%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SCT161+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 05:06:09 PM UTC 2026
% Result : Theorem 2.79s 5.74s
% Output : CNFRefutation 10.98s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 1070)
% Comments :
%------------------------------------------------------------------------------
fof(fact_setsum__delta,axiom,
! [X26,X28,X14,X5,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( c_Finite__Set_Ofinite(X5,X14)
=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X28),X14))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X7,hAPP(hAPP(c_COMBC(X5,X7,X7),c_COMBS(X5,X7,tc_fun(X7,X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X5,c_If(X7)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X28)),X26)),c_Groups_Ozero__class_Ozero(X7)),X14) = hAPP(X26,X28) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X28),X14))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X7,hAPP(hAPP(c_COMBC(X5,X7,X7),c_COMBS(X5,X7,tc_fun(X7,X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X5,c_If(X7)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X28)),X26)),c_Groups_Ozero__class_Ozero(X7)),X14) = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta) ).
fof(fact_setsum__delta_H,axiom,
! [X26,X28,X14,X5,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( c_Finite__Set_Ofinite(X5,X14)
=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X28),X14))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X7,hAPP(hAPP(c_COMBC(X5,X7,X7),c_COMBS(X5,X7,tc_fun(X7,X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X5,c_If(X7)),hAPP(c_fequal,X28)),X26)),c_Groups_Ozero__class_Ozero(X7)),X14) = hAPP(X26,X28) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X28),X14))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X7,hAPP(hAPP(c_COMBC(X5,X7,X7),c_COMBS(X5,X7,tc_fun(X7,X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X5,c_If(X7)),hAPP(c_fequal,X28)),X26)),c_Groups_Ozero__class_Ozero(X7)),X14) = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__delta_H) ).
fof(fact_pigeonhole,axiom,
! [X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X5,c_Set_Oimage(X7,X5,X2,X25))),c_Finite__Set_Ocard(X7,X25)))
=> ~ c_Fun_Oinj__on(X7,X5,X2,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pigeonhole) ).
fof(fact_notin__Lin__iff,axiom,
! [X13,X4,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),c_Arrow__Order__Mirabelle_OLin))
=> ( X4 != X13
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X13)),X16))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X13),X4)),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(fact_Lin__irrefl,axiom,
! [X26,X28,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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),X28),X26)),X16))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X28)),X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(fact_PiE,axiom,
! [X4,X30,X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,X30)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X4)),hAPP(X30,X4)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X4),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiE) ).
fof(fact_setsum__op__ivl__Suc,axiom,
! [X2,X9,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,hAPP(c_Nat_OSuc,X6))) = c_Groups_Ozero__class_Ozero(X5) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,hAPP(c_Nat_OSuc,X6))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,X6))),hAPP(X2,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).
fof(fact_bot2E,axiom,
! [X13,X4,X7,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X7,tc_HOL_Obool))),X4),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
fof(fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X39] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X39))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X39),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X38))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X38),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X5,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X7)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X7),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X7),X1),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_add__leE,axiom,
! [X8,X62,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X62)),X8))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_not__add__less1,axiom,
! [X63,X64] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X64),X63)),X64)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X64,X63] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X63),X64)),X64)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(conj_0,conjecture,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> v_Lba____ = v_Lab____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_not__psubset__empty,axiom,
! [X25,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
fof(fact_not__less__eq__eq,axiom,
! [X6,X9] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X6,X9] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_OSuc,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_xt1_I9_J,axiom,
! [X19,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X19))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_order__less__not__sym,axiom,
! [X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__imp__not__less,axiom,
! [X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__asym_H,axiom,
! [X20,X19,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__asym,axiom,
! [X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X4))
| X4 = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_empty__iff,axiom,
! [X31,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X31),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
fof(fact_emptyE,axiom,
! [X28,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X28),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
fof(fact_less__le__not__le,axiom,
! [X13,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X13),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_less__SucE,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X8)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> X12 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_less__antisym,axiom,
! [X12,X8] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X12))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,X12)))
=> X12 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X9,X6] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_OSuc,X9)))
<=> X6 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> X4 = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_linorder__not__less,axiom,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X13),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_leD,axiom,
! [X11,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__le,axiom,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_atLeastLessThan__empty__iff2,axiom,
! [X26,X28,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
fof(fact_atLeastLessThan__empty__iff,axiom,
! [X26,X28,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
fof(fact_le__SucE,axiom,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),hAPP(c_Nat_OSuc,X8)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
=> X12 = hAPP(c_Nat_OSuc,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X8] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8)),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
<=> X4 = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_all__not__in__conv,axiom,
! [X25,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
<=> X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X10,X11,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X11 != X10
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X4,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X4))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> X4 = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE,axiom,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( X11 != X10
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__cases,axiom,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ( X11 != X10
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_equals0D,axiom,
! [X28,X5,X25] :
( X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X28),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
fof(fact_not__leE,axiom,
! [X11,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__neqE__nat,axiom,
! [X10,X11] :
( X11 != X10
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_equalityE,axiom,
! [X5,X30,X25] :
( X25 = X30
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
fof(fact_order__less__irrefl,axiom,
! [X11,X5] :
( class_Orderings_Opreorder(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_linorder__le__cases,axiom,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_not__less0,axiom,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__nat__zero__code,axiom,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_less__zeroE,axiom,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__irrefl__nat,axiom,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(help_c__fequal__1,axiom,
! [X13,X4] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4),X13))
| X4 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(fact_card__eq__0__iff,axiom,
! [X25,X5] :
( c_Finite__Set_Ocard(X5,X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X5,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
fof(fact_card__infinite,axiom,
! [X25,X5] :
( ~ c_Finite__Set_Ofinite(X5,X25)
=> c_Finite__Set_Ocard(X5,X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
fof(fact__C0_C,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),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____)),X6))),v_Lab____)),v_Lba____))),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C0_C) ).
fof(fact__C1_C,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____)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_Lab____)),v_Lba____)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
fof(fact_PiProf,axiom,
! [X6] : hBOOL(hAPP(hAPP(c_member(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____)),X6))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_PiProf) ).
fof(fact_pred__subset__eq2,axiom,
! [X14,X15,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X5,c_COMBC(X7,tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_prod(X5,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X7),tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool),X7,c_member(tc_prod(X5,X7)))),c_Product__Type_OPair(X5,X7)))),X15)),hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X5,c_COMBC(X7,tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_prod(X5,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X7),tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool),X7,c_member(tc_prod(X5,X7)))),c_Product__Type_OPair(X5,X7)))),X14)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact__C2_C,axiom,
! [X40,X21,X41,X42,X26,X28] :
( X28 != X26
=> ( X42 != X41
=> ( X28 != X41
=> ( X26 != X42
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X21),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))),X40),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(X21,X43)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X42),X41)),hAPP(X40,X43))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(v_F,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),X42),X41)),hAPP(v_F,X40))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).
fof(fact__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_059_Aa_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Aa_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_096,axiom,
! [X40,X21,X41,X42,X26,X28] :
( X28 != X26
=> ( X42 != X41
=> ( X28 != X41
=> ( X26 != X42
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X21),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))),X40),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(X21,X43)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X42),X41)),hAPP(X40,X43))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(v_F,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),X42),X41)),hAPP(v_F,X40))) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_059_Aa_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Aa_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_096) ).
fof(fact_pairwise__neutrality,axiom,
! [X40,X21,X41,X42,X26,X28] :
( X28 != X26
=> ( X42 != 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))),X21),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))),X40),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(X21,X43)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X42),X41)),hAPP(X40,X43))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(v_F,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),X42),X41)),hAPP(v_F,X40))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pairwise__neutrality) ).
fof(fact_max__extp__max__ext__eq,axiom,
! [X71,X4,X15,X5] :
( c_Wellfounded_Omax__extp(X5,hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X5,c_COMBC(X5,tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X5,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X5),tc_fun(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X5,X5)))),c_Product__Type_OPair(X5,X5)))),X15),X4,X71)
<=> 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)),X4),X71)),c_Wellfounded_Omax__ext(X5,X15))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).
fof(fact_pred__equals__eq2,axiom,
! [X14,X15,X7,X5] :
( hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X5,c_COMBC(X7,tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_prod(X5,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X7),tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool),X7,c_member(tc_prod(X5,X7)))),c_Product__Type_OPair(X5,X7)))),X15) = hAPP(hAPP(c_COMBC(X5,tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X5,c_COMBC(X7,tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X7,tc_prod(X5,X7)),tc_fun(X7,tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool)),X5,c_COMBB(tc_prod(X5,X7),tc_fun(tc_fun(tc_prod(X5,X7),tc_HOL_Obool),tc_HOL_Obool),X7,c_member(tc_prod(X5,X7)))),c_Product__Type_OPair(X5,X7)))),X14)
<=> X15 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_Pi__mono,axiom,
! [X37,X30,X7,X25,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),hAPP(X30,X3)),hAPP(X37,X3))) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X7),tc_HOL_Obool),c_FuncSet_OPi(X5,X7,X25,X30)),c_FuncSet_OPi(X5,X7,X25,X37))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mono) ).
fof(fact_Pi__I,axiom,
! [X30,X2,X7,X25,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X3)),hAPP(X30,X3))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,X30))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(fact_folding__one__idem_Ohom__commute,axiom,
! [X58,X54,X45,X2,X5] :
( c_Finite__Set_Ofolding__one__idem(X5,X2,X45)
=> ( ! [X3,X27] : hAPP(X54,hAPP(hAPP(X2,X3),X27)) = hAPP(hAPP(X2,hAPP(X54,X3)),hAPP(X54,X27))
=> ( c_Finite__Set_Ofinite(X5,X58)
=> ( X58 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
=> hAPP(X54,hAPP(X45,X58)) = hAPP(X45,c_Set_Oimage(X5,X5,X54,X58)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
fof(fact_IIA__def,axiom,
! [X45] :
( c_Arrow__Order__Mirabelle_OIIA(X45)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X32),c_Arrow__Order__Mirabelle_OProf))
=> ! [X46,X47] :
( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X46),X47)),hAPP(X3,X43)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X46),X47)),hAPP(X32,X43))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X46),X47)),hAPP(X45,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),X46),X47)),hAPP(X45,X32))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
fof(fact__C4_C,axiom,
! [X40,X21,X31,X26,X28] :
( X28 != X26
=> ( X26 != X31
=> ( X28 != X31
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X21),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))),X40),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(X21,X43)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X31)),hAPP(X40,X43))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(v_F,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),X26),X31)),hAPP(v_F,X40))) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C4_C) ).
fof(fact_funcsetI,axiom,
! [X30,X2,X7,X25,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X3)),X30)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X5),X30)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(fact_max__ext_Osimps,axiom,
! [X15,X79,X80,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)),X80),X79)),c_Wellfounded_Omax__ext(X5,X15)))
<=> ( c_Finite__Set_Ofinite(X5,X80)
& c_Finite__Set_Ofinite(X5,X79)
& X79 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X80))
=> ? [X32] :
( hBOOL(hAPP(hAPP(c_member(X5),X32),X79))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X32)),X15)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).
fof(fact_dictatorI,axiom,
! [X44,X45] :
( 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))),X45),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))
=> ! [X46,X47] :
( X46 != X47
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X46),X47)),hAPP(X3,X44)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X46),X47)),hAPP(X45,X3))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X45,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(fact_max__ext_Ointros,axiom,
! [X15,X33,X81,X5] :
( c_Finite__Set_Ofinite(X5,X81)
=> ( c_Finite__Set_Ofinite(X5,X33)
=> ( X33 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X81))
=> ? [X32] :
( hBOOL(hAPP(hAPP(c_member(X5),X32),X33))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X32)),X15)) ) )
=> 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)),X81),X33)),c_Wellfounded_Omax__ext(X5,X15))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).
fof(fact_in__lex__prod,axiom,
! [X59,X60,X41,X42,X26,X28,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X7),tc_prod(X5,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X7),tc_prod(X5,X7)),hAPP(hAPP(c_Product__Type_OPair(X5,X7),X28),X26)),hAPP(hAPP(c_Product__Type_OPair(X5,X7),X42),X41))),c_Wellfounded_Olex__prod(X5,X7,X60,X59)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X28),X42)),X60))
| ( X28 = X42
& hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X26),X41)),X59)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
fof(fact__C3_C,axiom,
! [X40,X21,X26,X28] :
( X28 != X26
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X21),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))),X40),c_Arrow__Order__Mirabelle_OProf))
=> ( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(X21,X43)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X28)),hAPP(X40,X43))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),hAPP(v_F,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),X26),X28)),hAPP(v_F,X40))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C3_C) ).
