X2976,c_Orderings_Otop__class_Otop(tc_fun(X2978,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,
! [X3150,X3151,X3152,X3153] :
( ~ c_Finite__Set_Ofinite(X3153,X3152)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3151,c_Set_Oimage(X3153,X3151,X3150,X3152))),c_Finite__Set_Ocard(X3153,X3152))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_617,plain,
! [X3060,X3061,X3062,X3063,X3064] :
( ~ c_Fun_Oinj__on(X3064,X3063,X3062,X3061)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3064,tc_HOL_Obool)),X3060),X3061))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X3063,tc_HOL_Obool)),c_Set_Oimage(X3064,X3063,X3062,X3060)),c_Set_Oimage(X3064,X3063,X3062,X3061))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_618,plain,
! [X3163,X3164,X3165] :
( ~ c_Finite__Set_Ofinite(X3165,X3164)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3165,tc_HOL_Obool),c_Set_Oimage(X3165,X3165,X3163,X3164)),X3164))
| ~ c_Fun_Oinj__on(X3165,X3165,X3163,X3164)
| c_Set_Oimage(X3165,X3165,X3163,X3164) = X3164 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_619,plain,
! [X1902,X1903,X1904,X1905,X1906] :
( ( hAPP(X1903,X1905) = hAPP(X1903,X1904)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1903,X1905)),hAPP(X1903,X1904)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1906,X1906)),hAPP(hAPP(c_Product__Type_OPair(X1906,X1906),X1905),X1904)),c_List_Omeasures(X1906,c_List_Olist_OCons(tc_fun(X1906,tc_Nat_Onat),X1903,X1902)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1906,X1906)),hAPP(hAPP(c_Product__Type_OPair(X1906,X1906),X1905),X1904)),c_List_Omeasures(X1906,X1902)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1903,X1905)),hAPP(X1903,X1904)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1906,X1906)),hAPP(hAPP(c_Product__Type_OPair(X1906,X1906),X1905),X1904)),c_List_Omeasures(X1906,c_List_Olist_OCons(tc_fun(X1906,tc_Nat_Onat),X1903,X1902)))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1903,X1905)),hAPP(X1903,X1904)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1906,X1906)),hAPP(hAPP(c_Product__Type_OPair(X1906,X1906),X1905),X1904)),c_List_Omeasures(X1906,c_List_Olist_OCons(tc_fun(X1906,tc_Nat_Onat),X1903,X1902)))) )
& ( hAPP(X1903,X1905) != hAPP(X1903,X1904)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1906,X1906)),hAPP(hAPP(c_Product__Type_OPair(X1906,X1906),X1905),X1904)),c_List_Omeasures(X1906,X1902)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1906,X1906)),hAPP(hAPP(c_Product__Type_OPair(X1906,X1906),X1905),X1904)),c_List_Omeasures(X1906,c_List_Olist_OCons(tc_fun(X1906,tc_Nat_Onat),X1903,X1902)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).
fof(i_0_620,plain,
! [X3204,X3205,X3206,X3207,X3208] :
( ~ c_Fun_Oinj__on(X3208,X3207,X3206,X3205)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3207,tc_HOL_Obool),c_Set_Oimage(X3208,X3207,X3206,X3205)),X3204))
| ~ c_Finite__Set_Ofinite(X3207,X3204)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X3208,X3205)),c_Finite__Set_Ocard(X3207,X3204))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).
fof(i_0_621,plain,
! [X3075,X3076,X3077,X3078,X3079,X3081,X3082,X3083,X3084,X3085,X3086] :
( ( hBOOL(hAPP(hAPP(c_member(X3077),esk43_4(X3075,X3076,X3077,X3078)),X3075))
| ~ hBOOL(hAPP(hAPP(c_member(X3079),X3078),c_Set_Oimage(X3077,X3079,X3076,X3075))) )
& ( X3078 = hAPP(X3076,esk43_4(X3075,X3076,X3077,X3078))
| ~ hBOOL(hAPP(hAPP(c_member(X3079),X3078),c_Set_Oimage(X3077,X3079,X3076,X3075))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3083),X3085),X3081))
| X3084 != hAPP(X3082,X3085)
| hBOOL(hAPP(hAPP(c_member(X3086),X3084),c_Set_Oimage(X3083,X3086,X3082,X3081))) ) ),
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_622,plain,
! [X1959,X1960,X1961,X1962,X1963] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1963,X1962)),hAPP(X1963,X1961)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1960,X1960)),hAPP(hAPP(c_Product__Type_OPair(X1960,X1960),X1962),X1961)),c_List_Omeasures(X1960,X1959)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1960,X1960)),hAPP(hAPP(c_Product__Type_OPair(X1960,X1960),X1962),X1961)),c_List_Omeasures(X1960,c_List_Olist_OCons(tc_fun(X1960,tc_Nat_Onat),X1963,X1959)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).
fof(i_0_623,plain,
! [X1716,X1717,X1718] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1717),X1716)),X1718))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1716),X1717)),X1718))
| X1717 = X1716
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1718),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),X1716),X1717)),X1718))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1717),X1716)),X1718))
| X1717 = X1716
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1718),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_521])])]) ).
fof(i_0_624,plain,
! [X1719,X1720,X1721] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1721),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),X1720),X1719)),X1721))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1719),X1720)),X1721)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_522])]) ).
fof(i_0_625,plain,
! [X2505,X2506,X2507,X2508,X2509] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2509,X2508)),X2507),c_FuncSet_OPi(X2509,X2508,X2506,hAPP(c_COMBK(tc_fun(X2508,tc_HOL_Obool),X2509),X2505))))
| ~ c_Fun_Oinj__on(X2509,X2508,X2507,X2506)
| ~ c_Finite__Set_Ofinite(X2508,X2505)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2509,X2506)),c_Finite__Set_Ocard(X2508,X2505))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj])]) ).
fof(i_0_626,plain,
! [X2256,X2257,X2258,X2259,X2260] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2260,tc_HOL_Obool),X2259),X2258))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2260,X2257),tc_HOL_Obool),c_FuncSet_OPi(X2260,X2257,X2258,X2256)),c_FuncSet_OPi(X2260,X2257,X2259,X2256))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_627,plain,
! [X3065,X3066,X3067,X3068,X3069] :
( ~ c_Finite__Set_Ofinite(X3069,c_Set_Oimage(X3068,X3069,X3067,c_Orderings_Otop__class_Otop(tc_fun(X3068,tc_HOL_Obool))))
| c_Finite__Set_Ofinite(X3066,c_Set_Oimage(X3068,X3066,hAPP(c_COMBB(X3069,X3066,X3068,X3065),X3067),c_Orderings_Otop__class_Otop(tc_fun(X3068,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).
fof(i_0_628,plain,
! [X1709] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1709),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),X1709)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_629,plain,
! [X2319,X2320,X2321,X2322,X2323,X2324] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2324,X2323)),X2322),c_FuncSet_OPi(X2324,X2323,X2321,hAPP(c_COMBK(tc_fun(X2323,tc_HOL_Obool),X2324),X2320))))
| ~ hBOOL(hAPP(hAPP(c_member(X2324),X2319),X2321))
| hBOOL(hAPP(hAPP(c_member(X2323),hAPP(X2322,X2319)),X2320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_630,plain,
! [X3103,X3104,X3105,X3106,X3107] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3107,tc_HOL_Obool),X3106),X3105))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3104,tc_HOL_Obool),c_Set_Oimage(X3107,X3104,X3103,X3106)),c_Set_Oimage(X3107,X3104,X3103,X3105))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_631,plain,
! [X2472,X2473,X2474,X2475,X2476] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2476,X2475)),hAPP(X2476,X2474)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2473,X2473)),hAPP(hAPP(c_Product__Type_OPair(X2473,X2473),X2475),X2474)),X2472))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2473,X2473)),hAPP(hAPP(c_Product__Type_OPair(X2473,X2473),X2475),X2474)),c_Wellfounded_Omlex__prod(X2473,X2476,X2472))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_632,plain,
! [X1907,X1908,X1909,X1910,X1911] :
( ( ~ c_FunDef_Oin__rel(X1911,X1910,X1909,X1908,X1907)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1911,X1910)),hAPP(hAPP(c_Product__Type_OPair(X1911,X1910),X1908),X1907)),X1909)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1911,X1910)),hAPP(hAPP(c_Product__Type_OPair(X1911,X1910),X1908),X1907)),X1909))
| c_FunDef_Oin__rel(X1911,X1910,X1909,X1908,X1907) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_633,plain,
! [X3033,X3034,X3035,X3036,X3037] :
( ~ hBOOL(hAPP(hAPP(c_member(X3037),X3036),c_Set_Oimage(X3035,X3037,X3034,X3033)))
| hAPP(X3034,hAPP(c_Hilbert__Choice_Oinv__into(X3035,X3037,X3033,X3034),X3036)) = X3036 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).
fof(i_0_634,plain,
! [X3052,X3053,X3054,X3055,X3056,X3057,X3058] :
( ( c_Set_Oimage(X3054,X3053,X3052,c_Orderings_Otop__class_Otop(tc_fun(X3054,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3053,tc_HOL_Obool))
| hAPP(X3052,hAPP(c_Hilbert__Choice_Oinv__into(X3054,X3053,c_Orderings_Otop__class_Otop(tc_fun(X3054,tc_HOL_Obool)),X3052),X3055)) = X3055 )
& ( hAPP(X3056,hAPP(c_Hilbert__Choice_Oinv__into(X3058,X3057,c_Orderings_Otop__class_Otop(tc_fun(X3058,tc_HOL_Obool)),X3056),esk42_3(X3056,X3057,X3058))) != esk42_3(X3056,X3057,X3058)
| c_Set_Oimage(X3058,X3057,X3056,c_Orderings_Otop__class_Otop(tc_fun(X3058,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3057,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_635,plain,
! [X3169,X3170,X3171,X3172,X3173] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3173,tc_HOL_Obool),X3172),c_Set_Oimage(X3171,X3173,X3170,X3169)))
| c_Fun_Oinj__on(X3173,X3171,c_Hilbert__Choice_Oinv__into(X3171,X3173,X3169,X3170),X3172) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).
fof(i_0_636,plain,
! [X1731,X1732,X1733,X1734] :
( ( X1733 != X1731
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1732),X1731))) )
& ( X1734 != X1731
| X1734 != X1733
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1732),X1731))) )
& ( X1734 = X1731
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),X1732))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1732),X1731))) )
& ( X1734 != X1731
| X1734 = X1731
| X1733 = X1731
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1732),X1731))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),X1732))
| X1734 = X1731
| X1733 = X1731
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1732),X1731))) )
& ( X1734 != X1731
| X1734 = X1733
| X1733 = X1731
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1732),X1731))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),X1732))
| X1734 = X1733
| X1733 = X1731
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1734),X1733)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X1732),X1731))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_637,plain,
! [X1735,X1736,X1737,X1738] :
( ( X1738 != X1735
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1736),X1735))) )
& ( X1737 != X1735
| X1738 != X1737
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1736),X1735))) )
& ( X1737 = X1735
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),X1736))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1736),X1735))) )
& ( X1737 != X1735
| X1737 = X1735
| X1738 = X1735
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1736),X1735))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),X1736))
| X1737 = X1735
| X1738 = X1735
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1736),X1735))) )
& ( X1737 != X1735
| X1738 = X1737
| X1738 = X1735
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1736),X1735))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),X1736))
| X1738 = X1737
| X1738 = X1735
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1738),X1737)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop,X1736),X1735))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_638,plain,
! [X3242,X3243,X3244,X3245,X3246,X3247] : hAPP(c_COMBS(X3247,X3246,X3245,X3244,X3243),X3242) = hAPP(hAPP(X3244,X3242),hAPP(X3243,X3242)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_639,plain,
! [X2313,X2314,X2315,X2316,X2317,X2318] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2318,X2317)),X2316),c_FuncSet_OPi(X2318,X2317,X2315,X2314)))
| ~ hBOOL(hAPP(hAPP(c_member(X2318),X2313),X2315))
| hBOOL(hAPP(hAPP(c_member(X2317),hAPP(X2316,X2313)),hAPP(X2314,X2313))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_640,plain,
! [X2246,X2247,X2248,X2249,X2250,X2251] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2251,X2250)),X2249),c_FuncSet_OPi(X2251,X2250,X2248,X2247)))
| hBOOL(hAPP(hAPP(c_member(X2250),hAPP(X2249,X2246)),hAPP(X2247,X2246)))
| ~ hBOOL(hAPP(hAPP(c_member(X2251),X2246),X2248)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])]) ).
fof(i_0_641,plain,
! [X2983,X2984,X2985,X2986,X2987] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2986),hAPP(X2985,X2984)),c_Set_Oimage(X2987,X2986,X2985,X2983)))
| hBOOL(hAPP(hAPP(c_member(X2987),X2984),X2983))
| ~ c_Fun_Oinj__on(X2987,X2986,X2985,c_Orderings_Otop__class_Otop(tc_fun(X2987,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2987),X2984),X2983))
| hBOOL(hAPP(hAPP(c_member(X2986),hAPP(X2985,X2984)),c_Set_Oimage(X2987,X2986,X2985,X2983)))
| ~ c_Fun_Oinj__on(X2987,X2986,X2985,c_Orderings_Otop__class_Otop(tc_fun(X2987,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,
! [X3044,X3045,X3046,X3047] :
( c_Set_Oimage(X3047,X3046,X3045,c_Orderings_Otop__class_Otop(tc_fun(X3047,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3046,tc_HOL_Obool))
| c_Set_Oimage(X3047,X3046,X3045,c_Set_Oimage(X3046,X3047,c_Hilbert__Choice_Oinv__into(X3047,X3046,c_Orderings_Otop__class_Otop(tc_fun(X3047,tc_HOL_Obool)),X3045),X3044)) = X3044 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).
fof(i_0_643,plain,
! [X3038,X3039,X3040,X3041,X3042,X3043] :
( c_Set_Oimage(X3043,X3042,X3041,X3040) != X3039
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3042,tc_HOL_Obool),X3038),X3039))
| c_Set_Oimage(X3043,X3042,X3041,c_Set_Oimage(X3042,X3043,c_Hilbert__Choice_Oinv__into(X3043,X3042,X3040,X3041),X3038)) = X3038 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).
fof(i_0_644,plain,
! [X1871,X1872,X1873,X1874,X1875,X1876,X1877,X1878,X1879,X1880] :
( ( ~ c_Fun_Oinj__on(X1874,X1873,X1872,X1871)
| ~ hBOOL(hAPP(hAPP(c_member(X1874),X1875),X1871))
| ~ hBOOL(hAPP(hAPP(c_member(X1874),X1876),X1871))
| hAPP(X1872,X1875) != hAPP(X1872,X1876)
| X1875 = X1876 )
& ( hBOOL(hAPP(hAPP(c_member(X1880),esk5_4(X1877,X1878,X1879,X1880)),X1877))
| c_Fun_Oinj__on(X1880,X1879,X1878,X1877) )
& ( hBOOL(hAPP(hAPP(c_member(X1880),esk6_4(X1877,X1878,X1879,X1880)),X1877))
| c_Fun_Oinj__on(X1880,X1879,X1878,X1877) )
& ( hAPP(X1878,esk5_4(X1877,X1878,X1879,X1880)) = hAPP(X1878,esk6_4(X1877,X1878,X1879,X1880))
| c_Fun_Oinj__on(X1880,X1879,X1878,X1877) )
& ( esk5_4(X1877,X1878,X1879,X1880) != esk6_4(X1877,X1878,X1879,X1880)
| c_Fun_Oinj__on(X1880,X1879,X1878,X1877) ) ),
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,
! [X1739,X1740,X1741] :
( X1741 = X1740
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1739),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,X1739),X1741),X1740)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_646,plain,
! [X3070,X3071,X3072,X3073,X3074] : c_Set_Oimage(X3074,X3073,hAPP(c_COMBB(X3072,X3073,X3074,X3071),X3070),c_Orderings_Otop__class_Otop(tc_fun(X3074,tc_HOL_Obool))) = c_Set_Oimage(X3072,X3073,X3071,c_Set_Oimage(X3074,X3072,X3070,c_Orderings_Otop__class_Otop(tc_fun(X3074,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_range__composition]) ).
fof(i_0_647,plain,
! [X1897,X1898,X1899,X1900,X1901] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1901,X1900)),hAPP(X1901,X1899)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1898,X1898)),hAPP(hAPP(c_Product__Type_OPair(X1898,X1898),X1900),X1899)),c_List_Omeasures(X1898,c_List_Olist_OCons(tc_fun(X1898,tc_Nat_Onat),X1901,X1897)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).
fof(i_0_648,plain,
! [X3166,X3167,X3168] :
( ~ c_Finite__Set_Ofinite(X3168,X3167)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3168,tc_HOL_Obool),X3167),c_Set_Oimage(X3168,X3168,X3166,X3167)))
| c_Fun_Oinj__on(X3168,X3168,X3166,X3167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_649,plain,
! [X1649,X1650,X1651,X1652,X1653] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X1650,X1649)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1651),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X1650,X1651) = hAPP(X1651,X1649) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk2_2(X1652,X1653)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X1653,X1652) )
& ( hAPP(X1653,esk2_2(X1652,X1653)) != hAPP(esk2_2(X1652,X1653),X1652)
| c_Arrow__Order__Mirabelle_Odictator(X1653,X1652) ) ),
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,
! [X1939,X1940,X1941] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1941,X1941)),hAPP(hAPP(c_Product__Type_OPair(X1941,X1941),X1940),X1939)),c_List_Omeasures(X1941,c_List_Olist_ONil(tc_fun(X1941,tc_Nat_Onat))))),
inference(variable_rename,[status(thm)],[i_0_524]) ).
fof(i_0_651,plain,
! [X1844,X1845,X1846,X1847] :
( ~ c_Fun_Oinj__on(X1847,X1846,X1845,c_Orderings_Otop__class_Otop(tc_fun(X1847,tc_HOL_Obool)))
| c_Fun_Oinj__on(X1847,tc_fun(X1844,X1846),hAPP(c_COMBB(X1846,tc_fun(X1844,X1846),X1847,c_COMBK(X1846,X1844)),X1845),c_Orderings_Otop__class_Otop(tc_fun(X1847,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).
fof(i_0_652,plain,
! [X2308,X2309] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2309,X2309)),c_COMBI(X2309)),c_FuncSet_OPi(X2309,X2309,X2308,hAPP(c_COMBK(tc_fun(X2309,tc_HOL_Obool),X2309),X2308)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_653,plain,
! [X3120,X3121,X3122,X3123,X3124,X3125] : c_Set_Oimage(X3125,X3124,X3123,c_Set_Oimage(X3122,X3125,X3121,X3120)) = c_Set_Oimage(X3122,X3124,hAPP(c_COMBB(X3125,X3124,X3122,X3123),X3121),X3120),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_654,plain,
! [X1848,X1849,X1850] :
( X1850 = X1849
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1848),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(X1848,X1850,X1849)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_655,plain,
! [X1964,X1965,X1966,X1967] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1967,X1967)),hAPP(hAPP(c_Product__Type_OPair(X1967,X1967),X1966),X1965)),c_Wellfounded_Omeasure(X1967,X1964)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1964,X1966)),hAPP(X1964,X1965))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1964,X1966)),hAPP(X1964,X1965)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1967,X1967)),hAPP(hAPP(c_Product__Type_OPair(X1967,X1967),X1966),X1965)),c_Wellfounded_Omeasure(X1967,X1964))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_656,plain,
! [X3174,X3175,X3176,X3177,X3178] :
( ~ c_Fun_Oinj__on(X3178,X3177,X3176,X3175)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3178,tc_HOL_Obool),X3174),X3175))
| c_Set_Oimage(X3177,X3178,c_Hilbert__Choice_Oinv__into(X3178,X3177,X3175,X3176),c_Set_Oimage(X3178,X3177,X3176,X3174)) = X3174 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).
fof(i_0_657,plain,
! [X2988,X2989,X2990,X2991,X2992] :
( ~ c_Finite__Set_Ofinite(X2992,X2991)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2990,tc_HOL_Obool),X2989),c_Set_Oimage(X2992,X2990,X2988,X2991)))
| c_Finite__Set_Ofinite(X2990,X2989) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
fof(i_0_658,plain,
! [X1744,X1745] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1745),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,X1745),X1744)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_659,plain,
! [X1742,X1743] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1743),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,X1743),X1742)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_660,plain,
! [X3186,X3187,X3188,X3189] :
( ~ c_Fun_Oinj__on(X3189,X3188,X3187,c_Orderings_Otop__class_Otop(tc_fun(X3189,tc_HOL_Obool)))
| c_Set_Oimage(X3188,X3189,c_Hilbert__Choice_Oinv__into(X3189,X3188,c_Orderings_Otop__class_Otop(tc_fun(X3189,tc_HOL_Obool)),X3187),c_Set_Oimage(X3189,X3188,X3187,X3186)) = X3186 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).