fof(fact_subset__image__iff,axiom,
! [X25,X2,X7,X30,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),c_Set_Oimage(X7,X5,X2,X25)))
<=> ? [X57] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X57),X25))
& X30 = c_Set_Oimage(X7,X5,X2,X57) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(fact_same__fstI,axiom,
! [X5,X15,X13,X53,X7,X4,X21] :
( hBOOL(hAPP(X21,X4))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X53),X13)),hAPP(X15,X4)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X5,X7),tc_prod(X5,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X5,X7),tc_prod(X5,X7)),hAPP(hAPP(c_Product__Type_OPair(X5,X7),X4),X53)),hAPP(hAPP(c_Product__Type_OPair(X5,X7),X4),X13))),c_Recdef_Osame__fst(X5,X7,X21,X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
fof(fact_max__extp_Oequations,axiom,
! [X79,X80,X15,X5] :
( c_Wellfounded_Omax__extp(X5,X15,X80,X79)
<=> ( c_Finite__Set_Ofinite(X5,X80)
& c_Finite__Set_Ofinite(X5,X79)
& X79 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
& ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X80))
=> ? [X32] :
( hBOOL(hAPP(hAPP(c_member(X5),X32),X79))
& hBOOL(hAPP(hAPP(X15,X3),X32)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X5,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X7),X2),X1))
<=> ! [X3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,hAPP(X2,X3)),hAPP(X1,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
! [X30,X25,X45,X1,X35,X2,X7,X5] :
( c_Finite__Set_Ofolding__image__simple__idem(X5,X7,X2,X35,X1,X45)
=> ( c_Finite__Set_Ofinite(X7,X25)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X30),X25))
=> hAPP(hAPP(X2,hAPP(X45,X30)),hAPP(X45,X25)) = hAPP(X45,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [X4,X25,X45,X1,X35,X2,X7,X5] :
( c_Finite__Set_Ofolding__image__simple__idem(X5,X7,X2,X35,X1,X45)
=> ( c_Finite__Set_Ofinite(X7,X25)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X25))
=> hAPP(hAPP(X2,hAPP(X1,X4)),hAPP(X45,X25)) = hAPP(X45,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [X4,X45,X1,X35,X2,X7,X5] :
( c_Finite__Set_Ofolding__image__simple__idem(X5,X7,X2,X35,X1,X45)
=> hAPP(hAPP(X2,X4),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_ord_OatLeastLessThan__iff,axiom,
! [X48,X49,X50,X51,X44,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord_OatLeastLessThan(X5,X51,X50,X49,X48)))
<=> ( hBOOL(hAPP(hAPP(X51,X49),X44))
& hBOOL(hAPP(hAPP(X50,X44),X48)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
fof(fact_ord_OgreaterThanAtMost__iff,axiom,
! [X48,X49,X50,X51,X44,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord_OgreaterThanAtMost(X5,X51,X50,X49,X48)))
<=> ( hBOOL(hAPP(hAPP(X50,X49),X44))
& hBOOL(hAPP(hAPP(X51,X44),X48)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
fof(fact_card__bij__eq,axiom,
! [X1,X30,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X5,X7,X2,X25)),X30))
=> ( c_Fun_Oinj__on(X7,X5,X1,X30)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X7,X5,X1,X30)),X25))
=> ( c_Finite__Set_Ofinite(X5,X25)
=> ( c_Finite__Set_Ofinite(X7,X30)
=> c_Finite__Set_Ocard(X5,X25) = c_Finite__Set_Ocard(X7,X30) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(fact_unanimity__def,axiom,
! [X45] :
( c_Arrow__Order__Mirabelle_Ounanimity(X45)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
=> ! [X46,X47] :
( ! [X43] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X46),X47)),hAPP(X3,X43)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X46),X47)),hAPP(X45,X3))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
fof(fact_card__bij,axiom,
! [X1,X30,X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X5),X30))))
=> ( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X5)),X1),c_FuncSet_OPi(X7,X5,X30,hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X7),X25))))
=> ( c_Fun_Oinj__on(X7,X5,X1,X30)
=> ( c_Finite__Set_Ofinite(X5,X25)
=> ( c_Finite__Set_Ofinite(X7,X30)
=> c_Finite__Set_Ocard(X5,X25) = c_Finite__Set_Ocard(X7,X30) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij) ).
fof(fact_pred__subset__eq,axiom,
! [X14,X15,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)),X15)),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X14)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_the__inv__into__into,axiom,
! [X30,X4,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),c_Set_Oimage(X5,X7,X2,X25)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> hBOOL(hAPP(hAPP(c_member(X5),hAPP(c_Fun_Othe__inv__into(X5,X7,X25,X2),X4)),X30)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__into) ).
fof(fact_inj__on__iff__surj,axiom,
! [X56,X7,X5,X25] :
( X25 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
=> ( ? [X61] :
( c_Fun_Oinj__on(X5,X7,X61,X25)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X5,X7,X61,X25)),X56)) )
<=> ? [X76] : c_Set_Oimage(X7,X5,X76,X56) = X25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).
fof(fact_inj__on__iff__card__le,axiom,
! [X30,X7,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( c_Finite__Set_Ofinite(X7,X30)
=> ( ? [X61] :
( c_Fun_Oinj__on(X5,X7,X61,X25)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X5,X7,X61,X25)),X30)) )
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X25)),c_Finite__Set_Ocard(X7,X30))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_in__above,axiom,
! [X13,X4,X16,X26,X28] :
( X28 != X26
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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),X4),X13)),c_Arrow__Order__Mirabelle_Oabove(X16,X28,X26)))
<=> ( X4 != X13
& ( X4 = X26
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X13)),X16)) )
& ( X4 != X26
=> ( ( X13 = X26
=> ( X4 = X28
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X28)),X16)) ) )
& ( X13 != X26
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X13)),X16)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
fof(fact_in__below,axiom,
! [X13,X4,X16,X26,X28] :
( X28 != X26
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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),X4),X13)),c_Arrow__Order__Mirabelle_Obelow(X16,X28,X26)))
<=> ( X4 != X13
& ( X13 = X28
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X26)),X16)) )
& ( X13 != X28
=> ( ( X4 = X28
=> ( X13 = X26
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X13)),X16)) ) )
& ( X4 != X28
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X13)),X16)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
fof(fact_inj__image__subset__iff,axiom,
! [X30,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X5,X7,X2,X25)),c_Set_Oimage(X5,X7,X2,X30)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_in__finite__psubset,axiom,
! [X30,X25,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)),X25),X30)),c_Wellfounded_Ofinite__psubset(X5)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
& c_Finite__Set_Ofinite(X5,X30) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_funcset__image,axiom,
! [X30,X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X5),X30))))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X5,X7,X2,X25)),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__image) ).
fof(fact_range__ex1__eq,axiom,
! [X26,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),X26),c_Set_Oimage(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
<=> ? [X3] :
( X26 = hAPP(X2,X3)
& ! [X27] :
( X26 = hAPP(X2,X27)
=> X27 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_card__image__le,axiom,
! [X2,X7,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X7,c_Set_Oimage(X5,X7,X2,X25))),c_Finite__Set_Ocard(X5,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image__le) ).
fof(fact_inj__on__strict__subset,axiom,
! [X25,X30,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X30)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),c_Set_Oimage(X5,X7,X2,X25)),c_Set_Oimage(X5,X7,X2,X30))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_endo__inj__surj,axiom,
! [X2,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Set_Oimage(X5,X5,X2,X25)),X25))
=> ( c_Fun_Oinj__on(X5,X5,X2,X25)
=> c_Set_Oimage(X5,X5,X2,X25) = X25 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_card__inj__on__le,axiom,
! [X30,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X5,X7,X2,X25)),X30))
=> ( c_Finite__Set_Ofinite(X7,X30)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X25)),c_Finite__Set_Ocard(X7,X30))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_image__iff,axiom,
! [X25,X2,X7,X35,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X35),c_Set_Oimage(X7,X5,X2,X25)))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X7),X3),X25))
& X35 = hAPP(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__iff) ).
fof(fact_card__inj,axiom,
! [X30,X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X5),X30))))
=> ( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( c_Finite__Set_Ofinite(X7,X30)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X25)),c_Finite__Set_Ocard(X7,X30))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__inj) ).
fof(fact_Pi__anti__mono,axiom,
! [X30,X7,X25,X56,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X56),X25))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X5,X7),tc_HOL_Obool),c_FuncSet_OPi(X5,X7,X25,X30)),c_FuncSet_OPi(X5,X7,X56,X30))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__anti__mono) ).
fof(fact_finite__range__imageI,axiom,
! [X2,X34,X1,X7,X5] :
( c_Finite__Set_Ofinite(X5,c_Set_Oimage(X7,X5,X1,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))
=> c_Finite__Set_Ofinite(X34,c_Set_Oimage(X7,X34,hAPP(c_COMBB(X5,X34,X7,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_const__Lin__Prof,axiom,
! [X16] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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),X16)),c_Arrow__Order__Mirabelle_OProf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_const__Lin__Prof) ).
fof(fact_funcset__mem,axiom,
! [X4,X30,X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X5),X30))))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X4)),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__mem) ).
fof(fact_image__mono,axiom,
! [X2,X7,X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),c_Set_Oimage(X5,X7,X2,X25)),c_Set_Oimage(X5,X7,X2,X30))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__mono) ).
fof(fact_mlex__leq,axiom,
! [X15,X5,X13,X4,X2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2,X4)),hAPP(X2,X13)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X13)),X15))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X13)),c_Wellfounded_Omlex__prod(X5,X2,X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(fact_f__the__inv__into__f,axiom,
! [X13,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X13),c_Set_Oimage(X5,X7,X2,X25)))
=> hAPP(X2,hAPP(c_Fun_Othe__inv__into(X5,X7,X25,X2),X13)) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).
fof(fact_setsum__shift__bounds__nat__ivl,axiom,
! [X6,X52,X9,X2,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X52),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X52))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X52)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
fof(fact_in__rel__def,axiom,
! [X13,X4,X15,X7,X5] :
( c_FunDef_Oin__rel(X5,X7,X15,X4,X13)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X7)),hAPP(hAPP(c_Product__Type_OPair(X5,X7),X4),X13)),X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(fact_bot__empty__eq2,axiom,
! [X13,X4,X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X7,tc_HOL_Obool))),X4),X13))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X7)),hAPP(hAPP(c_Product__Type_OPair(X5,X7),X4),X13)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X7),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).
fof(fact_setsum__add__nat__ivl,axiom,
! [X2,X82,X6,X9,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6),X82))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,X6))),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X6,X82))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,X82)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).
fof(fact_Pi__eq__empty,axiom,
! [X30,X25,X7,X5] :
( c_FuncSet_OPi(X5,X7,X25,X30) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X5,X7),tc_HOL_Obool))
<=> ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
& hAPP(X30,X3) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__eq__empty) ).
fof(help_c__COMBS__1,axiom,
! [X15,X55,X21,X5,X34,X7] : hAPP(c_COMBS(X7,X34,X5,X21,X55),X15) = hAPP(hAPP(X21,X15),hAPP(X55,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(fact_Pi__mem,axiom,
! [X4,X30,X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,X30)))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X4)),hAPP(X30,X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__mem) ).
fof(fact_inj__image__mem__iff,axiom,
! [X25,X28,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X28)),c_Set_Oimage(X5,X7,X2,X25)))
<=> hBOOL(hAPP(hAPP(c_member(X5),X28),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_in__mkbot,axiom,
! [X35,X16,X13,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X13)),c_Arrow__Order__Mirabelle_Omkbot(X16,X35)))
<=> ( X13 != X35
& ( X4 = X35
=> X4 != X13 )
& ( X4 != X35
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X13)),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(fact_in__mktop,axiom,
! [X35,X16,X13,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X13)),c_Arrow__Order__Mirabelle_Omktop(X16,X35)))
<=> ( X4 != X35
& ( X13 = X35
=> X4 != X13 )
& ( X13 != X35
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X13)),X16)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(fact_inj__on__def,axiom,
! [X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
=> ! [X32] :
( hBOOL(hAPP(hAPP(c_member(X5),X32),X25))
=> ( hAPP(X2,X3) = hAPP(X2,X32)
=> X3 = X32 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).
fof(fact_range__composition,axiom,
! [X1,X2,X34,X5,X7] : c_Set_Oimage(X7,X5,hAPP(c_COMBB(X34,X5,X7,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Set_Oimage(X34,X5,X2,c_Set_Oimage(X7,X34,X1,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__composition) ).
fof(fact_finite__surj__inj,axiom,
! [X2,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),c_Set_Oimage(X5,X5,X2,X25)))
=> c_Fun_Oinj__on(X5,X5,X2,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_dictator__def,axiom,
! [X44,X45] :
( c_Arrow__Order__Mirabelle_Odictator(X45,X44)
<=> ! [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(X45,X3) = hAPP(X3,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(fact_inj__fun,axiom,
! [X34,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> c_Fun_Oinj__on(X5,tc_fun(X34,X7),hAPP(c_COMBB(X7,tc_fun(X34,X7),X5,c_COMBK(X7,X34)),X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__fun) ).
fof(fact_funcset__id,axiom,
! [X25,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X5)),c_COMBI(X5)),c_FuncSet_OPi(X5,X5,X25,hAPP(c_COMBK(tc_fun(X5,tc_HOL_Obool),X5),X25)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(fact_image__image,axiom,
! [X25,X1,X34,X2,X5,X7] : c_Set_Oimage(X7,X5,X2,c_Set_Oimage(X34,X7,X1,X25)) = c_Set_Oimage(X34,X5,hAPP(c_COMBB(X7,X5,X34,X2),X1),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__image) ).
fof(fact_above__Lin,axiom,
! [X16,X13,X4] :
( X4 != X13
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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_Oabove(X16,X4,X13)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
fof(fact_below__Lin,axiom,
! [X16,X13,X4] :
( X4 != X13
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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(X16,X4,X13)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(fact_in__measure,axiom,
! [X2,X13,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X13)),c_Wellfounded_Omeasure(X5,X2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X4)),hAPP(X2,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__measure) ).
fof(fact_finite__surj,axiom,
! [X2,X30,X7,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool),X30),c_Set_Oimage(X5,X7,X2,X25)))
=> c_Finite__Set_Ofinite(X7,X30) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(fact_ord_OatLeastAtMost__iff,axiom,
! [X48,X49,X51,X44,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord_OatLeastAtMost(X5,X51,X49,X48)))
<=> ( hBOOL(hAPP(hAPP(X51,X49),X44))
& hBOOL(hAPP(hAPP(X51,X44),X48)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
fof(fact_ord_OgreaterThanLessThan__iff,axiom,
! [X48,X49,X50,X44,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord_OgreaterThanLessThan(X5,X50,X49,X48)))
<=> ( hBOOL(hAPP(hAPP(X50,X49),X44))
& hBOOL(hAPP(hAPP(X50,X44),X48)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
! [X6,X9,X2,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X9),hAPP(c_Nat_OSuc,X6))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,hAPP(c_COMBB(tc_Nat_Onat,X5,tc_Nat_Onat,X2),c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
fof(fact_mkbot__Lin,axiom,
! [X4,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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_Omkbot(X16,X4)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
fof(fact_mktop__Lin,axiom,
! [X4,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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_Omktop(X16,X4)),c_Arrow__Order__Mirabelle_OLin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).
fof(fact_mlex__less,axiom,
! [X15,X5,X13,X4,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X4)),hAPP(X2,X13)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X13)),c_Wellfounded_Omlex__prod(X5,X2,X15))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__less) ).
fof(fact_the__inv__into__onto,axiom,
! [X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> c_Set_Oimage(X7,X5,c_Fun_Othe__inv__into(X5,X7,X25,X2),c_Set_Oimage(X5,X7,X2,X25)) = X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_subset__card__intvl__is__intvl,axiom,
! [X52,X25] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X25),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X52,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),c_Finite__Set_Ocard(tc_Nat_Onat,X25)))))
=> X25 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X52,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),c_Finite__Set_Ocard(tc_Nat_Onat,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).
fof(fact_inj__on__the__inv__into,axiom,
! [X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> c_Fun_Oinj__on(X7,X5,c_Fun_Othe__inv__into(X5,X7,X25,X2),c_Set_Oimage(X5,X7,X2,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_atLeastLessThan__subset__iff,axiom,
! [X36,X31,X26,X28,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26)),c_SetInterval_Oord__class_OatLeastLessThan(X5,X31,X36)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X26),X28))
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X31),X28))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X26),X36)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_rangeI,axiom,
! [X7,X4,X2,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(X2,X4)),c_Set_Oimage(X7,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rangeI) ).
fof(fact_setsum__head__upt__Suc,axiom,
! [X2,X6,X9,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,X6)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(X2,X9)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X9),X6))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).
fof(fact_imageI,axiom,
! [X2,X7,X25,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X4)),c_Set_Oimage(X5,X7,X2,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_imageI) ).
fof(fact__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
fof(fact__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lba____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
fof(fact_range__eqI,axiom,
! [X7,X5,X4,X2,X26] :
( X26 = hAPP(X2,X4)
=> hBOOL(hAPP(hAPP(c_member(X5),X26),c_Set_Oimage(X7,X5,X2,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).
fof(fact_image__eqI,axiom,
! [X5,X25,X7,X4,X2,X26] :
( X26 = hAPP(X2,X4)
=> ( hBOOL(hAPP(hAPP(c_member(X7),X4),X25))
=> hBOOL(hAPP(hAPP(c_member(X5),X26),c_Set_Oimage(X7,X5,X2,X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__eqI) ).
fof(fact_rev__image__eqI,axiom,
! [X7,X2,X26,X25,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> ( X26 = hAPP(X2,X4)
=> hBOOL(hAPP(hAPP(c_member(X7),X26),c_Set_Oimage(X5,X7,X2,X25))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_inj__image__eq__iff,axiom,
! [X30,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Set_Oimage(X5,X7,X2,X25) = c_Set_Oimage(X5,X7,X2,X30)
<=> X25 = X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_add__less__imp__less__right,axiom,
! [X20,X18,X19,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),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X18)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X26,X31,X28,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),X28),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X26),X31)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X20,X19,X18,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),X18),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X20)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X26,X28,X31,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),X31),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X31),X26)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_finite__imageD,axiom,
! [X25,X2,X7,X5] :
( c_Finite__Set_Ofinite(X5,c_Set_Oimage(X7,X5,X2,X25))
=> ( c_Fun_Oinj__on(X7,X5,X2,X25)
=> c_Finite__Set_Ofinite(X7,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).
fof(fact_psubset__trans,axiom,
! [X37,X30,X25,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X30),X37))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__trans) ).
fof(fact_add__le__cancel__right,axiom,
! [X26,X31,X28,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),X28),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X26),X31)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X28),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__right,axiom,
! [X20,X18,X19,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),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X18)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__left,axiom,
! [X26,X28,X31,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),X31),X28)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X31),X26)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X28),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [X20,X19,X18,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),X18),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X20)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_the__inv__f__f,axiom,
! [X4,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> hAPP(c_Fun_Othe__inv__into(X5,X7,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X2),hAPP(X2,X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__f__f) ).
fof(fact_pred__equals__eq,axiom,
! [X14,X15,X5] :
( hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X15) = hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X14)
<=> X15 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X6,X9,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X6)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_the__inv__into__f__f,axiom,
! [X4,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> hAPP(c_Fun_Othe__inv__into(X5,X7,X25,X2),hAPP(X2,X4)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).
fof(fact_the__inv__into__f__eq,axiom,
! [X13,X4,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hAPP(X2,X4) = X13
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> hAPP(c_Fun_Othe__inv__into(X5,X7,X25,X2),X13) = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [X2,X7,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( c_Finite__Set_Ocard(X7,c_Set_Oimage(X5,X7,X2,X25)) = c_Finite__Set_Ocard(X5,X25)
=> c_Fun_Oinj__on(X5,X7,X2,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [X2,X7,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( c_Fun_Oinj__on(X5,X7,X2,X25)
<=> c_Finite__Set_Ocard(X7,c_Set_Oimage(X5,X7,X2,X25)) = c_Finite__Set_Ocard(X5,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(help_c__COMBB__1,axiom,
! [X15,X55,X21,X34,X5,X7] : hAPP(hAPP(c_COMBB(X7,X5,X34,X21),X55),X15) = hAPP(X21,hAPP(X55,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__strict__mono,axiom,
! [X77,X18,X20,X19,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X18),X77))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X77))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_image__add__atLeastLessThan,axiom,
! [X67,X44,X52] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X52),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X44,X67)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X52),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X67),X52)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X6,X9,X52] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X9)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_add__le__less__mono,axiom,
! [X77,X18,X20,X19,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),X20))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X18),X77))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X77))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X77,X18,X20,X19,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X18),X77))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X77))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_subset__psubset__trans,axiom,
! [X37,X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X30),X37))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_psubset__subset__trans,axiom,
! [X37,X30,X25,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),X37))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [X6,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X9)),X6))
<=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_card__psubset,axiom,
! [X25,X30,X5] :
( c_Finite__Set_Ofinite(X5,X30)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X5,X25)),c_Finite__Set_Ocard(X5,X30)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(fact_add__mono,axiom,
! [X77,X18,X20,X19,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),X20))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X18),X77))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X77))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_even__less__0__iff,axiom,
! [X28,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X28),X28)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X28,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),X28),X28)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_complete__Lin,axiom,
! [X26,X28] :
( X28 != X26
=> ? [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))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X28),X26)),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complete__Lin) ).
fof(fact_add__less__mono,axiom,
! [X74,X62,X63,X64] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),X63))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X62),X74))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X64),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X63),X74))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_subset__inj__on,axiom,
! [X25,X30,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X30)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> c_Fun_Oinj__on(X5,X7,X2,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__inj__on) ).
fof(fact_card__image,axiom,
! [X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> c_Finite__Set_Ocard(X7,c_Set_Oimage(X5,X7,X2,X25)) = c_Finite__Set_Ocard(X5,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__image) ).
fof(fact_add__neg__neg,axiom,
! [X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_add__strict__right__mono,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X28,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),X28),X28)),c_Groups_Ozero__class_Ozero(X5)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X28),c_Groups_Ozero__class_Ozero(X5))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_add__nonpos__neg,axiom,
! [X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__le__mono,axiom,
! [X74,X62,X63,X64] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64),X63))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62),X74))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X64),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X63),X74))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_finite__Plus__iff,axiom,
! [X30,X25,X7,X5] :
( c_Finite__Set_Ofinite(tc_sum(X5,X7),c_Sum__Type_OPlus(X5,X7,X25,X30))
<=> ( c_Finite__Set_Ofinite(X5,X25)
& c_Finite__Set_Ofinite(X7,X30) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [X30,X25,X7,X5] :
( c_Finite__Set_Ofinite(tc_sum(X5,X7),c_Sum__Type_OPlus(X5,X7,X25,X30))
=> c_Finite__Set_Ofinite(X5,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [X30,X25,X7,X5] :
( c_Finite__Set_Ofinite(tc_sum(X5,X7),c_Sum__Type_OPlus(X5,X7,X25,X30))
=> c_Finite__Set_Ofinite(X7,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_add__right__mono,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X18))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Oordered__ab__semigroup__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),X20))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X19)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__lessD1,axiom,
! [X62,X63,X64] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X64),X63)),X62))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),X62)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),c_Groups_Ozero__class_Ozero(X5)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),c_Groups_Ozero__class_Ozero(X5)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20)),c_Groups_Ozero__class_Ozero(X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
! [X52,X2,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X5)
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X52)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X52)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
fof(fact_predicate2D,axiom,
! [X13,X4,X55,X21,X7,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X7,tc_HOL_Obool)),X21),X55))
=> ( hBOOL(hAPP(hAPP(X21,X4),X13))
=> hBOOL(hAPP(hAPP(X55,X4),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
fof(fact_rev__predicate2D,axiom,
! [X55,X7,X5,X13,X4,X21] :
( hBOOL(hAPP(hAPP(X21,X4),X13))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_fun(X7,tc_HOL_Obool)),X21),X55))
=> hBOOL(hAPP(hAPP(X55,X4),X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_add__less__mono1,axiom,
! [X62,X63,X64] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),X63))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X64),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X63),X62))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_inj__on__iff,axiom,
! [X13,X4,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X13),X25))
=> ( hAPP(X2,X4) = hAPP(X2,X13)
<=> X4 = X13 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__on__contraD,axiom,
! [X13,X4,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( X4 != X13
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X13),X25))
=> hAPP(X2,X4) != hAPP(X2,X13) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_inj__onD,axiom,
! [X13,X4,X25,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,X25)
=> ( hAPP(X2,X4) = hAPP(X2,X13)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X13),X25))
=> X4 = X13 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__onD) ).
fof(fact_add__leD1,axiom,
! [X8,X62,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X62)),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X8,X62,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X62)),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__pos__pos,axiom,
! [X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X19))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_ex__nat__less__eq,axiom,
! [X21,X6] :
( ? [X29] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X6))
& hBOOL(hAPP(X21,X29)) )
<=> ? [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),X6)))
& hBOOL(hAPP(X21,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
fof(fact_add__le__mono1,axiom,
! [X62,X63,X64] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64),X63))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X64),X62)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X63),X62))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_psubsetD,axiom,
! [X31,X30,X25,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X31),X25))
=> hBOOL(hAPP(hAPP(c_member(X5),X31),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubsetD) ).
fof(fact_psubset__card__mono,axiom,
! [X25,X30,X5] :
( c_Finite__Set_Ofinite(X5,X30)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X5,X25)),c_Finite__Set_Ocard(X5,X30))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_inj__on__add__nat,axiom,
! [X58,X52] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X52),X58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X77,X18,X20,X19,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X77)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_all__nat__less__eq,axiom,
! [X21,X6] :
( ! [X29] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29),X6))
=> hBOOL(hAPP(X21,X29)) )
<=> ! [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),X6)))
=> hBOOL(hAPP(X21,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_subset__trans,axiom,
! [X37,X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),X37))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X37)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
fof(fact_add__nonneg__pos,axiom,
! [X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X19))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X19))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_card__Plus,axiom,
! [X30,X7,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( c_Finite__Set_Ofinite(X7,X30)
=> c_Finite__Set_Ocard(tc_sum(X5,X7),c_Sum__Type_OPlus(X5,X7,X25,X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X5,X25)),c_Finite__Set_Ocard(X7,X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus) ).
fof(fact_card__Plus__conv__if,axiom,
! [X30,X7,X25,X5] :
( ( ( c_Finite__Set_Ofinite(X5,X25)
& c_Finite__Set_Ofinite(X7,X30) )
=> c_Finite__Set_Ocard(tc_sum(X5,X7),c_Sum__Type_OPlus(X5,X7,X25,X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X5,X25)),c_Finite__Set_Ocard(X7,X30)) )
& ( ~ ( c_Finite__Set_Ofinite(X5,X25)
& c_Finite__Set_Ofinite(X7,X30) )
=> c_Finite__Set_Ocard(tc_sum(X5,X7),c_Sum__Type_OPlus(X5,X7,X25,X30)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_pos__add__strict,axiom,
! [X18,X20,X19,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X19))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X28,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),X28),X28)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X28)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_add__gr__0,axiom,
! [X6,X9] :
( 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),X9),X6)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_card__seteq,axiom,
! [X25,X30,X5] :
( c_Finite__Set_Ofinite(X5,X30)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X30)),c_Finite__Set_Ocard(X5,X25)))
=> X25 = X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(fact_add__strict__increasing2,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X19))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),X19))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X18))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X19))
=> ( 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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_psubset__eq,axiom,
! [X30,X25,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
& X25 != X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
| X25 = X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_psubset__imp__subset,axiom,
! [X30,X25,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_greaterThan__subset__iff,axiom,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X5,X4)),c_SetInterval_Oord__class_OgreaterThan(X5,X13)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X13),X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X28,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),X28),X28)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X28)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_Pi__UNIV,axiom,
! [X25,X7,X5] : c_FuncSet_OPi(X5,X7,X25,hAPP(c_COMBK(tc_fun(X7,tc_HOL_Obool),X5),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X7),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__UNIV) ).