fof(i_0_661,plain,
! [X3182,X3183,X3184,X3185] :
( ~ c_Fun_Oinj__on(X3185,X3184,X3183,c_Orderings_Otop__class_Otop(tc_fun(X3185,tc_HOL_Obool)))
| c_Set_Oimage(X3184,X3185,c_Hilbert__Choice_Oinv__into(X3185,X3184,c_Orderings_Otop__class_Otop(tc_fun(X3185,tc_HOL_Obool)),X3183),c_Set_Oimage(X3185,X3184,X3183,X3182)) = X3182 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).
fof(i_0_662,plain,
! [X3048,X3049,X3050,X3051] :
( c_Set_Oimage(X3051,X3050,X3049,c_Orderings_Otop__class_Otop(tc_fun(X3051,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3050,tc_HOL_Obool))
| hAPP(X3049,hAPP(c_Hilbert__Choice_Oinv__into(X3051,X3050,c_Orderings_Otop__class_Otop(tc_fun(X3051,tc_HOL_Obool)),X3049),X3048)) = X3048 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).
fof(i_0_663,plain,
! [X2477,X2478,X2479,X2480,X2481] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2481,X2480)),hAPP(X2481,X2479)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2478,X2478)),hAPP(hAPP(c_Product__Type_OPair(X2478,X2478),X2480),X2479)),c_Wellfounded_Omlex__prod(X2478,X2481,X2477))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_664,plain,
! [X3190,X3191,X3192] :
( c_Set_Oimage(X3192,X3191,X3190,c_Orderings_Otop__class_Otop(tc_fun(X3192,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3191,tc_HOL_Obool))
| c_Fun_Oinj__on(X3191,X3192,c_Hilbert__Choice_Oinv__into(X3192,X3191,c_Orderings_Otop__class_Otop(tc_fun(X3192,tc_HOL_Obool)),X3190),c_Orderings_Otop__class_Otop(tc_fun(X3191,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).
fof(i_0_665,plain,
! [X3128,X3129,X3130,X3131] : hBOOL(hAPP(hAPP(c_member(X3131),hAPP(X3130,X3129)),c_Set_Oimage(X3128,X3131,X3130,c_Orderings_Otop__class_Otop(tc_fun(X3128,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_666,plain,
! [X3179,X3180,X3181] :
( ~ c_Fun_Oinj__on(X3181,X3180,X3179,c_Orderings_Otop__class_Otop(tc_fun(X3181,tc_HOL_Obool)))
| c_Set_Oimage(X3180,X3181,c_Hilbert__Choice_Oinv__into(X3181,X3180,c_Orderings_Otop__class_Otop(tc_fun(X3181,tc_HOL_Obool)),X3179),c_Orderings_Otop__class_Otop(tc_fun(X3180,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3181,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).
fof(i_0_667,plain,
! [X3087,X3088,X3089,X3090,X3091] :
( ~ hBOOL(hAPP(hAPP(c_member(X3091),X3090),X3089))
| hBOOL(hAPP(hAPP(c_member(X3088),hAPP(X3087,X3090)),c_Set_Oimage(X3091,X3088,X3087,X3089))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_668,plain,
! [X1942,X1943,X1944,X1945,X1946,X1947] : c_List_Olist_Olist__case(X1947,X1946,X1945,X1944,c_List_Olist_OCons(X1946,X1943,X1942)) = hAPP(hAPP(X1944,X1943),X1942),
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_b____),v_a____)),v_Lab____)),
inference(fof_simplification,[status(thm)],[fact__096_Ib_M_Aa_J_A_126_058_ALab_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_a____),v_b____)),v_Lba____)),
inference(fof_simplification,[status(thm)],[fact__096_Ia_M_Ab_J_A_126_058_ALba_096]) ).
fof(i_0_671,plain,
! [X3132,X3133,X3134,X3135,X3136] :
( X3136 != hAPP(X3135,X3134)
| hBOOL(hAPP(hAPP(c_member(X3133),X3136),c_Set_Oimage(X3132,X3133,X3135,c_Orderings_Otop__class_Otop(tc_fun(X3132,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_672,plain,
! [X2961,X2962,X2963,X2964,X2965,X2966] :
( X2966 != hAPP(X2965,X2964)
| ~ hBOOL(hAPP(hAPP(c_member(X2963),X2964),X2962))
| hBOOL(hAPP(hAPP(c_member(X2961),X2966),c_Set_Oimage(X2963,X2961,X2965,X2962))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_673,plain,
! [X3092,X3093,X3094,X3095,X3096,X3097] :
( ~ hBOOL(hAPP(hAPP(c_member(X3097),X3096),X3095))
| X3094 != hAPP(X3093,X3096)
| hBOOL(hAPP(hAPP(c_member(X3092),X3094),c_Set_Oimage(X3097,X3092,X3093,X3095))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_674,plain,
! [X3013,X3014,X3015,X3016,X3017] :
( ( c_Set_Oimage(X3017,X3016,X3015,X3014) != c_Set_Oimage(X3017,X3016,X3015,X3013)
| X3014 = X3013
| ~ c_Fun_Oinj__on(X3017,X3016,X3015,c_Orderings_Otop__class_Otop(tc_fun(X3017,tc_HOL_Obool))) )
& ( X3014 != X3013
| c_Set_Oimage(X3017,X3016,X3015,X3014) = c_Set_Oimage(X3017,X3016,X3015,X3013)
| ~ c_Fun_Oinj__on(X3017,X3016,X3015,c_Orderings_Otop__class_Otop(tc_fun(X3017,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,
! [X2468,X2469,X2470,X2471] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2471),X2470),X2469)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2471),X2468),X2469)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2471),X2470),X2468))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2471) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2471),X2470),X2468))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2471),X2470),X2469)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2471),X2468),X2469)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2471) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_676,plain,
! [X2447,X2448,X2449,X2450] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2450)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2450),X2449),X2448)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2450),X2447),X2448)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2450),X2449),X2447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_677,plain,
! [X2464,X2465,X2466,X2467] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2467),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2467),X2466),X2465)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2467),X2466),X2464)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2467),X2465),X2464))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2467) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2467),X2465),X2464))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2467),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2467),X2466),X2465)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2467),X2466),X2464)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2467) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_678,plain,
! [X2443,X2444,X2445,X2446] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2446)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2446),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2446),X2445),X2444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2446),X2445),X2443)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2446),X2444),X2443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_679,plain,
! [X1922,X1923,X1924,X1925] : c_List_Olist_Olist__case(X1925,X1924,X1923,X1922,c_List_Olist_ONil(X1924)) = X1923,
inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).
fof(i_0_680,plain,
! [X2993,X2994,X2995,X2996] :
( ~ c_Finite__Set_Ofinite(X2996,c_Set_Oimage(X2995,X2996,X2994,X2993))
| ~ c_Fun_Oinj__on(X2995,X2996,X2994,X2993)
| c_Finite__Set_Ofinite(X2995,X2993) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_681,plain,
! [X1926,X1927,X1928,X1929] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1929,tc_HOL_Obool)),X1928),X1927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1929,tc_HOL_Obool)),X1927),X1926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1929,tc_HOL_Obool)),X1928),X1926)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_682,plain,
! [X2435,X2436,X2437,X2438] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2438)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2438,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2438),X2437),X2436)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2438),X2435),X2436)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2438,X2437),X2435)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_683,plain,
! [X2414,X2415,X2416,X2417] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2417,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2417),X2416),X2415)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2417),X2414),X2415)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2417,X2416),X2414))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2417) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2417,X2416),X2414))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2417,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2417),X2416),X2415)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2417),X2414),X2415)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2417) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_684,plain,
! [X2439,X2440,X2441,X2442] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2442)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2442,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2442),X2441),X2440)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2442),X2441),X2439)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2442,X2440),X2439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_685,plain,
! [X2418,X2419,X2420,X2421] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2421,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2421),X2420),X2419)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2421),X2420),X2418)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2421,X2419),X2418))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2421) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2421,X2419),X2418))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2421,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2421),X2420),X2419)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2421),X2420),X2418)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X2421) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_686,plain,
! [X2667,X2668,X2669,X2670] :
( ( hBOOL(hAPP(hAPP(c_member(X2670),X2669),X2667))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2670,tc_HOL_Obool),c_Set_Oinsert(X2670,X2669,X2668)),X2667)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2670,tc_HOL_Obool),X2668),X2667))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2670,tc_HOL_Obool),c_Set_Oinsert(X2670,X2669,X2668)),X2667)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2670),X2669),X2667))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2670,tc_HOL_Obool),X2668),X2667))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2670,tc_HOL_Obool),c_Set_Oinsert(X2670,X2669,X2668)),X2667)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).
fof(i_0_687,plain,
! [X1824,X1825,X1826,X1827] :
( ~ c_Fun_Oinj__on(X1827,X1826,X1825,c_Orderings_Otop__class_Otop(tc_fun(X1827,tc_HOL_Obool)))
| hAPP(c_Hilbert__Choice_Oinv__into(X1827,X1826,c_Orderings_Otop__class_Otop(tc_fun(X1827,tc_HOL_Obool)),X1825),hAPP(X1825,X1824)) = X1824 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).
fof(i_0_688,plain,
! [X1828,X1829,X1830,X1831,X1832] :
( ~ c_Fun_Oinj__on(X1832,X1831,X1830,c_Orderings_Otop__class_Otop(tc_fun(X1832,tc_HOL_Obool)))
| hAPP(X1830,X1829) != X1828
| hAPP(c_Hilbert__Choice_Oinv__into(X1832,X1831,c_Orderings_Otop__class_Otop(tc_fun(X1832,tc_HOL_Obool)),X1830),X1828) = X1829 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).
fof(i_0_689,plain,
! [X1655,X1656,X1657] :
( ( hAPP(hAPP(c_COMBC(X1657,tc_fun(X1657,tc_HOL_Obool),tc_HOL_Obool),c_member(X1657)),X1656) != hAPP(hAPP(c_COMBC(X1657,tc_fun(X1657,tc_HOL_Obool),tc_HOL_Obool),c_member(X1657)),X1655)
| X1656 = X1655 )
& ( X1656 != X1655
| hAPP(hAPP(c_COMBC(X1657,tc_fun(X1657,tc_HOL_Obool),tc_HOL_Obool),c_member(X1657)),X1656) = hAPP(hAPP(c_COMBC(X1657,tc_fun(X1657,tc_HOL_Obool),tc_HOL_Obool),c_member(X1657)),X1655) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_690,plain,
! [X2185,X2186,X2187] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2187),X2186)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2187),X2185)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2186),X2185)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2186),X2185))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2187),X2186)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2187),X2185))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_691,plain,
! [X1833,X1834,X1835,X1836,X1837] :
( ~ c_Fun_Oinj__on(X1837,X1836,X1835,X1834)
| ~ hBOOL(hAPP(hAPP(c_member(X1837),X1833),X1834))
| hAPP(c_Hilbert__Choice_Oinv__into(X1837,X1836,X1834,X1835),hAPP(X1835,X1833)) = X1833 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).
fof(i_0_692,plain,
! [X1838,X1839,X1840,X1841,X1842,X1843] :
( ~ c_Fun_Oinj__on(X1843,X1842,X1841,X1840)
| ~ hBOOL(hAPP(hAPP(c_member(X1843),X1839),X1840))
| hAPP(X1841,X1839) != X1838
| hAPP(c_Hilbert__Choice_Oinv__into(X1843,X1842,X1840,X1841),X1838) = X1839 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).
fof(i_0_693,plain,
! [X3142,X3143,X3144,X3145] :
( ~ c_Finite__Set_Ofinite(X3145,X3144)
| c_Finite__Set_Ocard(X3143,c_Set_Oimage(X3145,X3143,X3142,X3144)) != c_Finite__Set_Ocard(X3145,X3144)
| c_Fun_Oinj__on(X3145,X3143,X3142,X3144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_694,plain,
! [X3146,X3147,X3148,X3149] :
( ( ~ c_Fun_Oinj__on(X3149,X3147,X3146,X3148)
| c_Finite__Set_Ocard(X3147,c_Set_Oimage(X3149,X3147,X3146,X3148)) = c_Finite__Set_Ocard(X3149,X3148)
| ~ c_Finite__Set_Ofinite(X3149,X3148) )
& ( c_Finite__Set_Ocard(X3147,c_Set_Oimage(X3149,X3147,X3146,X3148)) != c_Finite__Set_Ocard(X3149,X3148)
| c_Fun_Oinj__on(X3149,X3147,X3146,X3148)
| ~ c_Finite__Set_Ofinite(X3149,X3148) ) ),
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,
! [X2643,X2644,X2645,X2646] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2646,tc_HOL_Obool),X2645),X2644))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2646,tc_HOL_Obool),c_Set_Oinsert(X2646,X2643,X2645)),c_Set_Oinsert(X2646,X2643,X2644))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(i_0_696,plain,
! [X3230,X3231,X3232,X3233,X3234,X3235] : hAPP(hAPP(c_COMBB(X3235,X3234,X3233,X3232),X3231),X3230) = hAPP(X3232,hAPP(X3231,X3230)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_697,plain,
! [X2451,X2452,X2453,X2454,X2455] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2455)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2455),X2454),X2453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2455),X2452),X2451))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2455),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2455),X2454),X2452)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2455),X2453),X2451))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_698,plain,
! [X2909,X2910,X2911,X2912] : c_List_Olist_Olist__size(X2912,X2911,c_List_Olist_OCons(X2912,X2910,X2909)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X2911,X2910)),c_List_Olist_Olist__size(X2912,X2911,X2909))),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,
! [X2066,X2067,X2068] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2068),X2067)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2068),X2066)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2067),X2066)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2067),X2066))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2068),X2067)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2068),X2066))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_700,plain,
! [X2334,X2335,X2336,X2337,X2338] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2338)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2338,X2337),X2336))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2338),X2335),X2334))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2338),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2338),X2337),X2335)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2338),X2336),X2334))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_701,plain,
! [X2339,X2340,X2341,X2342,X2343] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2343)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2343),X2342),X2341))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2343,X2340),X2339))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2343),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2343),X2342),X2340)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2343),X2341),X2339))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_702,plain,
! [X2288,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)),X2289),X2288))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2291,tc_HOL_Obool)),X2290),X2288)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_703,plain,
! [X2292,X2293,X2294,X2295] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2295,tc_HOL_Obool)),X2294),X2293))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2295,tc_HOL_Obool),X2293),X2292))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2295,tc_HOL_Obool)),X2294),X2292)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_704,plain,
! [X3137,X3138,X3139,X3140,X3141] :
( ~ hBOOL(hAPP(hAPP(c_member(X3141),X3140),X3139))
| c_Set_Oinsert(X3138,hAPP(X3137,X3140),c_Set_Oimage(X3141,X3138,X3137,X3139)) = c_Set_Oimage(X3141,X3138,X3137,X3139) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
fof(i_0_705,plain,
! [X2528,X2529,X2530] :
( ~ c_Finite__Set_Ofinite(X2530,X2529)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2530,tc_HOL_Obool),X2528),X2529))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2530,X2528)),c_Finite__Set_Ocard(X2530,X2529)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2530,tc_HOL_Obool)),X2528),X2529)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_706,plain,
! [X1706,X1707] :
( X1707 = X1706
| c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X1707,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,X1706,c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt,esk4_2(X1706,X1707),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_707,plain,
! [X2430,X2431,X2432,X2433,X2434] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2434)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2434,X2433),X2432))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2434,X2431),X2430))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2434,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2434),X2433),X2431)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2434),X2432),X2430))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_708,plain,
! [X2757,X2758] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2758),X2757),X2757)),c_Groups_Ozero__class_Ozero(X2758)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2758),X2757),c_Groups_Ozero__class_Ozero(X2758)))
| ~ class_Groups_Olinordered__ab__group__add(X2758) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2758),X2757),c_Groups_Ozero__class_Ozero(X2758)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2758),X2757),X2757)),c_Groups_Ozero__class_Ozero(X2758)))
| ~ class_Groups_Olinordered__ab__group__add(X2758) ) ),
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_709,plain,
! [X2793,X2794] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2794),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2794),X2793),X2793)),c_Groups_Ozero__class_Ozero(X2794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2794),X2793),c_Groups_Ozero__class_Ozero(X2794)))
| ~ class_Rings_Olinordered__idom(X2794) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2794),X2793),c_Groups_Ozero__class_Ozero(X2794)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2794),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2794),X2793),X2793)),c_Groups_Ozero__class_Ozero(X2794)))
| ~ class_Rings_Olinordered__idom(X2794) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_710,plain,
! [X2172,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),X2173),X2172))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2175),X2173)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2174),X2172))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_711,plain,
! [X3098,X3099,X3100,X3101,X3102] : c_Set_Oimage(X3102,X3101,X3100,c_Set_Oinsert(X3102,X3099,X3098)) = c_Set_Oinsert(X3101,hAPP(X3100,X3099),c_Set_Oimage(X3102,X3101,X3100,X3098)),
inference(variable_rename,[status(thm)],[fact_image__insert]) ).
fof(i_0_712,plain,
! [X3161,X3162] :
( ~ c_Finite__Set_Ofinite(X3162,c_Orderings_Otop__class_Otop(tc_fun(X3162,tc_HOL_Obool)))
| c_Set_Oimage(X3162,X3162,X3161,c_Orderings_Otop__class_Otop(tc_fun(X3162,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X3162,tc_HOL_Obool))
| c_Fun_Oinj__on(X3162,X3162,X3161,c_Orderings_Otop__class_Otop(tc_fun(X3162,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_713,plain,
! [X2279,X2280,X2281,X2282,X2283] :
( ~ c_Fun_Oinj__on(X2283,X2282,X2281,X2280)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2283,tc_HOL_Obool),X2279),X2280))
| c_Fun_Oinj__on(X2283,X2282,X2281,X2279) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_714,plain,
! [X3018,X3019,X3020,X3021] :
( ~ c_Fun_Oinj__on(X3021,X3020,X3019,X3018)
| c_Finite__Set_Ocard(X3020,c_Set_Oimage(X3021,X3020,X3019,X3018)) = c_Finite__Set_Ocard(X3021,X3018) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_715,plain,
! [X2747,X2748,X2749] :
( ~ class_Groups_Oordered__comm__monoid__add(X2749)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2749),X2748),c_Groups_Ozero__class_Ozero(X2749)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2749),X2747),c_Groups_Ozero__class_Ozero(X2749)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2749),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2749),X2748),X2747)),c_Groups_Ozero__class_Ozero(X2749))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_716,plain,
! [X2916,X2917,X2918] :
( ~ class_Rings_Oring__1(X2918)
| ~ hBOOL(hAPP(hAPP(c_member(X2918),X2917),c_Int_Oring__1__class_OInts(X2918)))
| ~ hBOOL(hAPP(hAPP(c_member(X2918),X2916),c_Int_Oring__1__class_OInts(X2918)))
| hBOOL(hAPP(hAPP(c_member(X2918),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2918),X2917),X2916)),c_Int_Oring__1__class_OInts(X2918))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).
fof(i_0_717,plain,
! [X3159,X3160] :
( ~ c_Finite__Set_Ofinite(X3160,c_Orderings_Otop__class_Otop(tc_fun(X3160,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X3160,X3160,X3159,c_Orderings_Otop__class_Otop(tc_fun(X3160,tc_HOL_Obool)))
| c_Set_Oimage(X3160,X3160,X3159,c_Orderings_Otop__class_Otop(tc_fun(X3160,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X3160,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_718,plain,
! [X2460,X2461,X2462,X2463] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2463)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2463),X2462),X2461))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2463),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2463),X2462),X2460)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2463),X2461),X2460))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_719,plain,
! [X2456,X2457,X2458,X2459] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X2459)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2459),X2458),X2457))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2459),X2456),X2458)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2459),X2456),X2457))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_720,plain,
! [X2743,X2744] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2744,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2744),X2743),X2743)),c_Groups_Ozero__class_Ozero(X2744)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2744,X2743),c_Groups_Ozero__class_Ozero(X2744)))
| ~ class_Groups_Olinordered__ab__group__add(X2744) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2744,X2743),c_Groups_Ozero__class_Ozero(X2744)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2744,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2744),X2743),X2743)),c_Groups_Ozero__class_Ozero(X2744)))
| ~ class_Groups_Olinordered__ab__group__add(X2744) ) ),
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_721,plain,
! [X2663,X2664,X2665,X2666] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2666,tc_HOL_Obool),X2664),c_Set_Oinsert(X2666,X2665,X2663)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2666,tc_HOL_Obool),X2664),X2663))
| hBOOL(hAPP(hAPP(c_member(X2666),X2665),X2664)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2666,tc_HOL_Obool),X2664),X2663))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2666,tc_HOL_Obool),X2664),c_Set_Oinsert(X2666,X2665,X2663)))
| hBOOL(hAPP(hAPP(c_member(X2666),X2665),X2664)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])])]) ).
fof(i_0_722,plain,
! [X2769,X2770,X2771] :
( ~ class_Groups_Oordered__comm__monoid__add(X2771)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2771,X2770),c_Groups_Ozero__class_Ozero(X2771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2771),X2769),c_Groups_Ozero__class_Ozero(X2771)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2771),X2770),X2769)),c_Groups_Ozero__class_Ozero(X2771))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_723,plain,
! [X2772,X2773,X2774] :
( ~ class_Groups_Oordered__comm__monoid__add(X2774)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2774),X2773),c_Groups_Ozero__class_Ozero(X2774)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2774,X2772),c_Groups_Ozero__class_Ozero(X2774)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2774),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2774),X2773),X2772)),c_Groups_Ozero__class_Ozero(X2774))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_724,plain,
! [X2046,X2047,X2048,X2049] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2049),X2048))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2047),X2046))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2049),X2047)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2048),X2046))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_725,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),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_526])])]) ).