fof(fact_add__increasing,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X19))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X18))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X19,X20,X18,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X18))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X19))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_ord_OatMost__iff,axiom,
! [X52,X51,X44,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord_OatMost(X5,X51,X52)))
<=> hBOOL(hAPP(hAPP(X51,X44),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
fof(fact_ord_OlessThan__iff,axiom,
! [X52,X50,X44,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord_OlessThan(X5,X50,X52)))
<=> hBOOL(hAPP(hAPP(X50,X44),X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
fof(fact_ord_OatLeast__iff,axiom,
! [X52,X51,X44,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord_OatLeast(X5,X51,X52)))
<=> hBOOL(hAPP(hAPP(X51,X52),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
fof(fact_ord_OgreaterThan__iff,axiom,
! [X52,X50,X44,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord_OgreaterThan(X5,X50,X52)))
<=> hBOOL(hAPP(hAPP(X50,X52),X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
fof(fact_finite__Plus,axiom,
! [X30,X7,X25,X5] :
( c_Finite__Set_Ofinite(X5,X25)
=> ( c_Finite__Set_Ofinite(X7,X30)
=> c_Finite__Set_Ofinite(tc_sum(X5,X7),c_Sum__Type_OPlus(X5,X7,X25,X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus) ).
fof(help_c__COMBC__1,axiom,
! [X15,X55,X21,X5,X34,X7] : hAPP(hAPP(hAPP(c_COMBC(X7,X34,X5),X21),X55),X15) = hAPP(hAPP(X21,X15),X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(fact_set__eq__subset,axiom,
! [X5,X30,X25] :
( X25 = X30
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(fact_equalityI,axiom,
! [X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),X25))
=> X25 = X30 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
fof(fact_set__rev__mp,axiom,
! [X30,X25,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
fof(fact_set__mp,axiom,
! [X4,X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
fof(fact_in__mono,axiom,
! [X4,X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> hBOOL(hAPP(hAPP(c_member(X5),X4),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
fof(fact_subsetD,axiom,
! [X31,X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( hBOOL(hAPP(hAPP(c_member(X5),X31),X25))
=> hBOOL(hAPP(hAPP(c_member(X5),X31),X30)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
fof(fact_folding__one__idem_Osubset__idem,axiom,
! [X30,X25,X45,X2,X5] :
( c_Finite__Set_Ofolding__one__idem(X5,X2,X45)
=> ( c_Finite__Set_Ofinite(X5,X25)
=> ( X30 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),X25))
=> hAPP(hAPP(X2,hAPP(X45,X30)),hAPP(X45,X25)) = hAPP(X45,X25) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
fof(fact_Plus__eq__empty__conv,axiom,
! [X30,X25,X7,X5] :
( c_Sum__Type_OPlus(X5,X7,X25,X30) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X5,X7),tc_HOL_Obool))
<=> ( X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
& X30 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).
fof(fact_le__funD,axiom,
! [X4,X1,X2,X5,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X7),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,hAPP(X2,X4)),hAPP(X1,X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_le__funE,axiom,
! [X4,X1,X2,X5,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X7),X2),X1))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X7,hAPP(X2,X4)),hAPP(X1,X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_finite__imageI,axiom,
! [X54,X7,X45,X5] :
( c_Finite__Set_Ofinite(X5,X45)
=> c_Finite__Set_Ofinite(X7,c_Set_Oimage(X5,X7,X54,X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(fact_card__mono,axiom,
! [X25,X30,X5] :
( c_Finite__Set_Ofinite(X5,X30)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X5,X25)),c_Finite__Set_Ocard(X5,X30))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X18,X20,X19,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20)),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_inj__eq,axiom,
! [X13,X4,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hAPP(X2,X4) = hAPP(X2,X13)
<=> X4 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__eq) ).
fof(fact_injD,axiom,
! [X13,X4,X2,X7,X5] :
( c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( hAPP(X2,X4) = hAPP(X2,X13)
=> X4 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injD) ).
fof(fact_atLeastLessThan__eq__iff,axiom,
! [X36,X31,X26,X28,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X31),X36))
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26) = c_SetInterval_Oord__class_OatLeastLessThan(X5,X31,X36)
<=> ( X28 = X31
& X26 = X36 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [X36,X31,X26,X28,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26) = c_SetInterval_Oord__class_OatLeastLessThan(X5,X31,X36)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X31),X36))
=> X28 = X31 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__inj_I2_J,axiom,
! [X36,X31,X26,X28,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26) = c_SetInterval_Oord__class_OatLeastLessThan(X5,X31,X36)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X31),X36))
=> X26 = X36 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_less__by__empty,axiom,
! [X30,X5,X25] :
( X25 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X5,X5),tc_HOL_Obool))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X5,X5),tc_HOL_Obool),X25),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
fof(fact_less__add__Suc1,axiom,
! [X12,X64] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X64),X12)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X12,X64] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X64)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_less__trans__Suc,axiom,
! [X62,X63,X64] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),X63))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X63),X62))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X64)),X62)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_bot__empty__eq,axiom,
! [X4,X5] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X4))
<=> hBOOL(hAPP(hAPP(c_member(X5),X4),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__empty__eq) ).
fof(fact_subset__empty,axiom,
! [X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
<=> X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
fof(fact_empty__is__image,axiom,
! [X25,X2,X7,X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_Set_Oimage(X7,X5,X2,X25)
<=> X25 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__is__image) ).
fof(fact_image__is__empty,axiom,
! [X25,X2,X5,X7] :
( c_Set_Oimage(X7,X5,X2,X25) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> X25 = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__is__empty) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X24] :
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X24,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
=> c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,X24,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_Suc__less__SucD,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),hAPP(c_Nat_OSuc,X8)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__less__eq,axiom,
! [X6,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X9)),hAPP(c_Nat_OSuc,X6)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [X7,X5] :
( c_Finite__Set_Ofinite(tc_fun(X5,X7),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X7),tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,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/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_order__less__trans,axiom,
! [X17,X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X17,X11,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_image__Suc__atLeastLessThan,axiom,
! [X67,X44] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X44,X67)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X44),hAPP(c_Nat_OSuc,X67)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X13,X4,X5] :
( class_Groups_Oordered__comm__monoid__add(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5)),X13))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X4),X13) = c_Groups_Ozero__class_Ozero(X5)
<=> ( X4 = c_Groups_Ozero__class_Ozero(X5)
& X13 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [X7,X5] : c_Sum__Type_OPlus(X5,X7,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X7),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X17,X10,X11] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X12,X63,X64] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),X63))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X63),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X10,X17,X11] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X12,X63,X64] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),X63))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X64),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X63))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X6,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),hAPP(c_Nat_OSuc,X6)))
<=> ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X70] :
( X9 = hAPP(c_Nat_OSuc,X70)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X70),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X18,X20,X19,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20)),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Oab__semigroup__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20)),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X77,X18,X19,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X77)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)),X77) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_Suc__le__mono,axiom,
! [X9,X6] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6)),hAPP(c_Nat_OSuc,X9)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_order__le__less__trans,axiom,
! [X17,X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X17,X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X17))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I8_J,axiom,
! [X17,X11,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X17,X11,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X17),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X17),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [X7,X5] :
( c_Finite__Set_Ofinite(tc_sum(X5,X7),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X5,X7),tc_HOL_Obool)))
<=> ( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
& c_Finite__Set_Ofinite(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [X7,X5] :
( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Finite__Set_Ofinite(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(tc_prod(X5,X7),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X5,X7),tc_HOL_Obool))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_less__add__eq__less,axiom,
! [X8,X12,X74,X62] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X62),X74))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X74) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X62),X8)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_Suc__lessD,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X8))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_empty__subsetI,axiom,
! [X25,X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(fact_Suc__mono,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),hAPP(c_Nat_OSuc,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_Pi__empty,axiom,
! [X30,X7,X5] : c_FuncSet_OPi(X5,X7,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),X30) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X7),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__empty) ).
fof(fact_trans__le__add1,axiom,
! [X12,X63,X64] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64),X63))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X63),X12))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X17,X10,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add2,axiom,
! [X12,X63,X64] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64),X63))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X63))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X10,X17,X11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [X7,X5] :
( c_Finite__Set_Ofinite(tc_fun(X5,X7),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X5,X7),tc_HOL_Obool)))
=> c_Finite__Set_Ofinite(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_greaterThan__iff,axiom,
! [X52,X44,X5] :
( class_Orderings_Oord(X5)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X44),c_SetInterval_Oord__class_OgreaterThan(X5,X52)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X52),X44)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_nat__add__assoc,axiom,
! [X62,X8,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X8)),X62) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8),X62)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_less__eq__Suc__le,axiom,
! [X9,X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6)),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__le__eq,axiom,
! [X6,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X9)),X6))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12)),X8))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_folding__one__idem_Oin__idem,axiom,
! [X4,X25,X45,X2,X5] :
( c_Finite__Set_Ofolding__one__idem(X5,X2,X45)
=> ( c_Finite__Set_Ofinite(X5,X25)
=> ( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
=> hAPP(hAPP(X2,X4),hAPP(X45,X25)) = hAPP(X45,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
fof(fact_predicate1D,axiom,
! [X4,X55,X21,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X21),X55))
=> ( hBOOL(hAPP(X21,X4))
=> hBOOL(hAPP(X55,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate1D,axiom,
! [X55,X5,X4,X21] :
( hBOOL(hAPP(X21,X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X21),X55))
=> hBOOL(hAPP(X55,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_order__trans,axiom,
! [X17,X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X17))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X17,X11,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X17),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X17),X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_Suc__lessI,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> ( hAPP(c_Nat_OSuc,X12) != X8
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_le__less__Suc__eq,axiom,
! [X6,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_OSuc,X9)))
<=> X6 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__leD,axiom,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12)),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_image__empty,axiom,
! [X2,X5,X7] : c_Set_Oimage(X7,X5,X2,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
fof(fact_finite__nat__set__iff__bounded,axiom,
! [X58] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X58)
<=> ? [X29] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X58))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(fact_less__Suc__eq,axiom,
! [X6,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),hAPP(c_Nat_OSuc,X6)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
| X9 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__leI,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X12)),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X77,X18,X19,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X77)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X77)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_le__trans,axiom,
! [X62,X63,X64] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64),X63))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X63),X62))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64),X62)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_finite__subset,axiom,
! [X30,X25,X5] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ( c_Finite__Set_Ofinite(X5,X30)
=> c_Finite__Set_Ofinite(X5,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [X25,X30,X5] :
( c_Finite__Set_Ofinite(X5,X30)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> c_Finite__Set_Ofinite(X5,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_less__iff__Suc__add,axiom,
! [X6,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
<=> ? [X75] : X6 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X75)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_inj__on__empty,axiom,
! [X2,X7,X5] : c_Fun_Oinj__on(X5,X7,X2,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
fof(fact_less__Suc__eq__le,axiom,
! [X6,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),hAPP(c_Nat_OSuc,X6)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_finite__nat__set__iff__bounded__le,axiom,
! [X58] :
( c_Finite__Set_Ofinite(tc_Nat_Onat,X58)
<=> ? [X29] :
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X58))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(fact_card__gt__0__iff,axiom,
! [X25,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,X25)))
<=> ( X25 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
& c_Finite__Set_Ofinite(X5,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
fof(fact_less__SucI,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_nat__case__Suc,axiom,
! [X69,X72,X73,X5] : c_Nat_Onat_Onat__case(X5,X73,X72,hAPP(c_Nat_OSuc,X69)) = hAPP(X72,X69),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_le__Suc__eq,axiom,
! [X6,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),hAPP(c_Nat_OSuc,X6)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6))
| X9 = hAPP(c_Nat_OSuc,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_subset__UNIV,axiom,
! [X25,X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(fact_nat__less__cases,axiom,
! [X21,X6,X9] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
=> hBOOL(hAPP(hAPP(X21,X6),X9)) )
=> ( ( X9 = X6
=> hBOOL(hAPP(hAPP(X21,X6),X9)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9))
=> hBOOL(hAPP(hAPP(X21,X6),X9)) )
=> hBOOL(hAPP(hAPP(X21,X6),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_nat__add__left__commute,axiom,
! [X17,X10,X11] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),X17)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_order__eq__iff,axiom,
! [X13,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( X4 = X13
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X13),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__antisym__conv,axiom,
! [X4,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X13),X4))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
<=> X4 = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__antisym,axiom,
! [X10,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11))
=> X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I5_J,axiom,
! [X11,X10,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
=> X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_card__ge__0__finite,axiom,
! [X25,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,X25)))
=> c_Finite__Set_Ofinite(X5,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_le__imp__less__Suc,axiom,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X25,X5] :
( c_Finite__Set_Ofinite(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> ( c_Finite__Set_Ocard(X5,X25) = c_Finite__Set_Ocard(X5,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))
=> X25 = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_order__less__le,axiom,
! [X13,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
& X4 != X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_order__le__less,axiom,
! [X13,X4,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
| X4 = X13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__imp__le,axiom,
! [X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_le__add1,axiom,
! [X12,X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8),X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X12,X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_image__ident,axiom,
! [X33,X5] : c_Set_Oimage(X5,X5,c_COMBI(X5),X33) = X33,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
fof(fact_inj__on__id2,axiom,
! [X25,X5] : c_Fun_Oinj__on(X5,X5,c_COMBI(X5),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(fact_nat__case__0,axiom,
! [X72,X73,X5] : c_Nat_Onat_Onat__case(X5,X73,X72,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X73,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
fof(fact_order__neq__le__trans,axiom,
! [X20,X19,X5] :
( class_Orderings_Oorder(X5)
=> ( X19 != X20
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),X20))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X10,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
| X11 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [X20,X19,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X19),X20))
=> ( X19 != X20
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [X19,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X19))
=> ( X19 != X20
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_xt1_I12_J,axiom,
! [X20,X19,X5] :
( class_Orderings_Oorder(X5)
=> ( X19 != X20
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X20),X19))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_less__Suc0,axiom,
! [X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_inj__Suc,axiom,
! [X58] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(fact_le__antisym,axiom,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),X12))
=> X12 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_eq__mem,axiom,
! [X13,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),hAPP(c_fequal,X13)))
<=> X4 = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(fact_le__SucI,axiom,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),hAPP(c_Nat_OSuc,X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_ex__in__conv,axiom,
! [X25,X5] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
<=> X25 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X8,X12] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
| X12 = X8 )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_less__imp__le__nat,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X6,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
| X9 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [X6,X9] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6))
& X9 != X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X10,X11] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X11),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_linorder__neq__iff,axiom,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( X4 != X13
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
| X11 = X10
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
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/sandbox/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_atLeastLessThan__empty,axiom,
! [X28,X26,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X26),X28))
=> c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).
fof(fact_le__neq__implies__less,axiom,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
=> ( X12 != X8
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [X4,X5] : hBOOL(hAPP(hAPP(c_member(X5),X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_UNIV__I,axiom,
! [X4,X5] : hBOOL(hAPP(hAPP(c_member(X5),X4),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).
fof(fact_mem__def,axiom,
! [X25,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X4),X25))
<=> hBOOL(hAPP(X25,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(fact_linorder__le__less__linear,axiom,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_add__Suc,axiom,
! [X8,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X8) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_le__iff__add,axiom,
! [X6,X9] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6))
<=> ? [X75] : X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X75) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_nat__neq__iff,axiom,
! [X6,X9] :
( X9 != X6
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_gr0__conv__Suc,axiom,
! [X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6))
<=> ? [X29] : X6 = hAPP(c_Nat_OSuc,X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_less__imp__neq,axiom,
! [X10,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> X11 != X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X10,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> X11 != X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X10,X11,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> X10 != X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_equalityD1,axiom,
! [X5,X30,X25] :
( X25 = X30
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [X5,X30,X25] :
( X25 = X30
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
fof(fact_subset__refl,axiom,
! [X25,X5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(fact_neq0__conv,axiom,
! [X6] :
( X6 != 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)),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_add__right__imp__eq,axiom,
! [X18,X19,X20,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X20),X19) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X19)
=> X20 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X31,X28,X26,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X26),X28) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X31),X28)
<=> X26 = X31 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Ocancel__ab__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)
=> X20 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X18,X20,X19,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X20) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18)
=> X20 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X31,X26,X28,X5] :
( class_Groups_Ocancel__semigroup__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X28),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X28),X31)
<=> X26 = X31 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_linorder__linear,axiom,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_add__Suc__right,axiom,
! [X8,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X8)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_add__Suc__shift,axiom,
! [X8,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X8) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_nat_Osize_I4_J,axiom,
! [X78] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X78)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X78)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I4_J) ).
fof(fact_gr__implies__not0,axiom,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> X8 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_nat__le__linear,axiom,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zero__less__Suc,axiom,
! [X8] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_less__not__refl3,axiom,
! [X22,X23] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23),X22))
=> X23 != X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X12,X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X12))
=> X12 != X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_nat__add__right__cancel,axiom,
! [X6,X52,X9] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X52) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X6),X52)
<=> X9 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X6,X9,X52] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X9) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X52),X6)
<=> X9 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_lessI,axiom,
! [X8] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_top1I,axiom,
! [X4,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_le__0__eq,axiom,
! [X6] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_add__is__1,axiom,
! [X6,X9] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X6) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X9 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X6 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(fact_one__is__add,axiom,
! [X6,X9] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X6)
<=> ( ( X9 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X6 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_folding__one__idem_Oidem,axiom,
! [X4,X45,X2,X5] :
( c_Finite__Set_Ofolding__one__idem(X5,X2,X45)
=> hAPP(hAPP(X2,X4),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
fof(fact_finite__atLeastLessThan,axiom,
! [X48,X49] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X49,X48)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(fact_nat_Osize_I2_J,axiom,
! [X78] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X78)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X78)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
fof(fact_bot__least,axiom,
! [X11,X5] :
( class_Orderings_Obot(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,c_Orderings_Obot__class_Obot(X5)),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X18,X19,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),X18) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X18),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_gr0I,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/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_top__greatest,axiom,
! [X11,X5] :
( class_Orderings_Otop(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),c_Orderings_Otop__class_Otop(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(fact_double__eq__0__iff,axiom,
! [X28,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X28),X28) = c_Groups_Ozero__class_Ozero(X5)
<=> X28 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X28,X5] :
( class_Groups_Olinordered__ab__group__add(X5)
=> ( c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X28),X28)
<=> X28 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__iff,axiom,
! [X28,X26,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X26 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X26),X28)
<=> X28 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_order__eq__refl,axiom,
! [X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( X11 = X10
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(help_c__COMBK__1,axiom,
! [X86,X85,X7,X5] : hAPP(hAPP(c_COMBK(X5,X7),X85),X86) = X85,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_infinite__UNIV__nat,axiom,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
fof(fact_nat__add__commute,axiom,
! [X8,X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X8) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X8),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_order__refl,axiom,
! [X11,X5] :
( class_Orderings_Opreorder(X5)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_UNIV__not__empty,axiom,
! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
fof(fact_bot__apply,axiom,
! [X4,X7,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,X5)),X4) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(fact_bot__fun__def,axiom,
! [X4,X7,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,X5)),X4) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_top__apply,axiom,
! [X4,X7,X5] :
( class_Orderings_Otop(X5)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X7,X5)),X4) = c_Orderings_Otop__class_Otop(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(fact_add__is__0,axiom,
! [X6,X9] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X9),X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X6 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_atLeastLessThan0,axiom,
! [X9] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
fof(fact_eq__imp__le,axiom,
! [X8,X12] :
( X12 = X8
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(help_c__fequal__2,axiom,
! [X13,X4] :
( X4 != X13
| hBOOL(hAPP(hAPP(c_fequal,X4),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(fact_add__eq__self__zero,axiom,
! [X8,X12] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X8) = X12
=> X8 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_le__refl,axiom,
! [X8] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8),X8)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_finite__UNIV) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X19,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X19) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0__left,axiom,
! [X19,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X19) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [X19,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X19) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_card_Oempty,axiom,
! [X5] : c_Finite__Set_Ocard(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X19,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),c_Groups_Ozero__class_Ozero(X5)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__right,axiom,
! [X19,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),c_Groups_Ozero__class_Ozero(X5)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X19,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X19),c_Groups_Ozero__class_Ozero(X5)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_finite_Oequations_I1_J,axiom,
! [X5] : c_Finite__Set_Ofinite(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(fact_finite_OemptyI,axiom,
! [X5] : c_Finite__Set_Ofinite(X5,c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_OemptyI) ).
fof(fact_greaterThan__eq__iff,axiom,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_SetInterval_Oord__class_OgreaterThan(X5,X4) = c_SetInterval_Oord__class_OgreaterThan(X5,X13)
<=> X4 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X8] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [X6] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(arity_sum__Finite__Set_Ofinite,axiom,
! [X84,X83] :
( ( class_Finite__Set_Ofinite(X83)
& class_Finite__Set_Ofinite(X84) )
=> class_Finite__Set_Ofinite(tc_sum(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(arity_prod__Finite__Set_Ofinite,axiom,
! [X84,X83] :
( ( class_Finite__Set_Ofinite(X83)
& class_Finite__Set_Ofinite(X84) )
=> class_Finite__Set_Ofinite(tc_prod(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(arity_fun__Finite__Set_Ofinite,axiom,
! [X84,X83] :
( ( class_Finite__Set_Ofinite(X83)
& class_Finite__Set_Ofinite(X84) )
=> class_Finite__Set_Ofinite(tc_fun(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(fact_nat_Oinject,axiom,
! [X68,X69] :
( hAPP(c_Nat_OSuc,X69) = hAPP(c_Nat_OSuc,X68)
<=> X69 = X68 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__inject,axiom,
! [X10,X11] :
( hAPP(c_Nat_OSuc,X11) = hAPP(c_Nat_OSuc,X10)
=> X11 = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(arity_fun__Orderings_Obot,axiom,
! [X83,X84] :
( class_Orderings_Obot(X84)
=> class_Orderings_Obot(tc_fun(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X83,X84] :
( class_Orderings_Oord(X84)
=> class_Orderings_Oord(tc_fun(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X83,X84] :
( class_Orderings_Oorder(X84)
=> class_Orderings_Oorder(tc_fun(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X83,X84] :
( class_Orderings_Opreorder(X84)
=> class_Orderings_Opreorder(tc_fun(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Otop,axiom,
! [X83,X84] :
( class_Orderings_Otop(X84)
=> class_Orderings_Otop(tc_fun(X83,X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(fact_Suc__not__Zero,axiom,
! [X12] : hAPP(c_Nat_OSuc,X12) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X65] : hAPP(c_Nat_OSuc,X65) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__neq__Zero,axiom,
! [X12] : hAPP(c_Nat_OSuc,X12) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_Zero__not__Suc,axiom,
! [X12] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X66] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [X12] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_finite,axiom,
! [X25,X5] :
( class_Finite__Set_Ofinite(X5)
=> c_Finite__Set_Ofinite(X5,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).
fof(fact_finite__code,axiom,
! [X25,X5] :
( class_Finite__Set_Ofinite(X5)
=> c_Finite__Set_Ofinite(X5,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(fact_Suc__n__not__n,axiom,
! [X8] : hAPP(c_Nat_OSuc,X8) != X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X8] : X8 != hAPP(c_Nat_OSuc,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(help_c__COMBI__1,axiom,
! [X85,X5] : hAPP(c_COMBI(X5),X85) = X85,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
! [X84] :
( class_Finite__Set_Ofinite(X84)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X84)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(fact_nat__size,axiom,
! [X8] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
fof(help_c__fFalse__1,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(fact_assms_I1_J,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(fact__096F_A_I_Fi_O_ALba_J_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)),hAPP(v_F,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),v_Lba____))),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096F_A_I_Fi_O_ALba_J_A_058_ALin_096) ).
fof(fact_Prof__def,axiom,
c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_Arrow__Order__Mirabelle_Oindi),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Prof__def) ).
fof(fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lba____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
fof(fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),v_Lab____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
fof(fact__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Lba_A_058_ALin_096) ).
fof(fact__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_Lab____),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Lab_A_058_ALin_096) ).
fof(fact_surjh,axiom,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_surjh) ).
fof(fact_greaterThan__0,axiom,
c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).
fof(fact_injh,axiom,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injh) ).
fof(fact_finite__indi,axiom,
c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__indi) ).
fof(fact_nat_Osize_I3_J,axiom,
c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I3_J) ).
fof(fact_nat_Osize_I1_J,axiom,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
fof(fact_bot__nat__def,axiom,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__nat__def) ).
fof(fact_bool_Osize_I1_J,axiom,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(fact_bool_Osize_I2_J,axiom,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(arity_Nat__Onat__Orderings_Obot,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(fact_assms_I3_J,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(fact_u,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(arity_HOL__Obool__Orderings_Otop,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(help_c__fTrue__1,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(fact__096a_A_126_061_Ab_096,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_126_061_Ab_096) ).
fof(i_0_522,plain,
! [X26,X28,X14,X5,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( c_Finite__Set_Ofinite(X5,X14)
=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X28),X14))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X7,hAPP(hAPP(c_COMBC(X5,X7,X7),c_COMBS(X5,X7,tc_fun(X7,X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X5,c_If(X7)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X28)),X26)),c_Groups_Ozero__class_Ozero(X7)),X14) = hAPP(X26,X28) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X28),X14))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X7,hAPP(hAPP(c_COMBC(X5,X7,X7),c_COMBS(X5,X7,tc_fun(X7,X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X5,c_If(X7)),hAPP(hAPP(c_COMBC(X5,X5,tc_HOL_Obool),c_fequal),X28)),X26)),c_Groups_Ozero__class_Ozero(X7)),X14) = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__delta]) ).
fof(i_0_523,plain,
! [X26,X28,X14,X5,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> ( c_Finite__Set_Ofinite(X5,X14)
=> ( ( hBOOL(hAPP(hAPP(c_member(X5),X28),X14))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X7,hAPP(hAPP(c_COMBC(X5,X7,X7),c_COMBS(X5,X7,tc_fun(X7,X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X5,c_If(X7)),hAPP(c_fequal,X28)),X26)),c_Groups_Ozero__class_Ozero(X7)),X14) = hAPP(X26,X28) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X5),X28),X14))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X5,X7,hAPP(hAPP(c_COMBC(X5,X7,X7),c_COMBS(X5,X7,tc_fun(X7,X7),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X7,tc_fun(X7,X7)),X5,c_If(X7)),hAPP(c_fequal,X28)),X26)),c_Groups_Ozero__class_Ozero(X7)),X14) = c_Groups_Ozero__class_Ozero(X7) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__delta_H]) ).