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____)),esk7_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk7_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])])]) ).
fof(i_0_727,plain,
! [X2659,X2660,X2661,X2662] :
( ( c_Finite__Set_Ofinite(X2662,X2660)
| ~ c_Finite__Set_Ofinite(tc_sum(X2662,X2661),c_Sum__Type_OPlus(X2662,X2661,X2660,X2659)) )
& ( c_Finite__Set_Ofinite(X2661,X2659)
| ~ c_Finite__Set_Ofinite(tc_sum(X2662,X2661),c_Sum__Type_OPlus(X2662,X2661,X2660,X2659)) )
& ( ~ c_Finite__Set_Ofinite(X2662,X2660)
| ~ c_Finite__Set_Ofinite(X2661,X2659)
| c_Finite__Set_Ofinite(tc_sum(X2662,X2661),c_Sum__Type_OPlus(X2662,X2661,X2660,X2659)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_728,plain,
! [X2651,X2652,X2653,X2654] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2654,X2653),c_Sum__Type_OPlus(X2654,X2653,X2652,X2651))
| c_Finite__Set_Ofinite(X2654,X2652) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_729,plain,
! [X2647,X2648,X2649,X2650] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2650,X2649),c_Sum__Type_OPlus(X2650,X2649,X2648,X2647))
| c_Finite__Set_Ofinite(X2649,X2647) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_730,plain,
! [X2422,X2423,X2424,X2425] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2425)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2425,X2424),X2423))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2425,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2425),X2424),X2422)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2425),X2423),X2422))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_731,plain,
! [X2426,X2427,X2428,X2429] :
( ~ class_Groups_Oordered__ab__semigroup__add(X2429)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2429,X2428),X2427))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2429,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2429),X2426),X2428)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2429),X2426),X2427))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_732,plain,
! [X2165,X2166,X2167] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2167),X2166)),X2165))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2167),X2165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_733,plain,
! [X2726,X2727,X2728] :
( ~ class_Groups_Oordered__comm__monoid__add(X2728)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2728,X2727),c_Groups_Ozero__class_Ozero(X2728)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2728,X2726),c_Groups_Ozero__class_Ozero(X2728)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2728,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2728),X2727),X2726)),c_Groups_Ozero__class_Ozero(X2728))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_734,plain,
! [X2284,X2285,X2286,X2287] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2286,X2287),X2285),X2284))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2286,X2287)),X2285),X2284))
| ~ class_Orderings_Oord(X2287) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2286,X2287),X2284),X2285))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2286,X2287)),X2285),X2284))
| ~ class_Orderings_Oord(X2287) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2286,X2287),X2285),X2284))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2286,X2287),X2284),X2285))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2286,X2287)),X2285),X2284))
| ~ class_Orderings_Oord(X2287) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])]) ).
fof(i_0_735,plain,
! [X2356,X2357,X2358,X2359,X2360,X2361] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2361,tc_fun(X2360,tc_HOL_Obool)),X2359),X2358))
| ~ hBOOL(hAPP(hAPP(X2359,X2357),X2356))
| hBOOL(hAPP(hAPP(X2358,X2357),X2356)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_736,plain,
! [X2347,X2348,X2349,X2350,X2351,X2352] :
( ~ hBOOL(hAPP(hAPP(X2352,X2351),X2350))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2349,tc_fun(X2348,tc_HOL_Obool)),X2352),X2347))
| hBOOL(hAPP(hAPP(X2347,X2351),X2350)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_737,plain,
! [X2176,X2177,X2178] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2178),X2177))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2178),X2176)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2177),X2176))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_738,plain,
! [X1891,X1892,X1893,X1894,X1895,X1896] :
( ( hAPP(X1894,X1892) != hAPP(X1894,X1891)
| X1892 = X1891
| ~ hBOOL(hAPP(hAPP(c_member(X1896),X1891),X1893))
| ~ hBOOL(hAPP(hAPP(c_member(X1896),X1892),X1893))
| ~ c_Fun_Oinj__on(X1896,X1895,X1894,X1893) )
& ( X1892 != X1891
| hAPP(X1894,X1892) = hAPP(X1894,X1891)
| ~ hBOOL(hAPP(hAPP(c_member(X1896),X1891),X1893))
| ~ hBOOL(hAPP(hAPP(c_member(X1896),X1892),X1893))
| ~ c_Fun_Oinj__on(X1896,X1895,X1894,X1893) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_739,plain,
! [X1885,X1886,X1887,X1888,X1889,X1890] :
( ~ c_Fun_Oinj__on(X1890,X1889,X1888,X1887)
| hAPP(X1888,X1886) != hAPP(X1888,X1885)
| ~ hBOOL(hAPP(hAPP(c_member(X1890),X1886),X1887))
| ~ hBOOL(hAPP(hAPP(c_member(X1890),X1885),X1887))
| X1886 = X1885 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_740,plain,
! [X1861,X1862,X1863,X1864,X1865,X1866] :
( ~ c_Fun_Oinj__on(X1866,X1865,X1864,X1863)
| X1862 = X1861
| ~ hBOOL(hAPP(hAPP(c_member(X1866),X1862),X1863))
| ~ hBOOL(hAPP(hAPP(c_member(X1866),X1861),X1863))
| hAPP(X1864,X1862) != hAPP(X1864,X1861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_741,plain,
! [X2037,X2038,X2039] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2039),X2037))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2039),X2038)),X2037)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2038),X2037))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2039),X2038)),X2037)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_529])])]) ).
fof(i_0_742,plain,
! [X2040,X2041,X2042] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2042),X2041)),X2040))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2042),X2040)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_743,plain,
! [X2043,X2044,X2045] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2045),X2044)),X2043))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2044),X2043)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_744,plain,
! [X2754,X2755,X2756] :
( ~ class_Groups_Oordered__comm__monoid__add(X2756)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2756),c_Groups_Ozero__class_Ozero(X2756)),X2755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2756),c_Groups_Ozero__class_Ozero(X2756)),X2754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2756),c_Groups_Ozero__class_Ozero(X2756)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2756),X2755),X2754))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_745,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_530])])]) ).
fof(i_0_746,plain,
! [X2997,X2998,X2999,X3001,X3002,X3003] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk38_2(X2997,X2998)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2999),X2998))
| ~ hBOOL(hAPP(X2997,X2999)) )
& ( hBOOL(hAPP(X2997,esk38_2(X2997,X2998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2999),X2998))
| ~ hBOOL(hAPP(X2997,X2999)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk39_2(X3001,X3002)),X3002))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3003),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3002)))
| ~ hBOOL(hAPP(X3001,X3003)) )
& ( hBOOL(hAPP(X3001,esk39_2(X3001,X3002)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3003),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3002)))
| ~ hBOOL(hAPP(X3001,X3003)) ) ),
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_747,plain,
! [X2055,X2056,X2057] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2057),X2056))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2057),X2055)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2056),X2055))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_748,plain,
! [X1867,X1868,X1869,X1870] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1870,tc_HOL_Obool)),X1869),X1868))
| ~ hBOOL(hAPP(hAPP(c_member(X1870),X1867),X1869))
| hBOOL(hAPP(hAPP(c_member(X1870),X1867),X1868)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_749,plain,
! [X2531,X2532,X2533] :
( ~ c_Finite__Set_Ofinite(X2533,X2532)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2533,tc_HOL_Obool)),X2531),X2532))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2533,X2531)),c_Finite__Set_Ocard(X2533,X2532))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_750,plain,
! [X2096,X2097] : 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)),X2097),X2096),
inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).
fof(i_0_751,plain,
! [X2950,X2951,X2952,X2953,X2954] :
( ~ class_Rings_Ocomm__semiring__1(X2954)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2954),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2954),X2953),X2952)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2954),X2951),X2950)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2954),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2954),X2953),X2951)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2954),X2952),X2950)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_752,plain,
! [X3005,X3006,X3008,X3009,X3010,X3012] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk40_2(X3005,X3006)),X3006))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3008),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3006)))
| hBOOL(hAPP(X3005,X3008)) )
& ( ~ hBOOL(hAPP(X3005,esk40_2(X3005,X3006)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3008),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3006)))
| hBOOL(hAPP(X3005,X3008)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk41_2(X3009,X3010)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3010)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3012),X3010))
| hBOOL(hAPP(X3009,X3012)) )
& ( ~ hBOOL(hAPP(X3009,esk41_2(X3009,X3010)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3012),X3010))
| hBOOL(hAPP(X3009,X3012)) ) ),
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_753,plain,
! [X2362,X2363,X2364,X2365] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2365,tc_HOL_Obool),X2364),X2363))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2365,tc_HOL_Obool),X2363),X2362))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2365,tc_HOL_Obool),X2364),X2362)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_754,plain,
! [X2783,X2784,X2785] :
( ~ class_Groups_Oordered__comm__monoid__add(X2785)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2785,c_Groups_Ozero__class_Ozero(X2785)),X2784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2785),c_Groups_Ozero__class_Ozero(X2785)),X2783))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2785),c_Groups_Ozero__class_Ozero(X2785)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2785),X2784),X2783))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_755,plain,
! [X2786,X2787,X2788] :
( ~ class_Groups_Oordered__comm__monoid__add(X2788)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2788),c_Groups_Ozero__class_Ozero(X2788)),X2787))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2788,c_Groups_Ozero__class_Ozero(X2788)),X2786))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2788),c_Groups_Ozero__class_Ozero(X2788)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2788),X2787),X2786))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_756,plain,
! [X2190,X2191] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2191),X2190)),X2191)),
inference(variable_rename,[status(thm)],[i_0_531]) ).
fof(i_0_757,plain,
! [X2188,X2189] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2189),X2188)),X2188)),
inference(variable_rename,[status(thm)],[i_0_532]) ).
fof(i_0_758,plain,
! [X2684,X2685,X2686,X2687] :
( ( ~ c_Finite__Set_Ofinite(X2687,X2686)
| ~ c_Finite__Set_Ofinite(X2685,X2684)
| c_Finite__Set_Ocard(tc_sum(X2687,X2685),c_Sum__Type_OPlus(X2687,X2685,X2686,X2684)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2687,X2686)),c_Finite__Set_Ocard(X2685,X2684)) )
& ( c_Finite__Set_Ofinite(X2687,X2686)
| c_Finite__Set_Ocard(tc_sum(X2687,X2685),c_Sum__Type_OPlus(X2687,X2685,X2686,X2684)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X2685,X2684)
| c_Finite__Set_Ocard(tc_sum(X2687,X2685),c_Sum__Type_OPlus(X2687,X2685,X2686,X2684)) = 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_759,plain,
! [X2563,X2564,X2565,X2566] :
( ~ c_Finite__Set_Ofinite(X2566,X2565)
| ~ c_Finite__Set_Ofinite(X2564,X2563)
| c_Finite__Set_Ocard(tc_sum(X2566,X2564),c_Sum__Type_OPlus(X2566,X2564,X2565,X2563)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2566,X2565)),c_Finite__Set_Ocard(X2564,X2563)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_760,plain,
! [X2750,X2751,X2752,X2753] :
( ~ class_Rings_Olinordered__semidom(X2753)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2753),c_Groups_Ozero__class_Ozero(X2753)),X2752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2753),X2751),X2750))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2753),X2751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2753),X2752),X2750))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_761,plain,
! [X2671,X2672,X2673] :
( ~ c_Finite__Set_Ofinite(X2673,X2672)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2673,X2672)),c_Finite__Set_Ocard(X2673,c_Set_Oinsert(X2673,X2671,X2672)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).
fof(i_0_762,plain,
! [X2924,X2925] :
( ~ class_Int_Oring__char__0(X2925)
| ~ hBOOL(hAPP(hAPP(c_member(X2925),X2924),c_Int_Oring__1__class_OInts(X2925)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2925),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2925),c_Groups_Oone__class_Oone(X2925)),X2924)),X2924) != c_Groups_Ozero__class_Ozero(X2925) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).
fof(i_0_763,plain,
! [X2759,X2760] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2760),c_Groups_Ozero__class_Ozero(X2760)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2760),X2759),X2759)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2760),c_Groups_Ozero__class_Ozero(X2760)),X2759))
| ~ class_Groups_Olinordered__ab__group__add(X2760) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2760),c_Groups_Ozero__class_Ozero(X2760)),X2759))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2760),c_Groups_Ozero__class_Ozero(X2760)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2760),X2759),X2759)))
| ~ class_Groups_Olinordered__ab__group__add(X2760) ) ),
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_764,plain,
! [X2765,X2766] :
( ( ~ 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),X2766),X2765)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2766))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2765)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2766))
| 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),X2766),X2765))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2765))
| 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),X2766),X2765))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_765,plain,
! [X2537,X2538,X2539] :
( ~ c_Finite__Set_Ofinite(X2539,X2538)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2539,tc_HOL_Obool),X2537),X2538))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2539,X2538)),c_Finite__Set_Ocard(X2539,X2537)))
| X2537 = X2538 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_766,plain,
! [X2639,X2640,X2641,X2642] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2642,tc_HOL_Obool),X2641),X2640))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2642,tc_HOL_Obool),X2641),c_Set_Oinsert(X2642,X2639,X2640))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).
fof(i_0_767,plain,
! [X2775,X2776,X2777,X2778] :
( ~ class_Groups_Oordered__comm__monoid__add(X2778)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2778,c_Groups_Ozero__class_Ozero(X2778)),X2777))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2778),X2776),X2775))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2778),X2776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2778),X2777),X2775))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_768,plain,
! [X2779,X2780,X2781,X2782] :
( ~ class_Groups_Oordered__comm__monoid__add(X2782)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2782),c_Groups_Ozero__class_Ozero(X2782)),X2781))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2782,X2780),X2779))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2782),X2780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2782),X2781),X2779))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_769,plain,
! [X2740,X2741,X2742] :
( ~ class_Groups_Oordered__comm__monoid__add(X2742)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2742,c_Groups_Ozero__class_Ozero(X2742)),X2741))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2742,c_Groups_Ozero__class_Ozero(X2742)),X2740))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2742,c_Groups_Ozero__class_Ozero(X2742)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2742),X2741),X2740))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_770,plain,
! [X1930,X1931,X1932,X1933,X1934] : c_List_Osplice(X1934,c_List_Olist_OCons(X1934,X1933,X1932),c_List_Olist_OCons(X1934,X1931,X1930)) = c_List_Olist_OCons(X1934,X1933,c_List_Olist_OCons(X1934,X1931,c_List_Osplice(X1934,X1932,X1930))),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).
fof(i_0_771,plain,
! [X2302,X2303,X2304] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2304,tc_HOL_Obool),X2303),X2302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2304,tc_HOL_Obool)),X2303),X2302)) )
& ( X2303 != X2302
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2304,tc_HOL_Obool)),X2303),X2302)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2304,tc_HOL_Obool),X2303),X2302))
| X2303 = X2302
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2304,tc_HOL_Obool)),X2303),X2302)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_772,plain,
! [X2299,X2300,X2301] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2301,tc_HOL_Obool),X2300),X2299))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2301,tc_HOL_Obool)),X2300),X2299))
| X2300 = X2299 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2301,tc_HOL_Obool)),X2300),X2299))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2301,tc_HOL_Obool),X2300),X2299)) )
& ( X2300 != X2299
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2301,tc_HOL_Obool),X2300),X2299)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_773,plain,
! [X2296,X2297,X2298] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2298,tc_HOL_Obool)),X2297),X2296))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2298,tc_HOL_Obool),X2297),X2296)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_774,plain,
! [X2610,X2611,X2612,X2613] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2613),X2612),c_Set_Oinsert(X2613,X2611,X2610)))
| X2612 = X2611
| hBOOL(hAPP(hAPP(c_member(X2613),X2612),X2610)) )
& ( X2612 != X2611
| hBOOL(hAPP(hAPP(c_member(X2613),X2612),c_Set_Oinsert(X2613,X2611,X2610))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2613),X2612),X2610))
| hBOOL(hAPP(hAPP(c_member(X2613),X2612),c_Set_Oinsert(X2613,X2611,X2610))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).
fof(i_0_775,plain,
! [X2578,X2579,X2580,X2581] :
( ~ hBOOL(hAPP(hAPP(c_member(X2581),X2580),c_Set_Oinsert(X2581,X2579,X2578)))
| X2580 = X2579
| hBOOL(hAPP(hAPP(c_member(X2581),X2580),X2578)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).
fof(i_0_776,plain,
! [X2745,X2746] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2746,c_Groups_Ozero__class_Ozero(X2746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2746),X2745),X2745)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2746,c_Groups_Ozero__class_Ozero(X2746)),X2745))
| ~ class_Groups_Olinordered__ab__group__add(X2746) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2746,c_Groups_Ozero__class_Ozero(X2746)),X2745))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2746,c_Groups_Ozero__class_Ozero(X2746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2746),X2745),X2745)))
| ~ class_Groups_Olinordered__ab__group__add(X2746) ) ),
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_777,plain,
! [X2310,X2311,X2312] : c_FuncSet_OPi(X2312,X2311,X2310,hAPP(c_COMBK(tc_fun(X2311,tc_HOL_Obool),X2312),c_Orderings_Otop__class_Otop(tc_fun(X2311,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2312,X2311),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pi__UNIV]) ).