fof(i_0_524,plain,
! [X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X5,c_Set_Oimage(X7,X5,X2,X25))),c_Finite__Set_Ocard(X7,X25)))
=> ~ c_Fun_Oinj__on(X7,X5,X2,X25) ),
inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).
fof(i_0_525,plain,
! [X13,X4,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),c_Arrow__Order__Mirabelle_OLin))
=> ( X4 != X13
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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),X13)),X16))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X13),X4)),X16)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_notin__Lin__iff]) ).
fof(i_0_526,plain,
! [X26,X28,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16),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),X28),X26)),X16))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X26),X28)),X16)) ) ),
inference(fof_simplification,[status(thm)],[fact_Lin__irrefl]) ).
fof(i_0_527,plain,
! [X4,X30,X25,X2,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X7)),X2),c_FuncSet_OPi(X5,X7,X25,X30)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X7),hAPP(X2,X4)),hAPP(X30,X4)))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X4),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_PiE]) ).
fof(i_0_528,plain,
! [X2,X9,X6,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,hAPP(c_Nat_OSuc,X6))) = c_Groups_Ozero__class_Ozero(X5) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9))
=> c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,hAPP(c_Nat_OSuc,X6))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X5,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X9,X6))),hAPP(X2,X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc]) ).
fof(i_0_529,plain,
! [X13,X4,X7,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X5,tc_fun(X7,tc_HOL_Obool))),X4),X13)),
inference(fof_simplification,[status(thm)],[fact_bot2E]) ).
fof(i_0_530,plain,
~ ! [X39] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),X39))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X39),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(i_0_531,plain,
~ ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),X38))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X38),c_Arrow__Order__Mirabelle_OLin)) ),
inference(fof_simplification,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_058_ALin_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(i_0_532,plain,
! [X1,X2,X5,X7] :
( class_Orderings_Oord(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,X7)),X2),X1))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X7),X2),X1))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,X7),X1),X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_533,plain,
! [X8,X62,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X62)),X8))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X62),X8)) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_534,plain,
! [X63,X64] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X64),X63)),X64)),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_535,plain,
! [X64,X63] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X63),X64)),X64)),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_536,negated_conjecture,
~ ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
=> v_Lba____ = v_Lab____ ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(i_0_537,plain,
! [X25,X5] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X5,tc_HOL_Obool)),X25),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_not__psubset__empty]) ).
fof(i_0_538,plain,
! [X6,X9] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9),X6))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X6)),X9)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_539,plain,
! [X6,X9] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X9),X6))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_OSuc,X9))) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_540,plain,
! [X19,X20,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X19))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20)) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_541,plain,
! [X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_542,plain,
! [X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_543,plain,
! [X20,X19,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X19),X20))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X20),X19)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_544,plain,
! [X10,X11,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_545,plain,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X4))
| X4 = X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_546,plain,
! [X31,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X31),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).
fof(i_0_547,plain,
! [X28,X5] : ~ hBOOL(hAPP(hAPP(c_member(X5),X28),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[fact_emptyE]) ).
fof(i_0_548,plain,
! [X13,X4,X5] :
( class_Orderings_Opreorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X13),X4)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_549,plain,
! [X8,X12] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X8)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X8))
=> X12 = X8 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_550,plain,
! [X12,X8] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X12))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),hAPP(c_Nat_OSuc,X12)))
=> X12 = X8 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_551,plain,
! [X9,X6] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X9))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Nat_OSuc,X9)))
<=> X6 = X9 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_552,plain,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> X4 = X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_553,plain,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X13),X4)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_554,plain,
! [X11,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_555,plain,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X4)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_556,plain,
! [X26,X28,X5] :
( class_Orderings_Oorder(X5)
=> ( c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).
fof(i_0_557,plain,
! [X26,X28,X5] :
( class_Orderings_Oorder(X5)
=> ( c_SetInterval_Oord__class_OatLeastLessThan(X5,X28,X26) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X28),X26)) ) ),
inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).
fof(i_0_558,plain,
! [X8,X12] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),hAPP(c_Nat_OSuc,X8)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X12),X8))
=> X12 = hAPP(c_Nat_OSuc,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_559,plain,
! [X8] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X8)),X8)),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_560,plain,
! [X13,X4,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X4),X13))
<=> X4 = X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_561,plain,
! [X25,X5] :
( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X25))
<=> X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).
fof(i_0_562,plain,
! [X10,X11,X5] :
( class_Rings_Olinordered__idom(X5)
=> ( X11 != X10
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_563,plain,
! [X4,X13,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X4))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X4),X13))
<=> X4 = X13 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_564,plain,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( X11 != X10
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_565,plain,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> ( X11 != X10
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X10),X11)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_566,plain,
! [X28,X5,X25] :
( X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(X5),X28),X25)) ),
inference(fof_simplification,[status(thm)],[fact_equals0D]) ).
fof(i_0_567,plain,
! [X11,X10,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_568,plain,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_569,plain,
! [X10,X11] :
( X11 != X10
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_570,plain,
! [X5,X30,X25] :
( X25 = X30
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X25),X30))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool),X30),X25)) ) ),
inference(fof_simplification,[status(thm)],[fact_equalityE]) ).
fof(i_0_571,plain,
! [X11,X5] :
( class_Orderings_Opreorder(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X11),X11)) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_572,plain,
! [X10,X11,X5] :
( class_Orderings_Olinorder(X5)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X11),X10))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X5,X10),X11)) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_573,plain,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_574,plain,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_575,plain,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_576,plain,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X8)),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_577,plain,
! [X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X8),X8)),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_578,plain,
! [X13,X4] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X4),X13))
| X4 = X13 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(i_0_579,plain,
! [X25,X5] :
( c_Finite__Set_Ocard(X5,X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X25 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X5,X25) ) ),
inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff]) ).
fof(i_0_580,plain,
! [X25,X5] :
( ~ c_Finite__Set_Ofinite(X5,X25)
=> c_Finite__Set_Ocard(X5,X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).
fof(i_0_581,plain,
! [X1680] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),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____)),X1680))),v_Lab____)),v_Lba____))),c_Arrow__Order__Mirabelle_OLin)),
inference(variable_rename,[status(thm)],[fact__C0_C]) ).
fof(i_0_582,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_Lab____)),v_Lba____)))),
inference(fof_simplification,[status(thm)],[fact__C1_C]) ).
fof(i_0_583,plain,
! [X1676] : hBOOL(hAPP(hAPP(c_member(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____)),X1676))),v_Lab____)),v_Lba____)),c_Arrow__Order__Mirabelle_OProf)),
inference(variable_rename,[status(thm)],[fact_PiProf]) ).
fof(i_0_584,plain,
! [X2599,X2600,X2601,X2602] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2602,tc_fun(X2601,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2602,tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_fun(X2601,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2601,tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_fun(X2601,tc_HOL_Obool)),X2602,c_COMBC(X2601,tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2601,tc_prod(X2602,X2601)),tc_fun(X2601,tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),X2602,c_COMBB(tc_prod(X2602,X2601),tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool),X2601,c_member(tc_prod(X2602,X2601)))),c_Product__Type_OPair(X2602,X2601)))),X2600)),hAPP(hAPP(c_COMBC(X2602,tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_fun(X2601,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2601,tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_fun(X2601,tc_HOL_Obool)),X2602,c_COMBC(X2601,tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2601,tc_prod(X2602,X2601)),tc_fun(X2601,tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),X2602,c_COMBB(tc_prod(X2602,X2601),tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool),X2601,c_member(tc_prod(X2602,X2601)))),c_Product__Type_OPair(X2602,X2601)))),X2599)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),X2600),X2599)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),X2600),X2599))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2602,tc_fun(X2601,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2602,tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_fun(X2601,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2601,tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_fun(X2601,tc_HOL_Obool)),X2602,c_COMBC(X2601,tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2601,tc_prod(X2602,X2601)),tc_fun(X2601,tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),X2602,c_COMBB(tc_prod(X2602,X2601),tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool),X2601,c_member(tc_prod(X2602,X2601)))),c_Product__Type_OPair(X2602,X2601)))),X2600)),hAPP(hAPP(c_COMBC(X2602,tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_fun(X2601,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2601,tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_fun(X2601,tc_HOL_Obool)),X2602,c_COMBC(X2601,tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2601,tc_prod(X2602,X2601)),tc_fun(X2601,tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool)),X2602,c_COMBB(tc_prod(X2602,X2601),tc_fun(tc_fun(tc_prod(X2602,X2601),tc_HOL_Obool),tc_HOL_Obool),X2601,c_member(tc_prod(X2602,X2601)))),c_Product__Type_OPair(X2602,X2601)))),X2599))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).
fof(i_0_585,plain,
! [X2007,X2008,X2009,X2010,X2011,X2012] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2012),X2011)),hAPP(v_F,X2008)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2010),X2009)),hAPP(v_F,X2007)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2012),X2011)),hAPP(X2008,esk14_6(X2007,X2008,X2009,X2010,X2011,X2012))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2010),X2009)),hAPP(X2007,esk14_6(X2007,X2008,X2009,X2010,X2011,X2012))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2007),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))),X2008),c_Arrow__Order__Mirabelle_OProf))
| X2011 = X2010
| X2012 = X2009
| X2010 = X2009
| X2012 = X2011 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2010),X2009)),hAPP(v_F,X2007)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2012),X2011)),hAPP(v_F,X2008)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2012),X2011)),hAPP(X2008,esk14_6(X2007,X2008,X2009,X2010,X2011,X2012))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2010),X2009)),hAPP(X2007,esk14_6(X2007,X2008,X2009,X2010,X2011,X2012))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2007),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))),X2008),c_Arrow__Order__Mirabelle_OProf))
| X2011 = X2010
| X2012 = X2009
| X2010 = X2009
| X2012 = X2011 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2012),X2011)),hAPP(v_F,X2008)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2010),X2009)),hAPP(v_F,X2007)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2012),X2011)),hAPP(X2008,esk14_6(X2007,X2008,X2009,X2010,X2011,X2012))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2010),X2009)),hAPP(X2007,esk14_6(X2007,X2008,X2009,X2010,X2011,X2012))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2007),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))),X2008),c_Arrow__Order__Mirabelle_OProf))
| X2011 = X2010
| X2012 = X2009
| X2010 = X2009
| X2012 = X2011 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2010),X2009)),hAPP(v_F,X2007)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2012),X2011)),hAPP(v_F,X2008)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2012),X2011)),hAPP(X2008,esk14_6(X2007,X2008,X2009,X2010,X2011,X2012))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2010),X2009)),hAPP(X2007,esk14_6(X2007,X2008,X2009,X2010,X2011,X2012))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2007),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))),X2008),c_Arrow__Order__Mirabelle_OProf))
| X2011 = X2010
| X2012 = X2009
| X2010 = X2009
| X2012 = X2011 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C2_C])])])]) ).
fof(i_0_586,plain,
! [X2014,X2015,X2016,X2017,X2018,X2019] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2019),X2018)),hAPP(X2015,esk15_6(X2014,X2015,X2016,X2017,X2018,X2019))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2017),X2016)),hAPP(X2014,esk15_6(X2014,X2015,X2016,X2017,X2018,X2019))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2019),X2018)),hAPP(v_F,X2015)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2017),X2016)),hAPP(v_F,X2014)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2014),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))),X2015),c_Arrow__Order__Mirabelle_OProf))
| X2018 = X2017
| X2019 = X2016
| X2017 = X2016
| X2019 = X2018 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2019),X2018)),hAPP(X2015,esk15_6(X2014,X2015,X2016,X2017,X2018,X2019))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2017),X2016)),hAPP(X2014,esk15_6(X2014,X2015,X2016,X2017,X2018,X2019))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2019),X2018)),hAPP(v_F,X2015)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2017),X2016)),hAPP(v_F,X2014)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2014),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))),X2015),c_Arrow__Order__Mirabelle_OProf))
| X2018 = X2017
| X2019 = X2016
| X2017 = X2016
| X2019 = X2018 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bb_H_Ab_Aa_H_Aa_AP_H_AP_O_A_091_124_Aa_A_126_061_Ab_059_Aa_H_A_126_061_Ab_H_059_Aa_A_126_061_Ab_H_059_Ab_A_126_061_Aa_H_059_AP_A_058_AProf_059_AP_H_A_058_AProf_059_AALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_H_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_H_J_059_Aa_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_A_124_093_A_061_061_062_Aa_H_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_H_096])])])]) ).
fof(i_0_587,plain,
! [X2027,X2028,X2029,X2030,X2031,X2032] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2032),X2031)),hAPP(v_F,X2028)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2030),X2029)),hAPP(v_F,X2027)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2032),X2031)),hAPP(X2028,esk17_6(X2027,X2028,X2029,X2030,X2031,X2032))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2030),X2029)),hAPP(X2027,esk17_6(X2027,X2028,X2029,X2030,X2031,X2032))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2027),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))),X2028),c_Arrow__Order__Mirabelle_OProf))
| X2030 = X2029
| X2032 = X2031 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2030),X2029)),hAPP(v_F,X2027)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2032),X2031)),hAPP(v_F,X2028)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2032),X2031)),hAPP(X2028,esk17_6(X2027,X2028,X2029,X2030,X2031,X2032))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2030),X2029)),hAPP(X2027,esk17_6(X2027,X2028,X2029,X2030,X2031,X2032))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2027),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))),X2028),c_Arrow__Order__Mirabelle_OProf))
| X2030 = X2029
| X2032 = X2031 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2032),X2031)),hAPP(v_F,X2028)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2030),X2029)),hAPP(v_F,X2027)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2032),X2031)),hAPP(X2028,esk17_6(X2027,X2028,X2029,X2030,X2031,X2032))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2030),X2029)),hAPP(X2027,esk17_6(X2027,X2028,X2029,X2030,X2031,X2032))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2027),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))),X2028),c_Arrow__Order__Mirabelle_OProf))
| X2030 = X2029
| X2032 = X2031 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2030),X2029)),hAPP(v_F,X2027)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2032),X2031)),hAPP(v_F,X2028)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2032),X2031)),hAPP(X2028,esk17_6(X2027,X2028,X2029,X2030,X2031,X2032))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2030),X2029)),hAPP(X2027,esk17_6(X2027,X2028,X2029,X2030,X2031,X2032))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2027),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))),X2028),c_Arrow__Order__Mirabelle_OProf))
| X2030 = X2029
| X2032 = X2031 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pairwise__neutrality])])])]) ).
fof(i_0_588,plain,
! [X2739,X2740,X2741,X2742] :
( ( ~ c_Wellfounded_Omax__extp(X2742,hAPP(hAPP(c_COMBC(X2742,tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_fun(X2742,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2742,tc_fun(tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_fun(X2742,tc_HOL_Obool)),X2742,c_COMBC(X2742,tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2742,tc_prod(X2742,X2742)),tc_fun(X2742,tc_fun(tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_HOL_Obool)),X2742,c_COMBB(tc_prod(X2742,X2742),tc_fun(tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_HOL_Obool),X2742,c_member(tc_prod(X2742,X2742)))),c_Product__Type_OPair(X2742,X2742)))),X2741),X2740,X2739)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2742,tc_HOL_Obool),tc_fun(X2742,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2742,tc_HOL_Obool),tc_fun(X2742,tc_HOL_Obool)),X2740),X2739)),c_Wellfounded_Omax__ext(X2742,X2741))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2742,tc_HOL_Obool),tc_fun(X2742,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2742,tc_HOL_Obool),tc_fun(X2742,tc_HOL_Obool)),X2740),X2739)),c_Wellfounded_Omax__ext(X2742,X2741)))
| c_Wellfounded_Omax__extp(X2742,hAPP(hAPP(c_COMBC(X2742,tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_fun(X2742,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2742,tc_fun(tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_fun(X2742,tc_HOL_Obool)),X2742,c_COMBC(X2742,tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2742,tc_prod(X2742,X2742)),tc_fun(X2742,tc_fun(tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_HOL_Obool)),X2742,c_COMBB(tc_prod(X2742,X2742),tc_fun(tc_fun(tc_prod(X2742,X2742),tc_HOL_Obool),tc_HOL_Obool),X2742,c_member(tc_prod(X2742,X2742)))),c_Product__Type_OPair(X2742,X2742)))),X2741),X2740,X2739) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])]) ).
fof(i_0_589,plain,
! [X1973,X1974,X1975,X1976] :
( ( hAPP(hAPP(c_COMBC(X1976,tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_fun(X1975,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1975,tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_fun(X1975,tc_HOL_Obool)),X1976,c_COMBC(X1975,tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1975,tc_prod(X1976,X1975)),tc_fun(X1975,tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),X1976,c_COMBB(tc_prod(X1976,X1975),tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool),X1975,c_member(tc_prod(X1976,X1975)))),c_Product__Type_OPair(X1976,X1975)))),X1974) != hAPP(hAPP(c_COMBC(X1976,tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_fun(X1975,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1975,tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_fun(X1975,tc_HOL_Obool)),X1976,c_COMBC(X1975,tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1975,tc_prod(X1976,X1975)),tc_fun(X1975,tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),X1976,c_COMBB(tc_prod(X1976,X1975),tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool),X1975,c_member(tc_prod(X1976,X1975)))),c_Product__Type_OPair(X1976,X1975)))),X1973)
| X1974 = X1973 )
& ( X1974 != X1973
| hAPP(hAPP(c_COMBC(X1976,tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_fun(X1975,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1975,tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_fun(X1975,tc_HOL_Obool)),X1976,c_COMBC(X1975,tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1975,tc_prod(X1976,X1975)),tc_fun(X1975,tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),X1976,c_COMBB(tc_prod(X1976,X1975),tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool),X1975,c_member(tc_prod(X1976,X1975)))),c_Product__Type_OPair(X1976,X1975)))),X1974) = hAPP(hAPP(c_COMBC(X1976,tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_fun(X1975,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1975,tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_fun(X1975,tc_HOL_Obool)),X1976,c_COMBC(X1975,tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1975,tc_prod(X1976,X1975)),tc_fun(X1975,tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool)),X1976,c_COMBB(tc_prod(X1976,X1975),tc_fun(tc_fun(tc_prod(X1976,X1975),tc_HOL_Obool),tc_HOL_Obool),X1975,c_member(tc_prod(X1976,X1975)))),c_Product__Type_OPair(X1976,X1975)))),X1973) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).
fof(i_0_590,plain,
! [X2613,X2614,X2615,X2616,X2617] :
( ( hBOOL(hAPP(hAPP(c_member(X2617),esk42_5(X2613,X2614,X2615,X2616,X2617)),X2616))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2617,X2615),tc_HOL_Obool),c_FuncSet_OPi(X2617,X2615,X2616,X2614)),c_FuncSet_OPi(X2617,X2615,X2616,X2613))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2615,tc_HOL_Obool),hAPP(X2614,esk42_5(X2613,X2614,X2615,X2616,X2617))),hAPP(X2613,esk42_5(X2613,X2614,X2615,X2616,X2617))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2617,X2615),tc_HOL_Obool),c_FuncSet_OPi(X2617,X2615,X2616,X2614)),c_FuncSet_OPi(X2617,X2615,X2616,X2613))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mono])])])]) ).
fof(i_0_591,plain,
! [X2134,X2135,X2136,X2137,X2138] :
( ( hBOOL(hAPP(hAPP(c_member(X2138),esk32_5(X2134,X2135,X2136,X2137,X2138)),X2137))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2138,X2136)),X2135),c_FuncSet_OPi(X2138,X2136,X2137,X2134))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2136),hAPP(X2135,esk32_5(X2134,X2135,X2136,X2137,X2138))),hAPP(X2134,esk32_5(X2134,X2135,X2136,X2137,X2138))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2138,X2136)),X2135),c_FuncSet_OPi(X2138,X2136,X2137,X2134))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__I])])])]) ).
fof(i_0_592,plain,
! [X3243,X3244,X3245,X3246,X3247] :
( ~ c_Finite__Set_Ofolding__one__idem(X3247,X3246,X3245)
| hAPP(X3244,hAPP(hAPP(X3246,esk55_5(X3243,X3244,X3245,X3246,X3247)),esk56_5(X3243,X3244,X3245,X3246,X3247))) != hAPP(hAPP(X3246,hAPP(X3244,esk55_5(X3243,X3244,X3245,X3246,X3247))),hAPP(X3244,esk56_5(X3243,X3244,X3245,X3246,X3247)))
| ~ c_Finite__Set_Ofinite(X3247,X3243)
| X3243 = c_Orderings_Obot__class_Obot(tc_fun(X3247,tc_HOL_Obool))
| hAPP(X3244,hAPP(X3245,X3243)) = hAPP(X3245,c_Set_Oimage(X3247,X3247,X3244,X3243)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute])])]) ).
fof(i_0_593,plain,
! [X2111,X2112,X2113,X2114,X2115,X2117,X2122,X2123] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2111,X2112)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2111,X2113)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2112,esk23_5(X2111,X2112,X2113,X2114,X2115))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2113,esk23_5(X2111,X2112,X2113,X2114,X2115))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2113),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))),X2112),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2111) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2111,X2113)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2111,X2112)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2112,esk23_5(X2111,X2112,X2113,X2114,X2115))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2113,esk23_5(X2111,X2112,X2113,X2114,X2115))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2113),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))),X2112),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2111) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2111,X2112)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2111,X2113)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2112,esk23_5(X2111,X2112,X2113,X2114,X2115))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2113,esk23_5(X2111,X2112,X2113,X2114,X2115))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2113),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))),X2112),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2111) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2111,X2113)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2111,X2112)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2112,esk23_5(X2111,X2112,X2113,X2114,X2115))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2114),X2115)),hAPP(X2113,esk23_5(X2111,X2112,X2113,X2114,X2115))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2113),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))),X2112),c_Arrow__Order__Mirabelle_OProf))
| ~ c_Arrow__Order__Mirabelle_OIIA(X2111) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk24_1(X2117)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2117) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk25_1(X2117)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X2117) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2117)),esk27_1(X2117))),hAPP(esk24_1(X2117),X2122)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2117)),esk27_1(X2117))),hAPP(esk25_1(X2117),X2122)))
| c_Arrow__Order__Mirabelle_OIIA(X2117) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2117)),esk27_1(X2117))),hAPP(esk25_1(X2117),X2123)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2117)),esk27_1(X2117))),hAPP(esk24_1(X2117),X2123)))
| c_Arrow__Order__Mirabelle_OIIA(X2117) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2117)),esk27_1(X2117))),hAPP(X2117,esk24_1(X2117))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2117)),esk27_1(X2117))),hAPP(X2117,esk25_1(X2117))))
| c_Arrow__Order__Mirabelle_OIIA(X2117) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2117)),esk27_1(X2117))),hAPP(X2117,esk24_1(X2117))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X2117)),esk27_1(X2117))),hAPP(X2117,esk25_1(X2117))))
| c_Arrow__Order__Mirabelle_OIIA(X2117) ) ),
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_594,plain,
! [X2021,X2022,X2023,X2024,X2025] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2025),X2024)),hAPP(v_F,X2022)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2024),X2023)),hAPP(v_F,X2021)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2025),X2024)),hAPP(X2022,esk16_5(X2021,X2022,X2023,X2024,X2025))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2024),X2023)),hAPP(X2021,esk16_5(X2021,X2022,X2023,X2024,X2025))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2021),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))),X2022),c_Arrow__Order__Mirabelle_OProf))
| X2025 = X2023
| X2024 = X2023
| X2025 = X2024 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2024),X2023)),hAPP(v_F,X2021)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2025),X2024)),hAPP(v_F,X2022)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2025),X2024)),hAPP(X2022,esk16_5(X2021,X2022,X2023,X2024,X2025))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2024),X2023)),hAPP(X2021,esk16_5(X2021,X2022,X2023,X2024,X2025))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2021),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))),X2022),c_Arrow__Order__Mirabelle_OProf))
| X2025 = X2023
| X2024 = X2023
| X2025 = X2024 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2025),X2024)),hAPP(v_F,X2022)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2024),X2023)),hAPP(v_F,X2021)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2025),X2024)),hAPP(X2022,esk16_5(X2021,X2022,X2023,X2024,X2025))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2024),X2023)),hAPP(X2021,esk16_5(X2021,X2022,X2023,X2024,X2025))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2021),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))),X2022),c_Arrow__Order__Mirabelle_OProf))
| X2025 = X2023
| X2024 = X2023
| X2025 = X2024 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2024),X2023)),hAPP(v_F,X2021)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2025),X2024)),hAPP(v_F,X2022)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2025),X2024)),hAPP(X2022,esk16_5(X2021,X2022,X2023,X2024,X2025))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2024),X2023)),hAPP(X2021,esk16_5(X2021,X2022,X2023,X2024,X2025))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2021),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))),X2022),c_Arrow__Order__Mirabelle_OProf))
| X2025 = X2023
| X2024 = X2023
| X2025 = X2024 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C4_C])])])]) ).
fof(i_0_595,plain,
! [X2196,X2197,X2198,X2199,X2200] :
( ( hBOOL(hAPP(hAPP(c_member(X2200),esk33_5(X2196,X2197,X2198,X2199,X2200)),X2199))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2200,X2198)),X2197),c_FuncSet_OPi(X2200,X2198,X2199,hAPP(c_COMBK(tc_fun(X2198,tc_HOL_Obool),X2200),X2196)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2198),hAPP(X2197,esk33_5(X2196,X2197,X2198,X2199,X2200))),X2196))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2200,X2198)),X2197),c_FuncSet_OPi(X2200,X2198,X2199,hAPP(c_COMBK(tc_fun(X2198,tc_HOL_Obool),X2200),X2196)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcsetI])])])]) ).
fof(i_0_596,plain,
! [X3292,X3293,X3294,X3295,X3296] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3295),X3293),X3294))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3295,X3296,hAPP(hAPP(c_COMBC(X3295,X3296,X3296),c_COMBS(X3295,X3296,tc_fun(X3296,X3296),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3296,tc_fun(X3296,X3296)),X3295,c_If(X3296)),hAPP(hAPP(c_COMBC(X3295,X3295,tc_HOL_Obool),c_fequal),X3293)),X3292)),c_Groups_Ozero__class_Ozero(X3296)),X3294) = hAPP(X3292,X3293)
| ~ c_Finite__Set_Ofinite(X3295,X3294)
| ~ class_Groups_Ocomm__monoid__add(X3296) )
& ( hBOOL(hAPP(hAPP(c_member(X3295),X3293),X3294))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3295,X3296,hAPP(hAPP(c_COMBC(X3295,X3296,X3296),c_COMBS(X3295,X3296,tc_fun(X3296,X3296),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3296,tc_fun(X3296,X3296)),X3295,c_If(X3296)),hAPP(hAPP(c_COMBC(X3295,X3295,tc_HOL_Obool),c_fequal),X3293)),X3292)),c_Groups_Ozero__class_Ozero(X3296)),X3294) = c_Groups_Ozero__class_Ozero(X3296)
| ~ c_Finite__Set_Ofinite(X3295,X3294)
| ~ class_Groups_Ocomm__monoid__add(X3296) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_522])])]) ).