fof(i_0_778,plain,
! [X2733,X2734,X2735,X2736] :
( ~ class_Groups_Oordered__comm__monoid__add(X2736)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2736,c_Groups_Ozero__class_Ozero(X2736)),X2735))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2736,X2734),X2733))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2736,X2734),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2736),X2735),X2733))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_779,plain,
! [X2729,X2730,X2731,X2732] :
( ~ class_Groups_Oordered__comm__monoid__add(X2732)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2732,c_Groups_Ozero__class_Ozero(X2732)),X2731))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2732,X2730),X2729))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2732,X2730),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2732),X2729),X2731))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_780,plain,
! [X2655,X2656,X2657,X2658] :
( ~ c_Finite__Set_Ofinite(X2658,X2657)
| ~ c_Finite__Set_Ofinite(X2656,X2655)
| c_Finite__Set_Ofinite(tc_sum(X2658,X2656),c_Sum__Type_OPlus(X2658,X2656,X2657,X2655)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_781,plain,
! [X3236,X3237,X3238,X3239,X3240,X3241] : hAPP(hAPP(hAPP(c_COMBC(X3241,X3240,X3239),X3238),X3237),X3236) = hAPP(hAPP(X3238,X3236),X3237),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_782,plain,
! [X2380,X2381,X2382] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2380,tc_HOL_Obool),X2382),X2381))
| X2382 != X2381 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2380,tc_HOL_Obool),X2381),X2382))
| X2382 != X2381 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2380,tc_HOL_Obool),X2382),X2381))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2380,tc_HOL_Obool),X2381),X2382))
| X2382 = X2381 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_783,plain,
! [X2344,X2345,X2346] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2346,tc_HOL_Obool),X2345),X2344))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2346,tc_HOL_Obool),X2344),X2345))
| X2345 = X2344 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_784,plain,
! [X2269,X2270,X2271,X2272] :
( ~ hBOOL(hAPP(hAPP(c_member(X2272),X2271),X2270))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2272,tc_HOL_Obool),X2270),X2269))
| hBOOL(hAPP(hAPP(c_member(X2272),X2271),X2269)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_785,plain,
! [X2273,X2274,X2275,X2276] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2276,tc_HOL_Obool),X2275),X2274))
| ~ hBOOL(hAPP(hAPP(c_member(X2276),X2273),X2275))
| hBOOL(hAPP(hAPP(c_member(X2276),X2273),X2274)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_786,plain,
! [X2265,X2266,X2267,X2268] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2268,tc_HOL_Obool),X2267),X2266))
| ~ hBOOL(hAPP(hAPP(c_member(X2268),X2265),X2267))
| hBOOL(hAPP(hAPP(c_member(X2268),X2265),X2266)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_787,plain,
! [X2252,X2253,X2254,X2255] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2255,tc_HOL_Obool),X2254),X2253))
| ~ hBOOL(hAPP(hAPP(c_member(X2255),X2252),X2254))
| hBOOL(hAPP(hAPP(c_member(X2255),X2252),X2253)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_788,plain,
! [X2017,X2018,X2019,X2020,X2021] :
( ~ class_Orderings_Oord(X2021)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2020,X2021),X2019),X2018))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2021,hAPP(X2019,X2017)),hAPP(X2018,X2017))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_789,plain,
! [X1979,X1980,X1981,X1982,X1983] :
( ~ class_Orderings_Oord(X1983)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1982,X1983),X1981),X1980))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1983,hAPP(X1981,X1979)),hAPP(X1980,X1979))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_790,plain,
! [X2967,X2968,X2969,X2970] :
( ~ c_Finite__Set_Ofinite(X2970,X2969)
| c_Finite__Set_Ofinite(X2968,c_Set_Oimage(X2970,X2968,X2967,X2969)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
fof(i_0_791,plain,
! [X2534,X2535,X2536] :
( ~ c_Finite__Set_Ofinite(X2536,X2535)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2536,tc_HOL_Obool),X2534),X2535))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2536,X2534)),c_Finite__Set_Ocard(X2536,X2535))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_792,plain,
! [X2946,X2947,X2948,X2949] :
( ~ class_Rings_Ocomm__semiring__1(X2949)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2949),X2948),X2947)),X2946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2949),X2948),X2946)),X2947) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_793,plain,
! [X1856,X1857,X1858,X1859,X1860] :
( ( hAPP(X1858,X1857) != hAPP(X1858,X1856)
| X1857 = X1856
| ~ c_Fun_Oinj__on(X1860,X1859,X1858,c_Orderings_Otop__class_Otop(tc_fun(X1860,tc_HOL_Obool))) )
& ( X1857 != X1856
| hAPP(X1858,X1857) = hAPP(X1858,X1856)
| ~ c_Fun_Oinj__on(X1860,X1859,X1858,c_Orderings_Otop__class_Otop(tc_fun(X1860,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_794,plain,
! [X1851,X1852,X1853,X1854,X1855] :
( ~ c_Fun_Oinj__on(X1855,X1854,X1853,c_Orderings_Otop__class_Otop(tc_fun(X1855,tc_HOL_Obool)))
| hAPP(X1853,X1852) != hAPP(X1853,X1851)
| X1852 = X1851 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_795,plain,
! [X2957,X2958,X2960] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk35_2(X2957,X2958)),X2957))
| ~ hBOOL(hAPP(X2958,X2957))
| hBOOL(hAPP(X2958,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2960),esk35_2(X2957,X2958)))
| ~ hBOOL(hAPP(X2958,X2960))
| ~ hBOOL(hAPP(X2958,X2957))
| hBOOL(hAPP(X2958,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(X2958,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk35_2(X2957,X2958)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(X2958,X2957))
| hBOOL(hAPP(X2958,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_533])])])])]) ).
fof(i_0_796,plain,
! [X2881,X2882] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2882),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2882),X2881)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_797,plain,
! [X2879,X2880] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2880),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2879),X2880)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_798,plain,
! [X2618,X2619,X2620,X2621] :
( ~ hBOOL(hAPP(hAPP(c_member(X2621),X2620),X2619))
| hBOOL(hAPP(hAPP(c_member(X2621),X2620),c_Set_Oinsert(X2621,X2618,X2619))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).
fof(i_0_799,plain,
! [X2582,X2583,X2584,X2585] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2585),X2584),X2583))
| hBOOL(hAPP(hAPP(c_member(X2585),X2584),c_Set_Oinsert(X2585,X2582,X2583))) )
& ( X2584 != X2582
| hBOOL(hAPP(hAPP(c_member(X2585),X2584),c_Set_Oinsert(X2585,X2582,X2583))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_534])])]) ).
fof(i_0_800,plain,
! [X2840,X2841,X2842] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2842),X2841))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2841),X2840))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2842)),X2840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_801,plain,
! [X2792] :
( ~ c_Finite__Set_Ofinite(X2792,c_Orderings_Otop__class_Otop(tc_fun(X2792,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(X2792,c_Orderings_Otop__class_Otop(tc_fun(X2792,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_802,plain,
! [X2851,X2852] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2852)),hAPP(c_Nat_OSuc,X2851)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2852),X2851)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2852),X2851))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2852)),hAPP(c_Nat_OSuc,X2851))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_803,plain,
! [X2834,X2835] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2835)),hAPP(c_Nat_OSuc,X2834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2835),X2834)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_804,plain,
! [X2795,X2796] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2796,X2795),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2796,X2795),tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2795,c_Orderings_Otop__class_Otop(tc_fun(X2795,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Finite__Set_Ofinite(X2796,c_Orderings_Otop__class_Otop(tc_fun(X2796,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_805,plain,
! [X1800,X1801,X1802,X1803] :
( ~ class_Orderings_Opreorder(X1803)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1803),X1802),X1801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1803),X1801),X1800))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1803),X1802),X1800)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_806,plain,
! [X1804,X1805,X1806,X1807] :
( ~ class_Orderings_Oorder(X1807)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1807),X1806),X1805))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1807),X1804),X1806))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1807),X1804),X1805)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_807,plain,
! [X2737,X2738,X2739] :
( ( X2738 = c_Groups_Ozero__class_Ozero(X2739)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2739),X2738),X2737) != c_Groups_Ozero__class_Ozero(X2739)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2739,c_Groups_Ozero__class_Ozero(X2739)),X2737))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2739,c_Groups_Ozero__class_Ozero(X2739)),X2738))
| ~ class_Groups_Oordered__comm__monoid__add(X2739) )
& ( X2737 = c_Groups_Ozero__class_Ozero(X2739)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2739),X2738),X2737) != c_Groups_Ozero__class_Ozero(X2739)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2739,c_Groups_Ozero__class_Ozero(X2739)),X2737))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2739,c_Groups_Ozero__class_Ozero(X2739)),X2738))
| ~ class_Groups_Oordered__comm__monoid__add(X2739) )
& ( X2738 != c_Groups_Ozero__class_Ozero(X2739)
| X2737 != c_Groups_Ozero__class_Ozero(X2739)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2739),X2738),X2737) = c_Groups_Ozero__class_Ozero(X2739)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2739,c_Groups_Ozero__class_Ozero(X2739)),X2737))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2739,c_Groups_Ozero__class_Ozero(X2739)),X2738))
| ~ class_Groups_Oordered__comm__monoid__add(X2739) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_808,plain,
! [X2682,X2683] : c_Sum__Type_OPlus(X2683,X2682,c_Orderings_Otop__class_Otop(tc_fun(X2683,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2682,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2683,X2682),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_809,plain,
! [X2192,X2193,X2194] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2194),X2193))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2193),X2192))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_810,plain,
! [X2182,X2183,X2184] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2184),X2183))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2183),X2182))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_811,plain,
! [X2195,X2196,X2197] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2197),X2196))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2195),X2196))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_812,plain,
! [X2179,X2180,X2181] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2181),X2180))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2181),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2179),X2180))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_813,plain,
! [X2858,X2859,X2861,X2862,X2863] :
( ( X2859 = hAPP(c_Nat_OSuc,esk32_2(X2858,X2859))
| X2859 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2859),hAPP(c_Nat_OSuc,X2858))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_2(X2858,X2859)),X2858))
| X2859 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2859),hAPP(c_Nat_OSuc,X2858))) )
& ( X2862 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2862),hAPP(c_Nat_OSuc,X2861))) )
& ( X2862 != hAPP(c_Nat_OSuc,X2863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2863),X2861))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2862),hAPP(c_Nat_OSuc,X2861))) ) ),
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_814,plain,
! [X2942,X2943,X2944,X2945] :
( ~ class_Rings_Ocomm__semiring__1(X2945)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2945),X2944),X2943)),X2942) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2945),X2944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2945),X2943),X2942)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_815,plain,
! [X2388,X2389,X2390,X2391] :
( ~ class_Groups_Oab__semigroup__add(X2391)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2391),X2390),X2389)),X2388) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2391),X2390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2391),X2389),X2388)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_816,plain,
! [X2938,X2939,X2940,X2941] :
( ~ class_Rings_Ocomm__semiring__1(X2941)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2941),X2940),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2941),X2939),X2938)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2941),X2940),X2939)),X2938) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_817,plain,
! [X2625,X2626,X2627,X2628] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X2628,X2627,X2626),X2625))
| X2627 = X2625
| hBOOL(hAPP(X2626,X2625)) )
& ( X2627 != X2625
| hBOOL(hAPP(c_Set_Oinsert(X2628,X2627,X2626),X2625)) )
& ( ~ hBOOL(hAPP(X2626,X2625))
| hBOOL(hAPP(c_Set_Oinsert(X2628,X2627,X2626),X2625)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
fof(i_0_818,plain,
! [X2789] :
( ~ class_Rings_Olinordered__semidom(X2789)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2789),c_Groups_Ozero__class_Ozero(X2789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2789),c_Groups_Oone__class_Oone(X2789)),c_Groups_Oone__class_Oone(X2789)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_819,plain,
! [X2821,X2822] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2822)),hAPP(c_Nat_OSuc,X2821)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2822),X2821)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2822),X2821))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2822)),hAPP(c_Nat_OSuc,X2821))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_820,plain,
! [X2102,X2103,X2104,X2105] :
( ~ class_Orderings_Opreorder(X2105)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2105,X2104),X2103))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2105),X2103),X2102))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2105),X2104),X2102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_821,plain,
! [X2110,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,X2111),X2110))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2113),X2112),X2110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_822,plain,
! [X2098,X2099,X2100,X2101] :
( ~ class_Orderings_Oorder(X2101)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2101,X2100),X2099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2101),X2098),X2100))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2101),X2098),X2099)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_823,plain,
! [X2106,X2107,X2108,X2109] :
( ~ class_Orderings_Oorder(X2109)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2109),X2108),X2107))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2109,X2106),X2108))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2109),X2106),X2107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_824,plain,
! [X2551,X2552] :
( ( c_Finite__Set_Ofinite(X2552,c_Orderings_Otop__class_Otop(tc_fun(X2552,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2552,X2551),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2552,X2551),tc_HOL_Obool))) )
& ( c_Finite__Set_Ofinite(X2551,c_Orderings_Otop__class_Otop(tc_fun(X2551,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2552,X2551),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2552,X2551),tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2552,c_Orderings_Otop__class_Otop(tc_fun(X2552,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2551,c_Orderings_Otop__class_Otop(tc_fun(X2551,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_sum(X2552,X2551),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2552,X2551),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_825,plain,
! [X2553,X2554] :
( ~ c_Finite__Set_Ofinite(X2554,c_Orderings_Otop__class_Otop(tc_fun(X2554,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2553,c_Orderings_Otop__class_Otop(tc_fun(X2553,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_prod(X2554,X2553),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2554,X2553),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_826,plain,
! [X2168,X2169,X2170,X2171] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2171),X2170))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2169),X2170) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2171),X2168)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2169),X2168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_827,plain,
! [X2636,X2637,X2638] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2638,tc_HOL_Obool),X2637),c_Set_Oinsert(X2638,X2636,X2637))),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(i_0_828,plain,
! [X2614,X2615,X2616,X2617] :
( ( c_Set_Oinsert(X2617,X2616,X2615) != c_Set_Oinsert(X2617,X2616,X2614)
| X2615 = X2614
| hBOOL(hAPP(hAPP(c_member(X2617),X2616),X2614))
| hBOOL(hAPP(hAPP(c_member(X2617),X2616),X2615)) )
& ( X2615 != X2614
| c_Set_Oinsert(X2617,X2616,X2615) = c_Set_Oinsert(X2617,X2616,X2614)
| hBOOL(hAPP(hAPP(c_member(X2617),X2616),X2614))
| hBOOL(hAPP(hAPP(c_member(X2617),X2616),X2615)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_535])])]) ).
fof(i_0_829,plain,
! [X2836,X2837] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2837)),X2836))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2837),X2836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_830,plain,
! [X2825,X2826] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2826),X2825))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2825)),X2826)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2825)),X2826))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2826),X2825)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_536])]) ).
fof(i_0_831,plain,
! [X2800,X2801] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2801),X2800))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2801)),hAPP(c_Nat_OSuc,X2800))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_832,plain,
! [X2061,X2062,X2063] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2063),X2062))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2062),X2061))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_833,plain,
! [X1973,X1974,X1975] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1975),X1974))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1975),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1974),X1973))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_834,plain,
! [X2058,X2059,X2060] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2060),X2059))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2060),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2058),X2059))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_835,plain,
! [X1970,X1971,X1972] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1972),X1971))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1972),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1970),X1971))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_836,plain,
! [X2558,X2559] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2559,X2558),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2559,X2558),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2558,c_Orderings_Otop__class_Otop(tc_fun(X2558,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_837,plain,
! [X2855,X2856] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2856),X2855))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2855),hAPP(c_Nat_OSuc,X2856))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2855),hAPP(c_Nat_OSuc,X2856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2856),X2855)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_537])]) ).
fof(i_0_838,plain,
! [X2075,X2076,X2077] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2077),X2076)),X2075) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2076),X2075)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_839,plain,
! [X2895,X2896] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2896),X2895))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2896)),X2895)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2896)),X2895))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2896),X2895)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_840,plain,
! [X2891,X2892] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2892)),X2891))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2892),X2891)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2892),X2891))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2892)),X2891)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_841,plain,
! [X2883,X2884] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2884)),X2883))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2884),X2883)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_842,plain,
! [X2366,X2367,X2368,X2369] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2369,tc_HOL_Obool),X2368),X2367))
| ~ hBOOL(hAPP(X2368,X2366))
| hBOOL(hAPP(X2367,X2366)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_843,plain,
! [X2376,X2377,X2378,X2379] :
( ~ hBOOL(hAPP(X2379,X2378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2377,tc_HOL_Obool),X2379),X2376))
| hBOOL(hAPP(X2376,X2378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_844,plain,
! [X1991,X1992,X1993,X1994] :
( ~ class_Orderings_Opreorder(X1994)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1994,X1993),X1992))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1994,X1992),X1991))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1994,X1993),X1991)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_845,plain,
! [X1984,X1985,X1986,X1987] :
( ~ class_Orderings_Oorder(X1987)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1987,X1986),X1985))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1987,X1984),X1986))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1987,X1984),X1985)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_846,plain,
! [X2843,X2844] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2844),X2843))
| hAPP(c_Nat_OSuc,X2844) = X2843
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2844)),X2843)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_847,plain,
! [X1781,X1782,X1783] :
( ~ class_Orderings_Oorder(X1783)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1783),X1782),X1781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1783),X1781),X1782)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])]) ).
fof(i_0_848,plain,
! [X1751,X1752,X1753] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1753),X1752),X1751))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1753),X1751),X1752))
| X1752 = X1751
| ~ class_Orderings_Olinorder(X1753) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1753),X1751),X1752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1753),X1752),X1751))
| ~ class_Orderings_Olinorder(X1753) )
& ( X1752 != X1751
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1753),X1752),X1751))
| ~ class_Orderings_Olinorder(X1753) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])])]) ).
fof(i_0_849,plain,
! [X1808,X1809,X1810] :
( ~ class_Orderings_Opreorder(X1810)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1810),X1809),X1808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1810),X1808),X1809)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])]) ).
fof(i_0_850,plain,
! [X1778,X1779,X1780] :
( ~ class_Orderings_Opreorder(X1780)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1780),X1779),X1778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1780),X1778),X1779)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])]) ).
fof(i_0_851,plain,
! [X1769,X1770,X1771] :
( ~ class_Orderings_Opreorder(X1771)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1771),X1770),X1769))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1771),X1769),X1770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])]) ).
fof(i_0_852,plain,
! [X1766,X1767,X1768] :
( ~ class_Orderings_Opreorder(X1768)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1768),X1767),X1766))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1768),X1766),X1767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])]) ).
fof(i_0_853,plain,
! [X2332,X2333] :
( ~ class_Rings_Olinordered__semidom(X2333)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2333),X2332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2333),X2332),c_Groups_Oone__class_Oone(X2333)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_854,plain,
! [X2885,X2886] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2885),hAPP(c_Nat_OSuc,X2886)))
| X2885 = X2886
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2886),X2885)) )
& ( X2885 != X2886
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2885),hAPP(c_Nat_OSuc,X2886)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2886),X2885)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_855,plain,
! [X2815,X2816] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2816)),X2815))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2816),X2815)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_856,plain,
! [X2567,X2568,X2569] :
( ~ c_Finite__Set_Ofinite(X2569,X2568)
| hBOOL(hAPP(hAPP(c_member(X2569),X2567),X2568))
| c_Finite__Set_Ocard(X2569,c_Set_Oinsert(X2569,X2567,X2568)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Finite__Set_Ocard(X2569,X2568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])]) ).
fof(i_0_857,plain,
! [X2150,X2151,X2152] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2152,X2151),X2150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2152),X2151),X2150))
| ~ class_Orderings_Opreorder(X2152) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2152,X2150),X2151))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2152),X2151),X2150))
| ~ class_Orderings_Opreorder(X2152) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2152,X2151),X2150))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2152,X2150),X2151))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2152),X2151),X2150))
| ~ class_Orderings_Opreorder(X2152) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])])]) ).
fof(i_0_858,plain,
! [X2898,X2899,X2900] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2900),X2898),X2899))
| c_Finite__Set_Ocard(X2900,c_Set_Oinsert(X2900,X2898,X2899)) = c_Finite__Set_Ocard(X2900,X2899)
| ~ c_Finite__Set_Ofinite(X2900,X2899) )
& ( hBOOL(hAPP(hAPP(c_member(X2900),X2898),X2899))
| c_Finite__Set_Ocard(X2900,c_Set_Oinsert(X2900,X2898,X2899)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2900,X2899))
| ~ c_Finite__Set_Ofinite(X2900,X2899) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_546])])]) ).
fof(i_0_859,plain,
! [X2629,X2630,X2631,X2632] : c_Set_Oinsert(X2632,X2631,c_Set_Oinsert(X2632,X2630,X2629)) = c_Set_Oinsert(X2632,X2630,c_Set_Oinsert(X2632,X2631,X2629)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
fof(i_0_860,plain,
! [X2607,X2608,X2609] : hBOOL(hAPP(hAPP(c_member(X2609),X2608),c_Set_Oinsert(X2609,X2608,X2607))),
inference(variable_rename,[status(thm)],[fact_insertI1]) ).
fof(i_0_861,plain,
! [X2853,X2854] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2854),hAPP(c_Nat_OSuc,X2853)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2854),X2853))
| X2854 = X2853 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2854),X2853))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2854),hAPP(c_Nat_OSuc,X2853))) )
& ( X2854 != X2853
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2854),hAPP(c_Nat_OSuc,X2853))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_862,plain,
! [X2849,X2850] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2850),hAPP(c_Nat_OSuc,X2849)))
| X2850 = X2849
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2850),X2849)) )
& ( X2850 != X2849
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2850),hAPP(c_Nat_OSuc,X2849)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2850),X2849)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_547])])]) ).
fof(i_0_863,plain,
! [X2847,X2848] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2848),X2847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2848),hAPP(c_Nat_OSuc,X2847)))
| X2847 = X2848 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])]) ).
fof(i_0_864,plain,
! [X2838,X2839] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2839),hAPP(c_Nat_OSuc,X2838)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2839),X2838))
| X2839 = X2838 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])]) ).
fof(i_0_865,plain,
! [X2887,X2888] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2888),X2887))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2888)),X2887)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_866,plain,
! [X2934,X2935,X2936,X2937] :
( ~ class_Rings_Ocomm__semiring__1(X2937)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2937),X2936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2937),X2935),X2934)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2937),X2935),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2937),X2936),X2934)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_867,plain,
! [X2052,X2053,X2054] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2054),X2053))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2053),X2052))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2054),X2052)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_868,plain,
! [X2547,X2548,X2549] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2549,tc_HOL_Obool),X2548),X2547))
| ~ c_Finite__Set_Ofinite(X2549,X2547)
| c_Finite__Set_Ofinite(X2549,X2548) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_869,plain,
! [X2544,X2545,X2546] :
( ~ c_Finite__Set_Ofinite(X2546,X2545)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2546,tc_HOL_Obool),X2544),X2545))
| c_Finite__Set_Ofinite(X2546,X2544) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_870,plain,
! [X2123,X2124,X2125] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2125),X2124),X2123))
| X2124 = X2123
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2124),X2123))
| ~ class_Orderings_Olinorder(X2125) )
& ( X2124 != X2123
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2125),X2124),X2123))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2125,X2124),X2123))
| ~ class_Orderings_Olinorder(X2125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])])]) ).
fof(i_0_871,plain,
! [X2162,X2163,X2164] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2164),X2163),X2162))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2164,X2162),X2163))
| ~ class_Orderings_Olinorder(X2164) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2164,X2162),X2163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2164),X2163),X2162))
| ~ class_Orderings_Olinorder(X2164) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])])]) ).
fof(i_0_872,plain,
! [X2129,X2130,X2131] :
( ~ class_Orderings_Olinorder(X2131)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2131,X2130),X2129))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2131),X2129),X2130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])]) ).
fof(i_0_873,plain,
! [X2159,X2160,X2161] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2161,X2160),X2159))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2161),X2159),X2160))
| ~ class_Orderings_Olinorder(X2161) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2161),X2159),X2160))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2161,X2160),X2159))
| ~ class_Orderings_Olinorder(X2161) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])])]) ).
fof(i_0_874,plain,
! [X2873,X2874,X2876,X2877,X2878] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2874),X2873))
| X2873 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2874),esk34_2(X2873,X2874))) )
& ( X2876 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2877),X2878))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2877),X2876)) ) ),
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_875,plain,
! [X2893,X2894] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2894),hAPP(c_Nat_OSuc,X2893)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2894),X2893)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2894),X2893))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2894),hAPP(c_Nat_OSuc,X2893))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_876,plain,
! [X2901,X2902,X2903] :
( ~ c_Finite__Set_Ofinite(X2903,X2902)
| hBOOL(hAPP(hAPP(c_member(X2903),X2901),X2902))
| c_Finite__Set_Ocard(X2903,c_Set_Oinsert(X2903,X2901,X2902)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X2903,X2902)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])]) ).
fof(i_0_877,plain,
! [X2845,X2846] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2846),X2845))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2846),hAPP(c_Nat_OSuc,X2845))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_878,plain,
! [X2922,X2923] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2923),X2922),X2922) != c_Groups_Ozero__class_Ozero(X2923)
| X2922 = c_Groups_Ozero__class_Ozero(X2923)
| ~ hBOOL(hAPP(hAPP(c_member(X2923),X2922),c_Int_Oring__1__class_OInts(X2923)))
| ~ class_Int_Oring__char__0(X2923) )
& ( X2922 != c_Groups_Ozero__class_Ozero(X2923)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2923),X2922),X2922) = c_Groups_Ozero__class_Ozero(X2923)
| ~ hBOOL(hAPP(hAPP(c_member(X2923),X2922),c_Int_Oring__1__class_OInts(X2923)))
| ~ class_Int_Oring__char__0(X2923) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).
fof(i_0_879,plain,
! [X2823,X2824] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2824),hAPP(c_Nat_OSuc,X2823)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2824),X2823))
| X2824 = hAPP(c_Nat_OSuc,X2823) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2824),X2823))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2824),hAPP(c_Nat_OSuc,X2823))) )
& ( X2824 != hAPP(c_Nat_OSuc,X2823)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2824),hAPP(c_Nat_OSuc,X2823))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_880,plain,
! [X2817,X2818] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2818),hAPP(c_Nat_OSuc,X2817)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2818),X2817))
| X2818 = hAPP(c_Nat_OSuc,X2817) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])]) ).
fof(i_0_881,plain,
! [X2277,X2278] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2278,tc_HOL_Obool),X2277),c_Orderings_Otop__class_Otop(tc_fun(X2278,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_882,plain,
! [X1690,X1691,X1692] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1691),X1692))
| hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| X1692 = X1691
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1692),X1691)) )
& ( ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| X1692 = X1691
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1692),X1691)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1691),X1692))
| hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1692),X1691)) )
& ( ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1692),X1691)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1691),X1692))
| hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| X1692 = X1691
| ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692)) )
& ( ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| X1692 = X1691
| ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1691),X1692))
| hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692)) )
& ( ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692))
| ~ hBOOL(hAPP(hAPP(X1690,X1691),X1692)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_883,plain,
! [X2078,X2079,X2080] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2079),X2078)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2079),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2080),X2078)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_884,plain,
! [X2025,X2026,X2027] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2027,X2026),X2025))
| X2026 != X2025
| ~ class_Orderings_Oorder(X2027) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2027,X2025),X2026))
| X2026 != X2025
| ~ class_Orderings_Oorder(X2027) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2027,X2026),X2025))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2027,X2025),X2026))
| X2026 = X2025
| ~ class_Orderings_Oorder(X2027) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_885,plain,
! [X2014,X2015,X2016] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2016,X2014),X2015))
| X2014 = X2015
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2016,X2015),X2014))
| ~ class_Orderings_Oorder(X2016) )
& ( X2014 != X2015
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2016,X2014),X2015))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2016,X2015),X2014))
| ~ class_Orderings_Oorder(X2016) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_886,plain,
! [X1995,X1996,X1997] :
( ~ class_Orderings_Oorder(X1997)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1997,X1996),X1995))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1997,X1995),X1996))
| X1996 = X1995 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_887,plain,
! [X1988,X1989,X1990] :
( ~ class_Orderings_Oorder(X1990)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1990,X1989),X1988))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1990,X1988),X1989))
| X1988 = X1989 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_888,plain,
! [X2790,X2791] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2791,X2790)))
| c_Finite__Set_Ofinite(X2791,X2790) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
fof(i_0_889,plain,
! [X2827] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2827)),X2827)),
inference(variable_rename,[status(thm)],[i_0_556]) ).
fof(i_0_890,plain,
! [X2889,X2890] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2890),X2889))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2890),hAPP(c_Nat_OSuc,X2889))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_891,plain,
! [X2556,X2557] :
( ~ c_Finite__Set_Ofinite(X2557,c_Orderings_Otop__class_Otop(tc_fun(X2557,tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2557,X2556) != c_Finite__Set_Ocard(X2557,c_Orderings_Otop__class_Otop(tc_fun(X2557,tc_HOL_Obool)))
| X2556 = c_Orderings_Otop__class_Otop(tc_fun(X2557,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_892,plain,
! [X2153,X2154,X2155] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2155,X2154),X2153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2155),X2154),X2153))
| ~ class_Orderings_Oorder(X2155) )
& ( X2154 != X2153
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2155),X2154),X2153))
| ~ class_Orderings_Oorder(X2155) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2155,X2154),X2153))
| X2154 = X2153
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2155),X2154),X2153))
| ~ class_Orderings_Oorder(X2155) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_893,plain,
! [X2147,X2148,X2149] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2149,X2148),X2147))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2149),X2148),X2147))
| X2148 = X2147
| ~ class_Orderings_Oorder(X2149) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2149),X2148),X2147))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2149,X2148),X2147))
| ~ class_Orderings_Oorder(X2149) )
& ( X2148 != X2147
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2149,X2148),X2147))
| ~ class_Orderings_Oorder(X2149) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_894,plain,
! [X2126,X2127,X2128] :
( ~ class_Orderings_Opreorder(X2128)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2128),X2127),X2126))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2128,X2127),X2126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_895,plain,
! [X2091,X2092] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2092),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2092),X2091))),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_896,plain,
! [X2093,X2094] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2093),X2094))),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_897,plain,
! [X3126,X3127] : c_Set_Oimage(X3127,X3127,c_COMBI(X3127),X3126) = X3126,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_898,plain,
! [X1883,X1884] : c_Fun_Oinj__on(X1884,X1884,c_COMBI(X1884),X1883),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_899,plain,
! [X2135,X2136,X2137] :
( ~ class_Orderings_Oorder(X2137)
| X2136 = X2135
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2137,X2136),X2135))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2137),X2136),X2135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_900,plain,
! [X2120,X2121,X2122] :
( ~ class_Orderings_Oorder(X2122)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2122,X2121),X2120))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2122),X2121),X2120))
| X2121 = X2120 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_901,plain,
! [X2117,X2118,X2119] :
( ~ class_Orderings_Oorder(X2119)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2119,X2118),X2117))
| X2118 = X2117
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2119),X2118),X2117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_902,plain,
! [X2114,X2115,X2116] :
( ~ class_Orderings_Oorder(X2116)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2116,X2115),X2114))
| X2114 = X2115
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2116),X2115),X2114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_903,plain,
! [X2138,X2139,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_Olinorder(X2140) )
& ( X2139 != X2138
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2140,X2139),X2138))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2140),X2139),X2138))
| ~ class_Orderings_Olinorder(X2140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])])]) ).
fof(i_0_904,plain,
! [X2132,X2133,X2134] :
( ~ class_Orderings_Oorder(X2134)
| X2133 = X2132
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2134,X2132),X2133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2134),X2132),X2133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_905,plain,
! [X2864] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2864),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X2864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2864 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2864),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_906,plain,
! [X2857] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2857),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_907,plain,
! [X2050,X2051] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2051),X2050))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2050),X2051))
| X2051 = X2050 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_908,plain,
! [X1684,X1685,X1686] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1686),X1685),hAPP(c_fequal,X1684)))
| X1685 = X1684 )
& ( X1685 != X1684
| hBOOL(hAPP(hAPP(c_member(X1686),X1685),hAPP(c_fequal,X1684))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_909,plain,
! [X2819,X2820] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2820),X2819))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2820),hAPP(c_Nat_OSuc,X2819))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_910,plain,
! [X2764] :
( ~ class_Rings_Olinordered__semidom(X2764)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2764),c_Groups_Oone__class_Oone(X2764)),c_Groups_Ozero__class_Ozero(X2764))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).
fof(i_0_911,plain,
! [X2210,X2211] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2211),X2210))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2211),X2210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_912,plain,
! [X2208,X2209] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2209),X2208))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2209),X2208)) )
& ( X2209 != X2208
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2209),X2208)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2209),X2208))
| X2209 = X2208
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2209),X2208)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_913,plain,
! [X2206,X2207] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2207),X2206))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2207),X2206))
| X2207 = X2206 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2207),X2206))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2207),X2206)) )
& ( X2207 != X2206
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2207),X2206)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_914,plain,
! [X2204,X2205] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2205),X2204))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2205),X2204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_915,plain,
! [X2200,X2201] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2201),X2200))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2201),X2200)) )
& ( X2201 != X2200
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2201),X2200)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_916,plain,
! [X2622,X2623,X2624] :
( ~ hBOOL(hAPP(hAPP(c_member(X2624),X2623),X2622))
| c_Set_Oinsert(X2624,X2623,X2622) = X2622 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(i_0_917,plain,
! [X1748,X1749,X1750] :
( ( X1749 = X1748
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1750),X1749),X1748))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1750),X1748),X1749))
| ~ class_Orderings_Olinorder(X1750) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1750),X1749),X1748))
| X1749 != X1748
| ~ class_Orderings_Olinorder(X1750) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1750),X1748),X1749))
| X1749 != X1748
| ~ class_Orderings_Olinorder(X1750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_918,plain,
! [X2385,X2386,X2387] :
( ~ class_Rings_Olinordered__idom(X2387)
| X2386 = X2385
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2387),X2386),X2385))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2387),X2385),X2386)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_559])]) ).
fof(i_0_919,plain,
! [X1811,X1812,X1813] :
( ~ class_Orderings_Olinorder(X1813)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1813),X1812),X1811))
| X1812 = X1811
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1813),X1811),X1812)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])]) ).
fof(i_0_920,plain,
! [X1760,X1761,X1762] :
( ~ class_Orderings_Olinorder(X1762)
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1762),X1761),X1760))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1762),X1760),X1761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])]) ).
fof(i_0_921,plain,
! [X1757,X1758,X1759] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1759),X1757),X1758))
| X1757 = X1758
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1759),X1758),X1757))
| ~ class_Orderings_Olinorder(X1759) )
& ( X1757 != X1758
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1759),X1757),X1758))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1759),X1758),X1757))
| ~ class_Orderings_Olinorder(X1759) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])])]) ).
fof(i_0_922,plain,
! [X1754,X1755,X1756] :
( ~ class_Orderings_Olinorder(X1756)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1756),X1755),X1754))
| X1755 = X1754
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1756),X1754),X1755)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_923,plain,
! [X1912,X1913,X1914] : c_List_Osplice(X1914,c_List_Olist_OCons(X1914,X1913,X1912),c_List_Olist_ONil(X1914)) = c_List_Olist_OCons(X1914,X1913,X1912),
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).
fof(i_0_924,plain,
! [X2550] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X2550),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2550),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2550,c_Orderings_Otop__class_Otop(tc_fun(X2550,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2550,c_Orderings_Otop__class_Otop(tc_fun(X2550,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X2550),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2550),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_925,plain,
! [X2202,X2203] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2203),X2202))
| X2203 = X2202
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2203),X2202)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_926,plain,
! [X2633,X2634,X2635] : c_Set_Oinsert(X2635,X2634,c_Set_Oinsert(X2635,X2634,X2633)) = c_Set_Oinsert(X2635,X2634,X2633),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
fof(i_0_927,plain,
! [X1704,X1705] : hBOOL(hAPP(hAPP(c_member(X1705),X1704),c_Orderings_Otop__class_Otop(tc_fun(X1705,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_928,plain,
! [X1670,X1671] : hBOOL(hAPP(hAPP(c_member(X1671),X1670),c_Orderings_Otop__class_Otop(tc_fun(X1671,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_929,plain,
! [X2589,X2590,X2591] :
( ( ~ c_Finite__Set_Ofinite(X2591,c_Set_Oinsert(X2591,X2590,X2589))
| c_Finite__Set_Ofinite(X2591,X2589) )
& ( ~ c_Finite__Set_Ofinite(X2591,X2589)
| c_Finite__Set_Ofinite(X2591,c_Set_Oinsert(X2591,X2590,X2589)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).
fof(i_0_930,plain,
! [X1687,X1688,X1689] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1689),X1688),X1687))
| hBOOL(hAPP(X1687,X1688)) )
& ( ~ hBOOL(hAPP(X1687,X1688))
| hBOOL(hAPP(hAPP(c_member(X1689),X1688),X1687)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_931,plain,
! [X2156,X2157,X2158] :
( ~ class_Orderings_Olinorder(X2158)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2158,X2157),X2156))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2158),X2156),X2157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_932,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)],[i_0_563])]) ).
fof(i_0_933,plain,
! [X2144,X2145,X2146] :
( ~ class_Orderings_Olinorder(X2146)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2146),X2145),X2144))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2146,X2144),X2145)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])]) ).
fof(i_0_934,plain,
! [X2830,X2831] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2831)),X2830) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2831),X2830)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_935,plain,
! [X2762] :
( ~ class_Rings_Olinordered__semidom(X2762)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2762,c_Groups_Oone__class_Oone(X2762)),c_Groups_Ozero__class_Ozero(X2762))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])]) ).
fof(i_0_936,plain,
! [X2085,X2086,X2088,X2089,X2090] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2086),X2085))
| X2085 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2086),esk10_2(X2085,X2086)) )
& ( X2088 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2089),X2090)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2089),X2088)) ) ),
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_937,plain,
! [X1661,X1662] :
( X1662 = X1661
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1662),X1661))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1661),X1662)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])]) ).
fof(i_0_938,plain,
! [X1659,X1660] :
( ( X1660 = X1659
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1660),X1659))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1659),X1660)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1660),X1659))
| X1660 != X1659 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1659),X1660))
| X1660 != X1659 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_939,plain,
! [X2865,X2867,X2868] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2865))
| X2865 = hAPP(c_Nat_OSuc,esk33_1(X2865)) )
& ( X2867 != hAPP(c_Nat_OSuc,X2868)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2867)) ) ),
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_940,plain,
! [X1775,X1776,X1777] :
( ~ class_Orderings_Oorder(X1777)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1777),X1776),X1775))
| X1775 != X1776 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_941,plain,
! [X1772,X1773,X1774] :
( ~ class_Orderings_Oorder(X1774)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1774),X1773),X1772))
| X1773 != X1772 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_942,plain,
! [X1763,X1764,X1765] :
( ~ class_Orderings_Oorder(X1765)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1765),X1764),X1763))
| X1764 != X1763 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_943,plain,
! [X2353,X2354,X2355] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2353,tc_HOL_Obool),X2355),X2354))
| X2355 != X2354 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2353,tc_HOL_Obool),X2354),X2355))
| X2355 != X2354 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])])]) ).
fof(i_0_944,plain,
! [X2373,X2374,X2375] :
( X2375 != X2374
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2373,tc_HOL_Obool),X2375),X2374)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_945,plain,
! [X2370,X2371,X2372] :
( X2372 != X2371
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2370,tc_HOL_Obool),X2371),X2372)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_946,plain,
! [X1746,X1747] :
( ~ class_Orderings_Opreorder(X1747)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1747),X1746),X1746)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_947,plain,
! [X2383,X2384] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2384,tc_HOL_Obool),X2383),X2383)),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_948,plain,
! [X2716] :
( ( X2716 = 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)),X2716)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2716))
| X2716 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_949,plain,
! [X2408,X2409,X2410,X2411] :
( ~ class_Groups_Ocancel__semigroup__add(X2411)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2411),X2410),X2409) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2411),X2408),X2409)
| X2410 = X2408 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_950,plain,
! [X2396,X2397,X2398,X2399] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2399),X2398),X2397) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2399),X2396),X2397)
| X2398 = X2396
| ~ class_Groups_Ocancel__semigroup__add(X2399) )
& ( X2398 != X2396
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2399),X2398),X2397) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2399),X2396),X2397)
| ~ class_Groups_Ocancel__semigroup__add(X2399) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_951,plain,
! [X2404,X2405,X2406,X2407] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X2407)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2407),X2406),X2405) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2407),X2406),X2404)
| X2405 = X2404 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_952,plain,
! [X2400,X2401,X2402,X2403] :
( ~ class_Groups_Ocancel__semigroup__add(X2403)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2403),X2402),X2401) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2403),X2402),X2400)
| X2401 = X2400 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_953,plain,
! [X2392,X2393,X2394,X2395] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2395),X2394),X2393) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2395),X2394),X2392)
| X2393 = X2392
| ~ class_Groups_Ocancel__semigroup__add(X2395) )
& ( X2393 != X2392
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2395),X2394),X2393) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2395),X2394),X2392)
| ~ class_Groups_Ocancel__semigroup__add(X2395) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_954,plain,
! [X1814,X1815,X1816,X1817,X1818] :
( ( X1817 = X1815
| c_List_Olist_OCons(X1818,X1817,X1816) != c_List_Olist_OCons(X1818,X1815,X1814) )
& ( X1816 = X1814
| c_List_Olist_OCons(X1818,X1817,X1816) != c_List_Olist_OCons(X1818,X1815,X1814) )
& ( X1817 != X1815
| X1816 != X1814
| c_List_Olist_OCons(X1818,X1817,X1816) = c_List_Olist_OCons(X1818,X1815,X1814) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).
fof(i_0_955,plain,
! [X2028,X2029,X2030] :
( ~ class_Orderings_Olinorder(X2030)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2030,X2029),X2028))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2030,X2028),X2029)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_956,plain,
! [X1976,X1977,X1978] :
( ~ class_Orderings_Olinorder(X1978)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1978,X1977),X1976))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1978,X1976),X1977)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_957,plain,
! [X2832,X2833] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2833),hAPP(c_Nat_OSuc,X2832)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2833),X2832)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_958,plain,
! [X2828,X2829] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2829)),X2828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2829),hAPP(c_Nat_OSuc,X2828)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_959,plain,
! [X2717] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2717),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_570]) ).
fof(i_0_960,plain,
! [X2715] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2715),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_571]) ).
fof(i_0_961,plain,
! [X2696] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2696),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_572]) ).
fof(i_0_962,plain,
! [X2907] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2907)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X2907)),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_963,plain,
! [X2713,X2714] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2714),X2713))
| X2713 != 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_964,plain,
! [X2081,X2082] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2082),X2081))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2081),X2082)) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_965,plain,
! [X2802] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2802))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_966,plain,
! [X1666,X1667] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1667),X1666))
| X1667 != X1666 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_967,plain,
! [X1664,X1665] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1665),X1664))
| X1664 != X1665 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_968,plain,
! [X2763] :
( ~ class_Rings_Olinordered__semidom(X2763)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2763),c_Groups_Ozero__class_Ozero(X2763)),c_Groups_Oone__class_Oone(X2763))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_969,plain,
! [X2915] :
( ~ class_Rings_Oring__1(X2915)
| hBOOL(hAPP(hAPP(c_member(X2915),c_Groups_Ozero__class_Ozero(X2915)),c_Int_Oring__1__class_OInts(X2915))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).
fof(i_0_970,plain,
! [X2919] :
( ~ class_Rings_Oring__1(X2919)
| hBOOL(hAPP(hAPP(c_member(X2919),c_Groups_Oone__class_Oone(X2919)),c_Int_Oring__1__class_OInts(X2919))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).
fof(i_0_971,plain,
! [X1663] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1663),X1663)),
inference(variable_rename,[status(thm)],[i_0_573]) ).
fof(i_0_972,plain,
! [X1658] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1658),X1658)),
inference(variable_rename,[status(thm)],[i_0_574]) ).
fof(i_0_973,plain,
! [X2069,X2070,X2071] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2071),X2070) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2069),X2070)
| X2071 = X2069 )
& ( X2071 != X2069
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2071),X2070) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2069),X2070) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_974,plain,
! [X2072,X2073,X2074] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2074),X2073) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2074),X2072)
| X2073 = X2072 )
& ( X2073 != X2072
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2074),X2073) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2074),X2072) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_975,plain,
! [X2586,X2587,X2588] :
( ~ c_Finite__Set_Ofinite(X2588,X2587)
| c_Finite__Set_Ofinite(X2588,c_Set_Oinsert(X2588,X2586,X2587)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).
fof(i_0_976,plain,
! [X2799] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2799),hAPP(c_Nat_OSuc,X2799))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_977,plain,
! [X1668,X1669] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1669,tc_HOL_Obool)),X1668)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_978,plain,
! [X2724] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2724),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X2724 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2724 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2724),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_979,plain,
! [X2869,X2870] :
( ( X2870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2870 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2870),X2869) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2869 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2870 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2870),X2869) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2870),X2869) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2869 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2870),X2869) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2870 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2869 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2870),X2869) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2870 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2869 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2870),X2869) = 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_980,plain,
! [X2871,X2872] :
( ( X2872 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2872 = 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),X2872),X2871) )
& ( X2871 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2872 = 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),X2872),X2871) )
& ( X2872 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2871 = 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),X2872),X2871) )
& ( X2871 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2871 = 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),X2872),X2871) )
& ( X2872 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2871 != 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),X2872),X2871) )
& ( X2872 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2871 != 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),X2872),X2871) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_981,plain,
! [X1641,X1642] :
( hAPP(X1642,esk1_2(X1641,X1642)) != hAPP(X1641,esk1_2(X1641,X1642))
| X1642 = X1641 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_982,plain,
! [X2761] :
( ~ class_Rings_Olinordered__semidom(X2761)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2761,c_Groups_Ozero__class_Ozero(X2761)),c_Groups_Oone__class_Oone(X2761))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_983,plain,
! [X3248,X3249] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X3249),X3248))
| X3249 = X3248 ),
inference(variable_rename,[status(thm)],[i_0_575]) ).
fof(i_0_984,plain,
! [X2906] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X2906)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X2906)),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_985,plain,
! [X2931,X2932,X2933] :
( ~ class_Rings_Ocomm__semiring__1(X2933)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2933),X2932),X2931) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2933),X2931),X2932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_986,plain,
! [X2712] :
( X2712 = 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)),X2712)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_987,plain,
! [X2198,X2199] :
( ~ class_Orderings_Otop(X2199)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2199,X2198),c_Orderings_Otop__class_Otop(X2199))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_988,plain,
! [X2797,X2798] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2798),X2797),X2797) != c_Groups_Ozero__class_Ozero(X2798)
| X2797 = c_Groups_Ozero__class_Ozero(X2798)
| ~ class_Groups_Olinordered__ab__group__add(X2798) )
& ( X2797 != c_Groups_Ozero__class_Ozero(X2798)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2798),X2797),X2797) = c_Groups_Ozero__class_Ozero(X2798)
| ~ class_Groups_Olinordered__ab__group__add(X2798) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_989,plain,
! [X2704,X2705] :
( ( c_Groups_Ozero__class_Ozero(X2705) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2705),X2704),X2704)
| X2704 = c_Groups_Ozero__class_Ozero(X2705)
| ~ class_Groups_Olinordered__ab__group__add(X2705) )
& ( X2704 != c_Groups_Ozero__class_Ozero(X2705)
| c_Groups_Ozero__class_Ozero(X2705) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2705),X2704),X2704)
| ~ class_Groups_Olinordered__ab__group__add(X2705) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_990,plain,
! [X2926,X2927,X2928] :
( ( X2927 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2928),X2927),X2926)
| X2926 = c_Groups_Ozero__class_Ozero(X2928)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2928) )
& ( X2926 != c_Groups_Ozero__class_Ozero(X2928)
| X2927 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2928),X2927),X2926)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2928) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_991,plain,
! [X2022,X2023,X2024] :
( ~ class_Orderings_Opreorder(X2024)
| X2023 != X2022
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2024,X2023),X2022)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_992,plain,
! [X3226,X3227,X3228,X3229] : hAPP(hAPP(c_COMBK(X3229,X3228),X3227),X3226) = X3227,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_993,plain,
! [X1698,X1699,X1700] : c_List_Olist_OCons(X1700,X1699,X1698) != c_List_Olist_ONil(X1700),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).
fof(i_0_994,plain,
! [X1695,X1696,X1697] : c_List_Olist_ONil(X1697) != c_List_Olist_OCons(X1697,X1696,X1695),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
fof(i_0_995,plain,
! [X2083,X2084] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2084),X2083) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2083),X2084),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_996,plain,
! [X1968,X1969] :
( ~ class_Orderings_Opreorder(X1969)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1969,X1968),X1968)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_997,plain,
! [X2725] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2725)),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_998,plain,
! [X2697] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2697)),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_999,plain,
! [X1713,X1714,X1715] : c_List_Olist_OCons(X1715,X1714,X1713) != X1713,
inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).
fof(i_0_1000,plain,
! [X1710,X1711,X1712] : X1712 != c_List_Olist_OCons(X1711,X1710,X1712),
inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).
fof(i_0_1001,plain,
! [X1701,X1702,X1703] :
( ~ class_Orderings_Otop(X1703)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1702,X1703)),X1701) = c_Orderings_Otop__class_Otop(X1703) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_1002,plain,
! [X2720,X2721] :
( ( X2721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2721),X2720) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2720 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2721),X2720) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2721 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2720 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2721),X2720) = 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_1003,plain,
! [X2064,X2065] :
( X2065 != X2064
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2065),X2064)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1004,plain,
! [X3250,X3251] :
( X3251 != X3250
| hBOOL(hAPP(hAPP(c_fequal,X3251),X3250)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1005,plain,
! [X2718,X2719] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2719),X2718) != X2719
| X2718 = 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_1006,plain,
! [X2095] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2095),X2095)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1007,plain,
! [X2555] :
( ~ class_Finite__Set_Ofinite(X2555)
| c_Finite__Set_Ofinite(X2555,c_Orderings_Otop__class_Otop(tc_fun(X2555,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_1008,plain,
! [X2955,X2956] :
( ~ class_Rings_Ocomm__semiring__1(X2956)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2956),c_Groups_Ozero__class_Ozero(X2956)),X2955) = X2955 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_1009,plain,
! [X2708,X2709] :
( ~ class_Groups_Omonoid__add(X2709)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2709),c_Groups_Ozero__class_Ozero(X2709)),X2708) = X2708 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_1010,plain,
! [X2706,X2707] :
( ~ class_Groups_Ocomm__monoid__add(X2707)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2707),c_Groups_Ozero__class_Ozero(X2707)),X2706) = X2706 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_1011,plain,
! [X2929,X2930] :
( ~ class_Rings_Ocomm__semiring__1(X2930)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2930),X2929),c_Groups_Ozero__class_Ozero(X2930)) = X2929 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_1012,plain,
! [X2702,X2703] :
( ~ class_Groups_Omonoid__add(X2703)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2703),X2702),c_Groups_Ozero__class_Ozero(X2703)) = X2702 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_1013,plain,
! [X2700,X2701] :
( ~ class_Groups_Ocomm__monoid__add(X2701)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2701),X2700),c_Groups_Ozero__class_Ozero(X2701)) = X2700 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_1014,plain,
! [X2905] : hAPP(c_Nat_OSuc,X2905) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2905),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1015,plain,
! [X2920,X2921] : c_List_Olist_Olist__size(X2921,X2920,c_List_Olist_ONil(X2921)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J]) ).
fof(i_0_1016,plain,
! [X2904] : hAPP(c_Nat_OSuc,X2904) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2904),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1017,plain,
! [X1937,X1938] : c_List_Osplice(X1938,c_List_Olist_ONil(X1938),X1937) = X1937,
inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).
fof(i_0_1018,plain,
! [X1935,X1936] : c_List_Osplice(X1936,X1935,c_List_Olist_ONil(X1936)) = X1935,
inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).
fof(i_0_1019,plain,
! [X2723] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2723) = X2723,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_1020,plain,
! [X2897] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2897) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2897)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(i_0_1021,plain,
! [X2722] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2722),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2722,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_1022,plain,
! [X3219,X3220] :
( ~ class_Finite__Set_Ofinite(X3220)
| ~ class_Finite__Set_Ofinite(X3219)
| class_Finite__Set_Ofinite(tc_sum(X3220,X3219)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_1023,plain,
! [X3211,X3212] :
( ~ class_Finite__Set_Ofinite(X3212)
| ~ class_Finite__Set_Ofinite(X3211)
| class_Finite__Set_Ofinite(tc_fun(X3212,X3211)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_1024,plain,
! [X3222,X3223] :
( ~ class_Finite__Set_Ofinite(X3223)
| ~ class_Finite__Set_Ofinite(X3222)
| class_Finite__Set_Ofinite(tc_prod(X3223,X3222)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_1025,plain,
! [X2811,X2812] :
( ( hAPP(c_Nat_OSuc,X2812) != hAPP(c_Nat_OSuc,X2811)
| X2812 = X2811 )
& ( X2812 != X2811
| hAPP(c_Nat_OSuc,X2812) = hAPP(c_Nat_OSuc,X2811) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1026,plain,
! [X2809,X2810] :
( hAPP(c_Nat_OSuc,X2810) != hAPP(c_Nat_OSuc,X2809)
| X2810 = X2809 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1027,plain,
! [X3217,X3218] :
( ~ class_Orderings_Oord(X3218)
| class_Orderings_Oord(tc_fun(X3217,X3218)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1028,plain,
! [X3213,X3214] :
( ~ class_Orderings_Oorder(X3214)
| class_Orderings_Oorder(tc_fun(X3213,X3214)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1029,plain,
! [X3209,X3210] :
( ~ class_Orderings_Opreorder(X3210)
| class_Orderings_Opreorder(tc_fun(X3209,X3210)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1030,plain,
! [X3215,X3216] :
( ~ class_Orderings_Otop(X3216)
| class_Orderings_Otop(tc_fun(X3215,X3216)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_1031,plain,
! [X2767,X2768] :
( c_Finite__Set_Ofinite(X2768,X2767)
| c_Finite__Set_Ocard(X2768,X2767) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_576])]) ).
fof(i_0_1032,plain,
! [X2808] : hAPP(c_Nat_OSuc,X2808) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1033,plain,
! [X2806] : hAPP(c_Nat_OSuc,X2806) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1034,plain,
! [X2805] : hAPP(c_Nat_OSuc,X2805) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1035,plain,
! [X2807] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2807),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1036,plain,
! [X2804] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2804),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1037,plain,
! [X2803] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2803),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1038,plain,
! [X2542,X2543] :
( ~ class_Finite__Set_Ofinite(X2543)
| c_Finite__Set_Ofinite(X2543,X2542) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(i_0_1039,plain,
! [X2540,X2541] :
( ~ class_Finite__Set_Ofinite(X2541)
| c_Finite__Set_Ofinite(X2541,X2540) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_1040,plain,
! [X2813] : hAPP(c_Nat_OSuc,X2813) != X2813,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1041,plain,
! [X2814] : X2814 != hAPP(c_Nat_OSuc,X2814),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1042,plain,
! [X3224,X3225] : hAPP(c_COMBI(X3225),X3224) = X3224,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1043,plain,
! [X1694] : c_List_Odistinct(X1694,c_List_Olist_ONil(X1694)),
inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).
fof(i_0_1044,plain,
! [X2711] :
( ~ class_Rings_Ozero__neq__one(X2711)
| c_Groups_Oone__class_Oone(X2711) != c_Groups_Ozero__class_Ozero(X2711) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_1045,plain,
! [X2710] :
( ~ class_Rings_Ozero__neq__one(X2710)
| c_Groups_Ozero__class_Ozero(X2710) != c_Groups_Oone__class_Oone(X2710) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_1046,plain,
! [X3221] :
( ~ class_Finite__Set_Ofinite(X3221)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X3221)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_1047,plain,
! [X2908] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X2908) = X2908,
inference(variable_rename,[status(thm)],[fact_nat__size]) ).
cnf(i_0_1048,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(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)],[i_0_577]),
[final] ).
cnf(i_0_1049,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk17_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_578]),
[final] ).
cnf(i_0_1050,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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),esk11_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_579]),
[final] ).
cnf(i_0_1051,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_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_1052,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_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_b____),v_a____)),hAPP(v_F,hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),tc_Arrow__Order__Mirabelle_Oindi,c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,tc_HOL_Obool),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Oord__class_Oless(tc_Nat_Onat)),v_h____)),X1))),v_Lab____)),v_Lba____))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk17_0)) ),
inference(split_conjunct,[status(thm)],[i_0_578]),
[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_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),esk11_0)) ),
inference(split_conjunct,[status(thm)],[i_0_579]),
[final] ).
cnf(i_0_1055,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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_581]),
[final] ).
cnf(i_0_1056,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_582]),
[final] ).
cnf(i_0_1057,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_582]),
[final] ).
cnf(i_0_1058,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk16_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,esk16_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_583]),
[final] ).
cnf(i_0_1059,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk16_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,esk16_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_583]),
[final] ).
cnf(i_0_1060,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk15_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,esk15_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_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)))
| 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,esk13_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,esk13_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)))
| 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,esk13_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,esk13_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,
( 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_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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk16_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,esk16_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_583]),
[final] ).
cnf(i_0_1065,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk16_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,esk16_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_583]),
[final] ).
cnf(i_0_1066,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk15_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,esk15_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_584]),
[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,esk13_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,esk13_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_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,esk13_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,esk13_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_585]),
[final] ).
cnf(i_0_1069,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X1),tc_HOL_Obool),c_FuncSet_OPi(X5,X1,X4,X2)),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(X2,esk30_5(X3,X2,X1,X4,X5))),hAPP(X3,esk30_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_587]),
[final] ).
cnf(i_0_1070,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk31_5(X3,X2,X1,X4,X5))),hAPP(X3,esk31_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[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),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,esk25_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,esk25_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_589]),
[final] ).
cnf(i_0_1072,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,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,esk25_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,esk25_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_589]),
[final] ).
cnf(i_0_1073,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk14_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,esk14_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_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),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,esk14_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,esk14_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_590]),
[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(X4,esk25_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,esk25_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_589]),
[final] ).
cnf(i_0_1076,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk25_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,esk25_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_589]),
[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),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,esk14_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,esk14_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_590]),
[final] ).
cnf(i_0_1078,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk14_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,esk14_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_590]),
[final] ).
cnf(i_0_1079,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk19_2(X1,X2)),esk20_2(X1,X2))),hAPP(X2,esk18_2(X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_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),esk19_2(X1,X2)),esk20_2(X1,X2))),hAPP(esk18_2(X1,X2),X1)))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1081,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk18_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1082,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk19_2(X1,X2) != esk20_2(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1083,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_592]),
[final] ).
cnf(i_0_1084,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),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,esk12_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,esk12_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_593]),
[final] ).
cnf(i_0_1085,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk12_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,esk12_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_593]),
[final] ).
cnf(i_0_1086,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_592]),
[final] ).
cnf(i_0_1087,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk30_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X5,X3)),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_587]),
[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)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk12_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,esk12_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_593]),
[final] ).
cnf(i_0_1089,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk12_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,esk12_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_593]),
[final] ).
cnf(i_0_1090,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk44_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_594]),
[final] ).
cnf(i_0_1091,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk31_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1092,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_595]),
[final] ).
cnf(i_0_1093,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_1094,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_592]),
[final] ).
cnf(i_0_1095,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_592]),
[final] ).
cnf(i_0_1096,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk9_4(X3,X2,X4,X1))),hAPP(X3,esk9_4(X3,X2,X4,X1))))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1097,plain,
( hAPP(hAPP(X3,hAPP(X6,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
| ~ c_Finite__Set_Ofinite(X2,X7)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1098,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_598]),
[final] ).
cnf(i_0_1099,plain,
( hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
| ~ c_Finite__Set_Ofinite(X2,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1100,plain,
( hAPP(X6,c_Set_Oinsert(X2,X8,X7)) = hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7))
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
| ~ c_Finite__Set_Ofinite(X2,X7) ),
inference(split_conjunct,[status(thm)],[i_0_600]),
[final] ).
cnf(i_0_1101,plain,
( hAPP(hAPP(X3,X7),X7) = X7
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1102,plain,
( c_Finite__Set_Ocard(X1,X4) = c_Finite__Set_Ocard(X2,X5)
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
| ~ c_Fun_Oinj__on(X2,X1,X6,X5)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X6,X5)),X4))
| ~ c_Finite__Set_Ofinite(X1,X4)
| ~ c_Finite__Set_Ofinite(X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_602]),
[final] ).
cnf(i_0_1103,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk21_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[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_604]),
[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_605]),
[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_606]),
[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_607]),
[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_608]),
[final] ).
cnf(i_0_1109,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_609]),
[final] ).
cnf(i_0_1110,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_c____),v_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_1111,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_610]),
[final] ).
cnf(i_0_1112,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_611]),
[final] ).
cnf(i_0_1113,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_612]),
[final] ).
cnf(i_0_1114,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_611]),
[final] ).
cnf(i_0_1115,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_1116,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_607]),
[final] ).
cnf(i_0_1117,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_607]),
[final] ).
cnf(i_0_1118,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_607]),
[final] ).
cnf(i_0_1119,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_607]),
[final] ).
cnf(i_0_1120,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_608]),
[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)),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_608]),
[final] ).
cnf(i_0_1122,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_608]),
[final] ).
cnf(i_0_1123,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_608]),
[final] ).
cnf(i_0_1124,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_605]),
[final] ).
cnf(i_0_1125,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk44_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_594]),
[final] ).
cnf(i_0_1126,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_1127,plain,
( X1 = hAPP(X2,esk37_5(X1,X2,X3,X4,X5))
| hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| X1 != hAPP(X2,X5)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1128,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_1129,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_1130,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_1131,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_1132,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X5)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
| ~ c_Finite__Set_Ofinite(X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_620]),
[final] ).
cnf(i_0_1133,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_610]),
[final] ).
cnf(i_0_1134,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk43_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_621]),
[final] ).
cnf(i_0_1135,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_607]),
[final] ).
cnf(i_0_1136,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_607]),
[final] ).
cnf(i_0_1137,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_607]),
[final] ).
cnf(i_0_1138,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_622]),
[final] ).
cnf(i_0_1139,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_623]),
[final] ).
cnf(i_0_1140,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_624]),
[final] ).
cnf(i_0_1141,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_625]),
[final] ).
cnf(i_0_1142,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_611]),
[final] ).
cnf(i_0_1143,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| esk37_5(X1,X2,X3,X4,X5) != X5
| X1 != hAPP(X2,X5)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1144,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_626]),
[final] ).
cnf(i_0_1145,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_607]),
[final] ).
cnf(i_0_1146,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_607]),
[final] ).
cnf(i_0_1147,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_607]),
[final] ).
cnf(i_0_1148,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_607]),
[final] ).
cnf(i_0_1149,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_607]),
[final] ).
cnf(i_0_1150,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_608]),
[final] ).
cnf(i_0_1151,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_627]),
[final] ).
cnf(i_0_1152,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_608]),
[final] ).
cnf(i_0_1153,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_608]),
[final] ).
cnf(i_0_1154,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_628]),
[final] ).
cnf(i_0_1155,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),esk28_1(X1)),esk29_1(X1))),hAPP(X1,esk26_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),esk28_1(X1)),esk29_1(X1))),hAPP(X1,esk27_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1156,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_629]),
[final] ).
cnf(i_0_1157,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_608]),
[final] ).
cnf(i_0_1158,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_608]),
[final] ).
cnf(i_0_1159,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_608]),
[final] ).
cnf(i_0_1160,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_608]),
[final] ).
cnf(i_0_1161,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_608]),
[final] ).
cnf(i_0_1162,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_1163,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_630]),
[final] ).
cnf(i_0_1164,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_631]),
[final] ).
cnf(i_0_1165,plain,
( X1 = hAPP(X2,esk36_4(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1166,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_1167,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_1168,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_632]),
[final] ).
cnf(i_0_1169,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_607]),
[final] ).
cnf(i_0_1170,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X1)),esk29_1(X1))),hAPP(esk27_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),esk28_1(X1)),esk29_1(X1))),hAPP(esk26_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1171,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X1)),esk29_1(X1))),hAPP(esk26_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),esk28_1(X1)),esk29_1(X1))),hAPP(esk27_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1172,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_632]),
[final] ).
cnf(i_0_1173,plain,
( X3 = esk36_4(X1,X2,X4,X5)
| X1 != hAPP(X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_615]),
[final] ).
cnf(i_0_1174,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_633]),
[final] ).
cnf(i_0_1175,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_623]),
[final] ).
cnf(i_0_1176,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_608]),
[final] ).
cnf(i_0_1177,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),esk42_3(X1,X3,X2))) != esk42_3(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_634]),
[final] ).
cnf(i_0_1178,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_1179,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),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_1180,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_1181,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_1182,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_1183,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_1184,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_1185,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_1186,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_1187,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_1188,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_1189,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_1190,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_1191,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_1192,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_1193,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk28_1(X1)),esk29_1(X1))),hAPP(X1,esk26_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),esk28_1(X1)),esk29_1(X1))),hAPP(X1,esk27_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1194,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_1195,plain,
( X1 = hAPP(X2,esk43_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_621]),
[final] ).
cnf(i_0_1196,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_607]),
[final] ).
cnf(i_0_1197,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_1198,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_1199,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_1200,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_1201,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_1202,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_608]),
[final] ).
cnf(i_0_1203,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_1204,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_1205,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_1206,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_1207,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_1208,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_1209,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_1210,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_1211,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_1212,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_1213,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_1214,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_594]),
[final] ).
cnf(i_0_1215,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_1216,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_1217,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),esk23_1(X1)),esk24_1(X1))),hAPP(X1,esk22_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1218,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_634]),
[final] ).
cnf(i_0_1219,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_1220,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_1221,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_1222,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_1223,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_1224,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot,X4),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_636]),
[final] ).
cnf(i_0_1225,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_1226,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_1227,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))),esk2_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_1228,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_1229,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_1230,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_1231,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_1232,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_669]),
[final] ).
cnf(i_0_1233,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_670]),
[final] ).
cnf(i_0_1234,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_1235,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk27_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1236,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk26_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[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))),esk22_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1238,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_1239,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_1240,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_621]),
[final] ).
cnf(i_0_1241,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_1242,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_1243,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_1244,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_1245,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_1246,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_1247,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_1248,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_1249,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_1250,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_1251,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_1252,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_1253,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_1254,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_1255,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk23_1(X1)),esk24_1(X1))),hAPP(esk22_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_603]),
[final] ).
cnf(i_0_1256,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_1257,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_1258,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_1259,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_1260,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_1261,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_1262,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_1263,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_1264,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_1265,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_1266,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_1267,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_1268,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_1269,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_1270,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_1271,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_1272,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_1273,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_1274,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_1275,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_1276,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_1277,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_1278,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_1279,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_1280,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_704]),
[final] ).
cnf(i_0_1281,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_705]),
[final] ).
cnf(i_0_1282,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_706]),
[final] ).
cnf(i_0_1283,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_707]),
[final] ).
cnf(i_0_1284,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_708]),
[final] ).
cnf(i_0_1285,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_709]),
[final] ).
cnf(i_0_1286,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_1287,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_710]),
[final] ).
cnf(i_0_1288,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_711]),
[final] ).
cnf(i_0_1289,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_712]),
[final] ).
cnf(i_0_1290,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_713]),
[final] ).
cnf(i_0_1291,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_714]),
[final] ).
cnf(i_0_1292,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_715]),
[final] ).
cnf(i_0_1293,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_716]),
[final] ).
cnf(i_0_1294,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_717]),
[final] ).
cnf(i_0_1295,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_1296,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_718]),
[final] ).
cnf(i_0_1297,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_1298,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_719]),
[final] ).
cnf(i_0_1299,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_720]),
[final] ).
cnf(i_0_1300,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_721]),
[final] ).
cnf(i_0_1301,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_722]),
[final] ).
cnf(i_0_1302,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_723]),
[final] ).
cnf(i_0_1303,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_724]),
[final] ).
cnf(i_0_1304,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),esk8_0)),
inference(split_conjunct,[status(thm)],[i_0_725]),
[final] ).
cnf(i_0_1305,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1306,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),esk7_0)),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_1307,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__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_1308,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_727]),
[final] ).
cnf(i_0_1309,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_727]),
[final] ).
cnf(i_0_1310,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_728]),
[final] ).
cnf(i_0_1311,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_729]),
[final] ).
cnf(i_0_1312,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_730]),
[final] ).
cnf(i_0_1313,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_1314,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_731]),
[final] ).
cnf(i_0_1315,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_1316,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_732]),
[final] ).
cnf(i_0_1317,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_733]),
[final] ).
cnf(i_0_1318,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_734]),
[final] ).
cnf(i_0_1319,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_734]),
[final] ).
cnf(i_0_1320,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_735]),
[final] ).
cnf(i_0_1321,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_736]),
[final] ).
cnf(i_0_1322,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_737]),
[final] ).
cnf(i_0_1323,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_1324,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_738]),
[final] ).
cnf(i_0_1325,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_739]),
[final] ).
cnf(i_0_1326,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_1327,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_740]),
[final] ).
cnf(i_0_1328,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_721]),
[final] ).
cnf(i_0_1329,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_741]),
[final] ).
cnf(i_0_1330,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_741]),
[final] ).
cnf(i_0_1331,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_742]),
[final] ).
cnf(i_0_1332,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_743]),
[final] ).
cnf(i_0_1333,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_744]),
[final] ).
cnf(i_0_1334,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_745]),
[final] ).
cnf(i_0_1335,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_1336,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk39_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_746]),
[final] ).
cnf(i_0_1337,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_747]),
[final] ).
cnf(i_0_1338,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_1339,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_748]),
[final] ).
cnf(i_0_1340,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_749]),
[final] ).
cnf(i_0_1341,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_750]),
[final] ).
cnf(i_0_1342,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_751]),
[final] ).
cnf(i_0_1343,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk40_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_752]),
[final] ).
cnf(i_0_1344,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_708]),
[final] ).
cnf(i_0_1345,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_709]),
[final] ).
cnf(i_0_1346,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_753]),
[final] ).
cnf(i_0_1347,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_754]),
[final] ).
cnf(i_0_1348,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_755]),
[final] ).
cnf(i_0_1349,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_756]),
[final] ).
cnf(i_0_1350,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_757]),
[final] ).
cnf(i_0_1351,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_758]),
[final] ).
cnf(i_0_1352,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_1353,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_760]),
[final] ).
cnf(i_0_1354,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_734]),
[final] ).
cnf(i_0_1355,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_761]),
[final] ).
cnf(i_0_1356,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_762]),
[final] ).
cnf(i_0_1357,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_763]),
[final] ).
cnf(i_0_1358,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_764]),
[final] ).
cnf(i_0_1359,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_765]),
[final] ).
cnf(i_0_1360,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_766]),
[final] ).
cnf(i_0_1361,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_720]),
[final] ).
cnf(i_0_1362,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_767]),
[final] ).
cnf(i_0_1363,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_768]),
[final] ).
cnf(i_0_1364,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_769]),
[final] ).
cnf(i_0_1365,plain,
( hBOOL(hAPP(X1,X3))
| ~ 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))) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1366,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_770]),
[final] ).
cnf(i_0_1367,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_771]),
[final] ).
cnf(i_0_1368,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_1369,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_1370,plain,
( hBOOL(hAPP(X1,esk39_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_746]),
[final] ).
cnf(i_0_1371,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(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_746]),
[final] ).
cnf(i_0_1372,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_774]),
[final] ).
cnf(i_0_1373,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_1374,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_776]),
[final] ).
cnf(i_0_1375,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_777]),
[final] ).
cnf(i_0_1376,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_725]),
[final] ).
cnf(i_0_1377,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk7_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_726]),
[final] ).
cnf(i_0_1378,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_1379,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_1380,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk41_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_752]),
[final] ).
cnf(i_0_1381,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_778]),
[final] ).
cnf(i_0_1382,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_779]),
[final] ).
cnf(i_0_1383,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_727]),
[final] ).
cnf(i_0_1384,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_780]),
[final] ).
cnf(i_0_1385,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_771]),
[final] ).
cnf(i_0_1386,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_772]),
[final] ).
cnf(i_0_1387,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_781]),
[final] ).
cnf(i_0_1388,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_758]),
[final] ).
cnf(i_0_1389,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_758]),
[final] ).
cnf(i_0_1390,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_763]),
[final] ).
cnf(i_0_1391,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_782]),
[final] ).
cnf(i_0_1392,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_1393,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_784]),
[final] ).
cnf(i_0_1394,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_785]),
[final] ).
cnf(i_0_1395,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_1396,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_1397,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_788]),
[final] ).
cnf(i_0_1398,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_1399,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_596]),
[final] ).
cnf(i_0_1400,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_790]),
[final] ).
cnf(i_0_1401,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_791]),
[final] ).
cnf(i_0_1402,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_792]),
[final] ).
cnf(i_0_1403,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_793]),
[final] ).
cnf(i_0_1404,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_794]),
[final] ).
cnf(i_0_1405,plain,
( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk35_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_795]),
[final] ).
cnf(i_0_1406,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_796]),
[final] ).
cnf(i_0_1407,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_797]),
[final] ).
cnf(i_0_1408,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_798]),
[final] ).
cnf(i_0_1409,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_774]),
[final] ).
cnf(i_0_1410,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_1411,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_776]),
[final] ).
cnf(i_0_1412,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_800]),
[final] ).
cnf(i_0_1413,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_801]),
[final] ).
cnf(i_0_1414,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_1415,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_771]),
[final] ).
cnf(i_0_1416,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_802]),
[final] ).
cnf(i_0_1417,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_1418,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_804]),
[final] ).
cnf(i_0_1419,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_764]),
[final] ).
cnf(i_0_1420,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_764]),
[final] ).
cnf(i_0_1421,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_805]),
[final] ).
cnf(i_0_1422,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_806]),
[final] ).
cnf(i_0_1423,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_807]),
[final] ).
cnf(i_0_1424,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_807]),
[final] ).
cnf(i_0_1425,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_808]),
[final] ).
cnf(i_0_1426,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_809]),
[final] ).
cnf(i_0_1427,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_1428,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_811]),
[final] ).
cnf(i_0_1429,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_1430,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_2(X1,X2)),X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_813]),
[final] ).
cnf(i_0_1431,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_814]),
[final] ).
cnf(i_0_1432,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_815]),
[final] ).
cnf(i_0_1433,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_816]),
[final] ).
cnf(i_0_1434,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_817]),
[final] ).
cnf(i_0_1435,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_807]),
[final] ).
cnf(i_0_1436,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_818]),
[final] ).
cnf(i_0_1437,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_819]),
[final] ).
cnf(i_0_1438,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_820]),
[final] ).
cnf(i_0_1439,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_821]),
[final] ).
cnf(i_0_1440,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_822]),
[final] ).
cnf(i_0_1441,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_823]),
[final] ).
cnf(i_0_1442,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_824]),
[final] ).
cnf(i_0_1443,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_825]),
[final] ).
cnf(i_0_1444,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_826]),
[final] ).
cnf(i_0_1445,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_827]),
[final] ).
cnf(i_0_1446,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_828]),
[final] ).
cnf(i_0_1447,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_829]),
[final] ).
cnf(i_0_1448,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_830]),
[final] ).
cnf(i_0_1449,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_802]),
[final] ).
cnf(i_0_1450,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_831]),
[final] ).
cnf(i_0_1451,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_832]),
[final] ).
cnf(i_0_1452,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_1453,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_834]),
[final] ).
cnf(i_0_1454,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_1455,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_824]),
[final] ).
cnf(i_0_1456,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_824]),
[final] ).
cnf(i_0_1457,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_836]),
[final] ).
cnf(i_0_1458,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_837]),
[final] ).
cnf(i_0_1459,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_838]),
[final] ).
cnf(i_0_1460,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_839]),
[final] ).
cnf(i_0_1461,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_1462,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_1463,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_842]),
[final] ).
cnf(i_0_1464,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_843]),
[final] ).
cnf(i_0_1465,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_844]),
[final] ).
cnf(i_0_1466,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_845]),
[final] ).
cnf(i_0_1467,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_846]),
[final] ).
cnf(i_0_1468,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_847]),
[final] ).
cnf(i_0_1469,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_848]),
[final] ).
cnf(i_0_1470,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_849]),
[final] ).
cnf(i_0_1471,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_1472,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_1473,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_1474,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_853]),
[final] ).
cnf(i_0_1475,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_854]),
[final] ).
cnf(i_0_1476,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_855]),
[final] ).
cnf(i_0_1477,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk35_2(X2,X3)))
| ~ hBOOL(hAPP(X3,X1))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_795]),
[final] ).
cnf(i_0_1478,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_819]),
[final] ).
cnf(i_0_1479,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_856]),
[final] ).
cnf(i_0_1480,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_857]),
[final] ).
cnf(i_0_1481,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_858]),
[final] ).
cnf(i_0_1482,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_774]),
[final] ).
cnf(i_0_1483,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oinsert(X3,X2,X4)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_799]),
[final] ).
cnf(i_0_1484,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_859]),
[final] ).
cnf(i_0_1485,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_860]),
[final] ).
cnf(i_0_1486,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_861]),
[final] ).
cnf(i_0_1487,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_862]),
[final] ).
cnf(i_0_1488,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_1489,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_864]),
[final] ).
cnf(i_0_1490,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk17_0),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(split_conjunct,[status(thm)],[i_0_578]),
[final] ).
cnf(i_0_1491,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk11_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_579]),
[final] ).
cnf(i_0_1492,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_1493,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_839]),
[final] ).
cnf(i_0_1494,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_840]),
[final] ).
cnf(i_0_1495,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_865]),
[final] ).
cnf(i_0_1496,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_866]),
[final] ).
cnf(i_0_1497,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_867]),
[final] ).
cnf(i_0_1498,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_813]),
[final] ).
cnf(i_0_1499,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_868]),
[final] ).
cnf(i_0_1500,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_869]),
[final] ).
cnf(i_0_1501,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk41_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1502,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_870]),
[final] ).
cnf(i_0_1503,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_871]),
[final] ).
cnf(i_0_1504,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_872]),
[final] ).
cnf(i_0_1505,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_873]),
[final] ).
cnf(i_0_1506,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_857]),
[final] ).
cnf(i_0_1507,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk34_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_874]),
[final] ).
cnf(i_0_1508,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_875]),
[final] ).
cnf(i_0_1509,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X4,X1),X2))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_817]),
[final] ).
cnf(i_0_1510,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_1511,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_858]),
[final] ).
cnf(i_0_1512,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_876]),
[final] ).
cnf(i_0_1513,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_861]),
[final] ).
cnf(i_0_1514,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_877]),
[final] ).
cnf(i_0_1515,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_878]),
[final] ).
cnf(i_0_1516,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk35_2(X1,X2)),X1))
| hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_795]),
[final] ).
cnf(i_0_1517,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_879]),
[final] ).
cnf(i_0_1518,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_880]),
[final] ).
cnf(i_0_1519,plain,
( hBOOL(hAPP(X1,esk38_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_746]),
[final] ).
cnf(i_0_1520,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_881]),
[final] ).
cnf(i_0_1521,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_882]),
[final] ).
cnf(i_0_1522,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_883]),
[final] ).
cnf(i_0_1523,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_884]),
[final] ).
cnf(i_0_1524,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_885]),
[final] ).
cnf(i_0_1525,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_886]),
[final] ).
cnf(i_0_1526,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_887]),
[final] ).
cnf(i_0_1527,plain,
( X1 = hAPP(c_Nat_OSuc,esk32_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_813]),
[final] ).
cnf(i_0_1528,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_854]),
[final] ).
cnf(i_0_1529,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_888]),
[final] ).
cnf(i_0_1530,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_889]),
[final] ).
cnf(i_0_1531,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_875]),
[final] ).
cnf(i_0_1532,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1533,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_878]),
[final] ).
cnf(i_0_1534,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_891]),
[final] ).
cnf(i_0_1535,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_874]),
[final] ).
cnf(i_0_1536,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_892]),
[final] ).
cnf(i_0_1537,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_893]),
[final] ).
cnf(i_0_1538,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_857]),
[final] ).
cnf(i_0_1539,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_894]),
[final] ).
cnf(i_0_1540,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_895]),
[final] ).
cnf(i_0_1541,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_896]),
[final] ).
cnf(i_0_1542,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1543,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_898]),
[final] ).
cnf(i_0_1544,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_817]),
[final] ).
cnf(i_0_1545,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_892]),
[final] ).
cnf(i_0_1546,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_893]),
[final] ).
cnf(i_0_1547,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_899]),
[final] ).
cnf(i_0_1548,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_900]),
[final] ).
cnf(i_0_1549,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_1550,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_902]),
[final] ).
cnf(i_0_1551,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_903]),
[final] ).
cnf(i_0_1552,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_870]),
[final] ).
cnf(i_0_1553,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_904]),
[final] ).
cnf(i_0_1554,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_830]),
[final] ).
cnf(i_0_1555,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_905]),
[final] ).
cnf(i_0_1556,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_906]),
[final] ).
cnf(i_0_1557,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_907]),
[final] ).
cnf(i_0_1558,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1559,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_879]),
[final] ).
cnf(i_0_1560,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_909]),
[final] ).
cnf(i_0_1561,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_862]),
[final] ).
cnf(i_0_1562,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_837]),
[final] ).
cnf(i_0_1563,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_910]),
[final] ).
cnf(i_0_1564,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_911]),
[final] ).
cnf(i_0_1565,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_912]),
[final] ).
cnf(i_0_1566,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_1567,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_1568,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1569,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_916]),
[final] ).
cnf(i_0_1570,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_917]),
[final] ).
cnf(i_0_1571,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_918]),
[final] ).
cnf(i_0_1572,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_919]),
[final] ).
cnf(i_0_1573,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_920]),
[final] ).
cnf(i_0_1574,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_1575,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_922]),
[final] ).
cnf(i_0_1576,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_848]),
[final] ).
cnf(i_0_1577,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_923]),
[final] ).
cnf(i_0_1578,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_924]),
[final] ).
cnf(i_0_1579,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_912]),
[final] ).
cnf(i_0_1580,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_913]),
[final] ).
cnf(i_0_1581,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_925]),
[final] ).
cnf(i_0_1582,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_926]),
[final] ).
cnf(i_0_1583,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_927]),
[final] ).
cnf(i_0_1584,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_928]),
[final] ).
cnf(i_0_1585,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_929]),
[final] ).
cnf(i_0_1586,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_924]),
[final] ).
cnf(i_0_1587,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_903]),
[final] ).
cnf(i_0_1588,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1589,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_873]),
[final] ).
cnf(i_0_1590,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_931]),
[final] ).
cnf(i_0_1591,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_932]),
[final] ).
cnf(i_0_1592,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_871]),
[final] ).
cnf(i_0_1593,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_933]),
[final] ).
cnf(i_0_1594,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_934]),
[final] ).
cnf(i_0_1595,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_935]),
[final] ).
cnf(i_0_1596,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk10_2(X2,X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_936]),
[final] ).
cnf(i_0_1597,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_937]),
[final] ).
cnf(i_0_1598,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_938]),
[final] ).
cnf(i_0_1599,plain,
( X1 = hAPP(c_Nat_OSuc,esk33_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_939]),
[final] ).
cnf(i_0_1600,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_892]),
[final] ).
cnf(i_0_1601,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_848]),
[final] ).
cnf(i_0_1602,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_940]),
[final] ).
cnf(i_0_1603,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_941]),
[final] ).
cnf(i_0_1604,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_942]),
[final] ).
cnf(i_0_1605,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_917]),
[final] ).
cnf(i_0_1606,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_917]),
[final] ).
cnf(i_0_1607,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_782]),
[final] ).
cnf(i_0_1608,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_782]),
[final] ).
cnf(i_0_1609,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_943]),
[final] ).
cnf(i_0_1610,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_943]),
[final] ).
cnf(i_0_1611,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_944]),
[final] ).
cnf(i_0_1612,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_772]),
[final] ).
cnf(i_0_1613,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_945]),
[final] ).
cnf(i_0_1614,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1615,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1616,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_948]),
[final] ).
cnf(i_0_1617,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_949]),
[final] ).
cnf(i_0_1618,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_950]),
[final] ).
cnf(i_0_1619,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_951]),
[final] ).
cnf(i_0_1620,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_952]),
[final] ).
cnf(i_0_1621,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_953]),
[final] ).
cnf(i_0_1622,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X1,X4) != c_List_Olist_OCons(X3,X2,X5) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1623,plain,
( X1 = X2
| c_List_Olist_OCons(X3,X4,X1) != c_List_Olist_OCons(X3,X5,X2) ),
inference(split_conjunct,[status(thm)],[i_0_954]),
[final] ).
cnf(i_0_1624,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_955]),
[final] ).
cnf(i_0_1625,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_956]),
[final] ).
cnf(i_0_1626,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_957]),
[final] ).
cnf(i_0_1627,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_958]),
[final] ).
cnf(i_0_1628,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_905]),
[final] ).
cnf(i_0_1629,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_959]),
[final] ).
cnf(i_0_1630,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_960]),
[final] ).
cnf(i_0_1631,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_1632,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_962]),
[final] ).
cnf(i_0_1633,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1634,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1635,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_963]),
[final] ).
cnf(i_0_1636,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_964]),
[final] ).
cnf(i_0_1637,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_965]),
[final] ).
cnf(i_0_1638,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_912]),
[final] ).
cnf(i_0_1639,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_1640,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1641,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1642,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1643,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_936]),
[final] ).
cnf(i_0_1644,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_968]),
[final] ).
cnf(i_0_1645,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_969]),
[final] ).
cnf(i_0_1646,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_970]),
[final] ).
cnf(i_0_1647,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_971]),
[final] ).
cnf(i_0_1648,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_972]),
[final] ).
cnf(i_0_1649,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_973]),
[final] ).
cnf(i_0_1650,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_974]),
[final] ).
cnf(i_0_1651,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_813]),
[final] ).
cnf(i_0_1652,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_929]),
[final] ).
cnf(i_0_1653,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_975]),
[final] ).
cnf(i_0_1654,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_861]),
[final] ).
cnf(i_0_1655,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_879]),
[final] ).
cnf(i_0_1656,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk2_2(X2,X1)) != hAPP(esk2_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_649]),
[final] ).
cnf(i_0_1657,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_976]),
[final] ).
cnf(i_0_1658,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_977]),
[final] ).
cnf(i_0_1659,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_978]),
[final] ).
cnf(i_0_1660,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_979]),
[final] ).
cnf(i_0_1661,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_980]),
[final] ).
cnf(i_0_1662,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_939]),
[final] ).
cnf(i_0_1663,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1664,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_982]),
[final] ).
cnf(i_0_1665,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1666,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_979]),
[final] ).
cnf(i_0_1667,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_979]),
[final] ).
cnf(i_0_1668,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_980]),
[final] ).
cnf(i_0_1669,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_980]),
[final] ).
cnf(i_0_1670,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_984]),
[final] ).
cnf(i_0_1671,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_985]),
[final] ).
cnf(i_0_1672,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_948]),
[final] ).
cnf(i_0_1673,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_986]),
[final] ).
cnf(i_0_1674,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_979]),
[final] ).
cnf(i_0_1675,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_980]),
[final] ).
cnf(i_0_1676,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_987]),
[final] ).
cnf(i_0_1677,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_988]),
[final] ).
cnf(i_0_1678,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_989]),
[final] ).
cnf(i_0_1679,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_990]),
[final] ).
cnf(i_0_1680,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_979]),
[final] ).
cnf(i_0_1681,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_979]),
[final] ).
cnf(i_0_1682,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_980]),
[final] ).
cnf(i_0_1683,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_980]),
[final] ).
cnf(i_0_1684,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_884]),
[final] ).
cnf(i_0_1685,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_884]),
[final] ).
cnf(i_0_1686,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_991]),
[final] ).
cnf(i_0_1687,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_893]),
[final] ).
cnf(i_0_1688,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1689,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1690,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X1,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1691,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_995]),
[final] ).
cnf(i_0_1692,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_996]),
[final] ).
cnf(i_0_1693,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_997]),
[final] ).
cnf(i_0_1694,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_998]),
[final] ).
cnf(i_0_1695,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_978]),
[final] ).
cnf(i_0_1696,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1697,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(split_conjunct,[status(thm)],[i_0_1000]),
[final] ).
cnf(i_0_1698,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_1001]),
[final] ).
cnf(i_0_1699,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_1002]),
[final] ).
cnf(i_0_1700,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_1002]),
[final] ).
cnf(i_0_1701,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1702,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1703,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1704,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_1705,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_1005]),
[final] ).
cnf(i_0_1706,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1006]),
[final] ).
cnf(i_0_1707,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_1007]),
[final] ).
cnf(i_0_1708,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_1008]),
[final] ).
cnf(i_0_1709,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_1009]),
[final] ).
cnf(i_0_1710,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_1010]),
[final] ).
cnf(i_0_1711,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_988]),
[final] ).
cnf(i_0_1712,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_989]),
[final] ).
cnf(i_0_1713,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_990]),
[final] ).
cnf(i_0_1714,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_1011]),
[final] ).
cnf(i_0_1715,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_1012]),
[final] ).
cnf(i_0_1716,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_1013]),
[final] ).
cnf(i_0_1717,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_1014]),
[final] ).
cnf(i_0_1718,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_1015]),
[final] ).
cnf(i_0_1719,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_1016]),
[final] ).
cnf(i_0_1720,plain,
c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1721,plain,
c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1722,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_1723,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_1002]),
[final] ).
cnf(i_0_1724,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_1725,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_1019]),
[final] ).
cnf(i_0_1726,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_1020]),
[final] ).
cnf(i_0_1727,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_1021]),
[final] ).
cnf(i_0_1728,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_1022]),
[final] ).
cnf(i_0_1729,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_1023]),
[final] ).
cnf(i_0_1730,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_1024]),
[final] ).
cnf(i_0_1731,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1025]),
[final] ).
cnf(i_0_1732,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1026]),
[final] ).
cnf(i_0_1733,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1027]),
[final] ).
cnf(i_0_1734,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[final] ).
cnf(i_0_1735,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1736,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1737,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_1031]),
[final] ).
cnf(i_0_1738,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1739,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1740,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_1741,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1742,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1743,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_1744,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1745,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1746,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1747,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1748,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1749,plain,
c_List_Odistinct(X1,c_List_Olist_ONil(X1)),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1750,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_1044]),
[final] ).
cnf(i_0_1751,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_1045]),
[final] ).
cnf(i_0_1752,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_1753,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_1754,plain,
( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1755,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1756,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_1757,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_1758,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_1759,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_1760,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_1761,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_1762,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_1763,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_1764,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_1765,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_1766,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_1767,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_1768,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_1769,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_1770,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_1771,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_1772,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_1773,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_1774,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1775,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1776,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1777,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1778,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1779,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1780,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1781,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1782,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1783,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_1784,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1785,plain,
v_c____ != v_d____,
inference(split_conjunct,[status(thm)],[fact__096c_A_126_061_Ad_096]),
[final] ).
cnf(i_0_1786,axiom,
X1 = X1 ).
cnf(i_0_1787,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1788,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1789,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1790,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1791,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_1792,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1793,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1794,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1795,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1796,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1797,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1798,axiom,
( X1 != X2
| esk19_2(X1,X3) = esk19_2(X2,X3) ) ).
cnf(i_0_1799,axiom,
( X1 != X2
| esk19_2(X3,X1) = esk19_2(X3,X2) ) ).
cnf(i_0_1800,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1801,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1802,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1803,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1804,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1805,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1806,axiom,
( X1 != X2
| c_Set_Oinsert(X1,X3,X4) = c_Set_Oinsert(X2,X3,X4) ) ).
cnf(i_0_1807,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X1,X4) = c_Set_Oinsert(X3,X2,X4) ) ).
cnf(i_0_1808,axiom,
( X1 != X2
| c_Set_Oinsert(X3,X4,X1) = c_Set_Oinsert(X3,X4,X2) ) ).
cnf(i_0_1809,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1810,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1811,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1812,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1813,axiom,
( X1 != X2
| esk37_5(X1,X3,X4,X5,X6) = esk37_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1814,axiom,
( X1 != X2
| esk37_5(X3,X1,X4,X5,X6) = esk37_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1815,axiom,
( X1 != X2
| esk37_5(X3,X4,X1,X5,X6) = esk37_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1816,axiom,
( X1 != X2
| esk37_5(X3,X4,X5,X1,X6) = esk37_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1817,axiom,
( X1 != X2
| esk37_5(X3,X4,X5,X6,X1) = esk37_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1818,axiom,
( X1 != X2
| c_List_Olist_OCons(X1,X3,X4) = c_List_Olist_OCons(X2,X3,X4) ) ).
cnf(i_0_1819,axiom,
( X1 != X2
| c_List_Olist_OCons(X3,X1,X4) = c_List_Olist_OCons(X3,X2,X4) ) ).
cnf(i_0_1820,axiom,
( X1 != X2
| c_List_Olist_OCons(X3,X4,X1) = c_List_Olist_OCons(X3,X4,X2) ) ).
cnf(i_0_1821,axiom,
( X1 != X2
| esk36_4(X1,X3,X4,X5) = esk36_4(X2,X3,X4,X5) ) ).
cnf(i_0_1822,axiom,
( X1 != X2
| esk36_4(X3,X1,X4,X5) = esk36_4(X3,X2,X4,X5) ) ).
cnf(i_0_1823,axiom,
( X1 != X2
| esk36_4(X3,X4,X1,X5) = esk36_4(X3,X4,X2,X5) ) ).
cnf(i_0_1824,axiom,
( X1 != X2
| esk36_4(X3,X4,X5,X1) = esk36_4(X3,X4,X5,X2) ) ).
cnf(i_0_1825,axiom,
( X1 != X2
| esk42_3(X1,X3,X4) = esk42_3(X2,X3,X4) ) ).
cnf(i_0_1826,axiom,
( X1 != X2
| esk42_3(X3,X1,X4) = esk42_3(X3,X2,X4) ) ).
cnf(i_0_1827,axiom,
( X1 != X2
| esk42_3(X3,X4,X1) = esk42_3(X3,X4,X2) ) ).
cnf(i_0_1828,axiom,
( X1 != X2
| esk6_4(X1,X3,X4,X5) = esk6_4(X2,X3,X4,X5) ) ).
cnf(i_0_1829,axiom,
( X1 != X2
| esk6_4(X3,X1,X4,X5) = esk6_4(X3,X2,X4,X5) ) ).
cnf(i_0_1830,axiom,
( X1 != X2
| esk6_4(X3,X4,X1,X5) = esk6_4(X3,X4,X2,X5) ) ).
cnf(i_0_1831,axiom,
( X1 != X2
| esk6_4(X3,X4,X5,X1) = esk6_4(X3,X4,X5,X2) ) ).
cnf(i_0_1832,axiom,
( X1 != X2
| esk5_4(X1,X3,X4,X5) = esk5_4(X2,X3,X4,X5) ) ).
cnf(i_0_1833,axiom,
( X1 != X2
| esk5_4(X3,X1,X4,X5) = esk5_4(X3,X2,X4,X5) ) ).
cnf(i_0_1834,axiom,
( X1 != X2
| esk5_4(X3,X4,X1,X5) = esk5_4(X3,X4,X2,X5) ) ).
cnf(i_0_1835,axiom,
( X1 != X2
| esk5_4(X3,X4,X5,X1) = esk5_4(X3,X4,X5,X2) ) ).
cnf(i_0_1836,axiom,
( X1 != X2
| c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).
cnf(i_0_1837,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_1838,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_1839,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_1840,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_1841,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_1842,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).
cnf(i_0_1843,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).
cnf(i_0_1844,axiom,
( X1 != X2
| c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).
cnf(i_0_1845,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1846,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1847,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1848,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1849,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1850,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1851,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1852,axiom,
( X1 != X2
| c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).
cnf(i_0_1853,axiom,
( X1 != X2
| c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).
cnf(i_0_1854,axiom,
( X1 != X2
| c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).
cnf(i_0_1855,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1856,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1857,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1858,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1859,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1860,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1861,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1862,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1863,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1864,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1865,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1866,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1867,axiom,
( X1 != X2
| ~ c_List_Odistinct(X1,X3)
| c_List_Odistinct(X2,X3) ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| ~ c_List_Odistinct(X3,X1)
| c_List_Odistinct(X3,X2) ) ).
cnf(i_0_1869,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1870,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1871,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X3,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X2,X3,X4,X5,X6,X7) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X1,X4,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X2,X4,X5,X6,X7) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X1,X5,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X2,X5,X6,X7) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X1,X6,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X2,X6,X7) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X1,X7)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X2,X7) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X1)
| c_Finite__Set_Ofolding__image__simple__idem(X3,X4,X5,X6,X7,X2) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1902,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_1903,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_1904,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_1905,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_1906,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_1907,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_1908,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1913,plain,
X1 = X1,
inference(equality_inference,[],[1063]) ).
cnf(i_0_1942,plain,
X1 = X1,
inference(equality_inference,[],[1259]) ).
cnf(i_0_1948,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[1415]) ).
cnf(i_0_1950,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(equality_inference,[],[1483]) ).
cnf(i_0_1955,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(equality_inference,[],[1544]) ).
cnf(i_0_1961,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1612]) ).
cnf(i_0_1962,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1613]) ).
cnf(i_0_1966,plain,
X1 = X1,
inference(equality_inference,[],[1622]) ).
cnf(i_0_1967,plain,
X1 = X1,
inference(equality_inference,[],[1623]) ).
cnf(i_0_1968,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1633]) ).
cnf(i_0_1970,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1641]) ).
cnf(i_0_1971,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1642]) ).
cnf(i_0_1973,plain,
X1 = X1,
inference(equality_inference,[],[1649]) ).
cnf(i_0_1974,plain,
X1 = X1,
inference(equality_inference,[],[1650]) ).
cnf(i_0_1976,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[1654]) ).
cnf(i_0_1978,plain,
X1 = X1,
inference(equality_inference,[],[1663]) ).
cnf(i_0_1982,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(equality_inference,[],[1703]) ).
cnf(i_0_1983,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1704]) ).
cnf(i_0_1987,plain,
X1 = X1,
inference(equality_inference,[],[1732]) ).
cnf(i_0_1988,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X3,c_Set_Oinsert(X1,X2,X4)))),
inference(scs_inference,[],[i_0_1445,i_0_1268]) ).
cnf(i_0_1989,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_1445]) ).
cnf(i_0_2007,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1648]) ).
cnf(i_0_2036,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1615]) ).
cnf(i_0_2045,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1615]) ).
cnf(i_0_2048,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_1740]) ).
cnf(i_0_2051,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1657]) ).
cnf(i_0_2054,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1657]) ).
cnf(i_0_2057,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2081,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1657]) ).
cnf(i_0_2089,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1530]) ).
cnf(i_0_2092,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1530]) ).
cnf(i_0_2100,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2115,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1530]) ).
cnf(i_0_2136,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1530]) ).
cnf(i_0_2143,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1615]) ).
cnf(i_0_2146,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2151,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_1445]) ).
cnf(i_0_2159,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2176,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2179,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1697]) ).
cnf(i_0_2180,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2184,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2220,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2222,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2224,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2226,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2228,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2245,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2255,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2258,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_1445]) ).
cnf(i_0_2261,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_1445]) ).
cnf(i_0_2262,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2265,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1615]) ).
cnf(i_0_2268,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2271,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1556]) ).
cnf(i_0_2284,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_1445]) ).
cnf(i_0_2306,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1530]) ).
cnf(i_0_2310,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1648]) ).
cnf(i_0_2320,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1746]) ).
cnf(i_0_2337,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1746]) ).
cnf(i_0_2344,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1584]) ).
cnf(i_0_2345,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1697]) ).
cnf(i_0_2346,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(rename_variables,[],[i_0_1688]) ).
cnf(i_0_2349,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1648]) ).
cnf(i_0_2350,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2354,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_1727]) ).
cnf(i_0_2357,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1697]) ).
cnf(i_0_2360,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1696]) ).
cnf(i_0_2363,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_1445]) ).
cnf(i_0_2364,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2381,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2384,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2387,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1648]) ).
cnf(i_0_2390,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1648]) ).
cnf(i_0_2393,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1657]) ).
cnf(i_0_2402,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1530]) ).
cnf(i_0_2421,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1697]) ).
cnf(i_0_2422,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2425,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1696]) ).
cnf(i_0_2426,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2436,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2437,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2440,plain,
X1 != c_List_Olist_OCons(X2,X3,X1),
inference(rename_variables,[],[i_0_1697]) ).
cnf(i_0_2443,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1696]) ).
cnf(i_0_2447,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2448,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X1,X2,X3),
inference(rename_variables,[],[i_0_1690]) ).
cnf(i_0_2449,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1696]) ).
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_1727]) ).
cnf(i_0_2457,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2458,plain,
c_List_Olist_OCons(X1,X2,X3) != X3,
inference(rename_variables,[],[i_0_1696]) ).
cnf(i_0_2459,plain,
c_List_Olist_OCons(X1,X2,X3) != c_List_Olist_ONil(X1),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2460,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2463,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1615]) ).
cnf(i_0_2465,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2487,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2489,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2491,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2493,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1755]) ).
cnf(i_0_2498,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_1445]) ).
cnf(i_0_2504,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1657]) ).
cnf(i_0_2703,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1747]) ).
cnf(i_0_2719,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_2738,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2782,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1746]) ).
cnf(i_0_2953,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_2975,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1706]) ).
cnf(i_0_3012,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X3))),
inference(rename_variables,[],[i_0_1485]) ).
cnf(i_0_3015,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_3067,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_3278,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1543]) ).
cnf(i_0_3296,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1584]) ).
cnf(c_0_1779,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
i_0_1731 ).
cnf(c_0_1780,plain,
( X1 = hAPP(c_Nat_OSuc,esk33_1(X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
i_0_1599 ).
cnf(c_0_1781,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_1662 ).
cnf(c_0_1782,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_1294 ).
cnf(c_0_1783,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
i_0_1556 ).
cnf(c_0_1784,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
i_0_1744 ).
cnf(c_0_1785,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
i_0_1764 ).
cnf(c_0_1786,plain,
( esk33_1(X1) = X2
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_1779,c_0_1780]),c_0_1781]) ).
cnf(c_0_1787,plain,
( X1 = hAPP(X2,esk36_4(X1,X2,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
i_0_1165 ).
cnf(c_0_1788,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_1782,c_0_1783]) ).
cnf(c_0_1789,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
i_0_1583 ).
cnf(c_0_1790,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_1249 ).
cnf(c_0_1791,plain,
c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
inference(spm,[status(thm)],[c_0_1784,c_0_1785]) ).
cnf(c_0_1792,plain,
esk33_1(hAPP(c_Nat_OSuc,X1)) = X1,
inference(er,[status(thm)],[c_0_1786]) ).
cnf(c_0_1793,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_1242 ).
cnf(c_0_1794,plain,
( c_Fun_Oinj__on(X1,X2,X3,X4)
| esk5_4(X4,X3,X2,X1) != esk6_4(X4,X3,X2,X1) ),
i_0_1274 ).
cnf(c_0_1795,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
i_0_1741 ).
cnf(c_0_1796,plain,
( hAPP(c_Nat_OSuc,esk36_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_1787,c_0_1788]),c_0_1783]),c_0_1789])]) ).
cnf(c_0_1797,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2) ),
inference(spm,[status(thm)],[c_0_1790,c_0_1791]) ).
cnf(c_0_1798,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_1792,c_0_1793]),c_0_1792]),c_0_1794]) ).
cnf(c_0_1799,plain,
( c_Groups_Ozero__class_Ozero(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(spm,[status(thm)],[c_0_1795,c_0_1796]) ).
cnf(c_0_1800,plain,
c_Finite__Set_Ofinite(X1,X2),
inference(spm,[status(thm)],[c_0_1797,c_0_1798]) ).
cnf(c_0_1801,plain,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
i_0_1756 ).
cnf(c_0_1802,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_1799,c_0_1800])]) ).
cnf(c_0_1803,plain,
$false,
inference(sr,[status(thm)],[c_0_1801,c_0_1802]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT162+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % 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
% 0.15/0.32 % Computer : n018.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:59:02 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 144.41/116.04 % Version : CSE_E---1.7
% 144.41/116.04 % Problem : theBenchmark.p
% 144.41/116.04 % SZS status Theorem for theBenchmark.p
% 144.41/116.04 % SZS output start CNFRefutation
% See solution above
% 233.52/205.18 % Total time : 114.314s
%------------------------------------------------------------------------------