fof(i_0_597,plain,
! [X3250,X3251,X3252,X3253,X3254,X3256,X3257,X3258,X3259,X3261] :
( ( c_Finite__Set_Ofinite(X3253,X3252)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool)),X3252),X3251)),c_Wellfounded_Omax__ext(X3253,X3250))) )
& ( c_Finite__Set_Ofinite(X3253,X3251)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool)),X3252),X3251)),c_Wellfounded_Omax__ext(X3253,X3250))) )
& ( X3251 != c_Orderings_Obot__class_Obot(tc_fun(X3253,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool)),X3252),X3251)),c_Wellfounded_Omax__ext(X3253,X3250))) )
& ( hBOOL(hAPP(hAPP(c_member(X3253),esk57_5(X3250,X3251,X3252,X3253,X3254)),X3251))
| ~ hBOOL(hAPP(hAPP(c_member(X3253),X3254),X3252))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool)),X3252),X3251)),c_Wellfounded_Omax__ext(X3253,X3250))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3253,X3253)),hAPP(hAPP(c_Product__Type_OPair(X3253,X3253),X3254),esk57_5(X3250,X3251,X3252,X3253,X3254))),X3250))
| ~ hBOOL(hAPP(hAPP(c_member(X3253),X3254),X3252))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3253,tc_HOL_Obool),tc_fun(X3253,tc_HOL_Obool)),X3252),X3251)),c_Wellfounded_Omax__ext(X3253,X3250))) )
& ( hBOOL(hAPP(hAPP(c_member(X3259),esk58_4(X3256,X3257,X3258,X3259)),X3258))
| ~ c_Finite__Set_Ofinite(X3259,X3258)
| ~ c_Finite__Set_Ofinite(X3259,X3257)
| X3257 = c_Orderings_Obot__class_Obot(tc_fun(X3259,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3259,tc_HOL_Obool),tc_fun(X3259,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3259,tc_HOL_Obool),tc_fun(X3259,tc_HOL_Obool)),X3258),X3257)),c_Wellfounded_Omax__ext(X3259,X3256))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3259),X3261),X3257))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3259,X3259)),hAPP(hAPP(c_Product__Type_OPair(X3259,X3259),esk58_4(X3256,X3257,X3258,X3259)),X3261)),X3256))
| ~ c_Finite__Set_Ofinite(X3259,X3258)
| ~ c_Finite__Set_Ofinite(X3259,X3257)
| X3257 = c_Orderings_Obot__class_Obot(tc_fun(X3259,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3259,tc_HOL_Obool),tc_fun(X3259,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3259,tc_HOL_Obool),tc_fun(X3259,tc_HOL_Obool)),X3258),X3257)),c_Wellfounded_Omax__ext(X3259,X3256))) ) ),
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_max__ext_Osimps])])])])])]) ).
fof(i_0_598,plain,
! [X3287,X3288,X3289,X3290,X3291] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3290),X3288),X3289))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3290,X3291,hAPP(hAPP(c_COMBC(X3290,X3291,X3291),c_COMBS(X3290,X3291,tc_fun(X3291,X3291),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3291,tc_fun(X3291,X3291)),X3290,c_If(X3291)),hAPP(c_fequal,X3288)),X3287)),c_Groups_Ozero__class_Ozero(X3291)),X3289) = hAPP(X3287,X3288)
| ~ c_Finite__Set_Ofinite(X3290,X3289)
| ~ class_Groups_Ocomm__monoid__add(X3291) )
& ( hBOOL(hAPP(hAPP(c_member(X3290),X3288),X3289))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3290,X3291,hAPP(hAPP(c_COMBC(X3290,X3291,X3291),c_COMBS(X3290,X3291,tc_fun(X3291,X3291),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X3291,tc_fun(X3291,X3291)),X3290,c_If(X3291)),hAPP(c_fequal,X3288)),X3287)),c_Groups_Ozero__class_Ozero(X3291)),X3289) = c_Groups_Ozero__class_Ozero(X3291)
| ~ c_Finite__Set_Ofinite(X3290,X3289)
| ~ class_Groups_Ocomm__monoid__add(X3291) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_523])])]) ).
fof(i_0_599,plain,
! [X2062,X2063] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk19_2(X2062,X2063)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2063,X2062)
| ~ 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))),X2063),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( esk20_2(X2062,X2063) != esk21_2(X2062,X2063)
| c_Arrow__Order__Mirabelle_Odictator(X2063,X2062)
| ~ 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))),X2063),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_2(X2062,X2063)),esk21_2(X2062,X2063))),hAPP(esk19_2(X2062,X2063),X2062)))
| c_Arrow__Order__Mirabelle_Odictator(X2063,X2062)
| ~ 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))),X2063),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_2(X2062,X2063)),esk21_2(X2062,X2063))),hAPP(X2063,esk19_2(X2062,X2063))))
| c_Arrow__Order__Mirabelle_Odictator(X2063,X2062)
| ~ 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))),X2063),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_600,plain,
! [X3237,X3238,X3239,X3240,X3242] :
( ( hBOOL(hAPP(hAPP(c_member(X3240),esk54_4(X3237,X3238,X3239,X3240)),X3239))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3240,tc_HOL_Obool),tc_fun(X3240,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3240,tc_HOL_Obool),tc_fun(X3240,tc_HOL_Obool)),X3239),X3238)),c_Wellfounded_Omax__ext(X3240,X3237)))
| X3238 = c_Orderings_Obot__class_Obot(tc_fun(X3240,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X3240,X3238)
| ~ c_Finite__Set_Ofinite(X3240,X3239) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3240),X3242),X3238))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3240,X3240)),hAPP(hAPP(c_Product__Type_OPair(X3240,X3240),esk54_4(X3237,X3238,X3239,X3240)),X3242)),X3237))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X3240,tc_HOL_Obool),tc_fun(X3240,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X3240,tc_HOL_Obool),tc_fun(X3240,tc_HOL_Obool)),X3239),X3238)),c_Wellfounded_Omax__ext(X3240,X3237)))
| X3238 = c_Orderings_Obot__class_Obot(tc_fun(X3240,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X3240,X3238)
| ~ c_Finite__Set_Ofinite(X3240,X3239) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext_Ointros])])])])]) ).
fof(i_0_601,plain,
! [X2531,X2532,X2533,X2534,X2535,X2536,X2537,X2538] :
( ( X2536 = X2534
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2538,X2538)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2538),X2536),X2534)),X2532))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2538,X2537),tc_prod(X2538,X2537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2538,X2537),tc_prod(X2538,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2537),X2536),X2535)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2537),X2534),X2533))),c_Wellfounded_Olex__prod(X2538,X2537,X2532,X2531))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2537,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2537,X2537),X2535),X2533)),X2531))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2538,X2538)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2538),X2536),X2534)),X2532))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2538,X2537),tc_prod(X2538,X2537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2538,X2537),tc_prod(X2538,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2537),X2536),X2535)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2537),X2534),X2533))),c_Wellfounded_Olex__prod(X2538,X2537,X2532,X2531))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2538,X2538)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2538),X2536),X2534)),X2532))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2538,X2537),tc_prod(X2538,X2537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2538,X2537),tc_prod(X2538,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2537),X2536),X2535)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2537),X2534),X2533))),c_Wellfounded_Olex__prod(X2538,X2537,X2532,X2531))) )
& ( X2536 != X2534
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2537,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2537,X2537),X2535),X2533)),X2531))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2538,X2537),tc_prod(X2538,X2537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2538,X2537),tc_prod(X2538,X2537)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2537),X2536),X2535)),hAPP(hAPP(c_Product__Type_OPair(X2538,X2537),X2534),X2533))),c_Wellfounded_Olex__prod(X2538,X2537,X2532,X2531))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).
fof(i_0_602,plain,
! [X2034,X2035,X2036,X2037] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2037),X2036)),hAPP(v_F,X2035)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2036),X2037)),hAPP(v_F,X2034)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2037),X2036)),hAPP(X2035,esk18_4(X2034,X2035,X2036,X2037))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2036),X2037)),hAPP(X2034,esk18_4(X2034,X2035,X2036,X2037))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2034),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))),X2035),c_Arrow__Order__Mirabelle_OProf))
| X2037 = X2036 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2036),X2037)),hAPP(v_F,X2034)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2037),X2036)),hAPP(v_F,X2035)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2037),X2036)),hAPP(X2035,esk18_4(X2034,X2035,X2036,X2037))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2036),X2037)),hAPP(X2034,esk18_4(X2034,X2035,X2036,X2037))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2034),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))),X2035),c_Arrow__Order__Mirabelle_OProf))
| X2037 = X2036 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2037),X2036)),hAPP(v_F,X2035)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2036),X2037)),hAPP(v_F,X2034)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2037),X2036)),hAPP(X2035,esk18_4(X2034,X2035,X2036,X2037))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2036),X2037)),hAPP(X2034,esk18_4(X2034,X2035,X2036,X2037))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2034),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))),X2035),c_Arrow__Order__Mirabelle_OProf))
| X2037 = X2036 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2036),X2037)),hAPP(v_F,X2034)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2037),X2036)),hAPP(v_F,X2035)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2037),X2036)),hAPP(X2035,esk18_4(X2034,X2035,X2036,X2037))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2036),X2037)),hAPP(X2034,esk18_4(X2034,X2035,X2036,X2037))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2034),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))),X2035),c_Arrow__Order__Mirabelle_OProf))
| X2037 = X2036 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__C3_C])])])]) ).
fof(i_0_603,plain,
! [X2426,X2427,X2428,X2429,X2430,X2432,X2433,X2434,X2435,X2436,X2437] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2428,tc_HOL_Obool),esk36_5(X2426,X2427,X2428,X2429,X2430)),X2426))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2430,tc_HOL_Obool),X2429),c_Set_Oimage(X2428,X2430,X2427,X2426))) )
& ( X2429 = c_Set_Oimage(X2428,X2430,X2427,esk36_5(X2426,X2427,X2428,X2429,X2430))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2430,tc_HOL_Obool),X2429),c_Set_Oimage(X2428,X2430,X2427,X2426))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2434,tc_HOL_Obool),X2437),X2432))
| X2435 != c_Set_Oimage(X2434,X2436,X2433,X2437)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2436,tc_HOL_Obool),X2435),c_Set_Oimage(X2434,X2436,X2433,X2432))) ) ),
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_604,plain,
! [X2179,X2180,X2181,X2182,X2183,X2184,X2185] :
( ~ hBOOL(hAPP(X2185,X2184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2183,X2183)),hAPP(hAPP(c_Product__Type_OPair(X2183,X2183),X2182),X2181)),hAPP(X2180,X2184)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X2179,X2183),tc_prod(X2179,X2183))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X2179,X2183),tc_prod(X2179,X2183)),hAPP(hAPP(c_Product__Type_OPair(X2179,X2183),X2184),X2182)),hAPP(hAPP(c_Product__Type_OPair(X2179,X2183),X2184),X2181))),c_Recdef_Osame__fst(X2179,X2183,X2185,X2180))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).
fof(i_0_605,plain,
! [X3216,X3217,X3218,X3219,X3220,X3222,X3223,X3224,X3225,X3227] :
( ( c_Finite__Set_Ofinite(X3219,X3217)
| ~ c_Wellfounded_Omax__extp(X3219,X3218,X3217,X3216) )
& ( c_Finite__Set_Ofinite(X3219,X3216)
| ~ c_Wellfounded_Omax__extp(X3219,X3218,X3217,X3216) )
& ( X3216 != c_Orderings_Obot__class_Obot(tc_fun(X3219,tc_HOL_Obool))
| ~ c_Wellfounded_Omax__extp(X3219,X3218,X3217,X3216) )
& ( hBOOL(hAPP(hAPP(c_member(X3219),esk52_5(X3216,X3217,X3218,X3219,X3220)),X3216))
| ~ hBOOL(hAPP(hAPP(c_member(X3219),X3220),X3217))
| ~ c_Wellfounded_Omax__extp(X3219,X3218,X3217,X3216) )
& ( hBOOL(hAPP(hAPP(X3218,X3220),esk52_5(X3216,X3217,X3218,X3219,X3220)))
| ~ hBOOL(hAPP(hAPP(c_member(X3219),X3220),X3217))
| ~ c_Wellfounded_Omax__extp(X3219,X3218,X3217,X3216) )
& ( hBOOL(hAPP(hAPP(c_member(X3225),esk53_4(X3222,X3223,X3224,X3225)),X3223))
| ~ c_Finite__Set_Ofinite(X3225,X3223)
| ~ c_Finite__Set_Ofinite(X3225,X3222)
| X3222 = c_Orderings_Obot__class_Obot(tc_fun(X3225,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X3225,X3224,X3223,X3222) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X3225),X3227),X3222))
| ~ hBOOL(hAPP(hAPP(X3224,esk53_4(X3222,X3223,X3224,X3225)),X3227))
| ~ c_Finite__Set_Ofinite(X3225,X3223)
| ~ c_Finite__Set_Ofinite(X3225,X3222)
| X3222 = c_Orderings_Obot__class_Obot(tc_fun(X3225,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X3225,X3224,X3223,X3222) ) ),
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_max__extp_Oequations])])])])])]) ).
fof(i_0_606,plain,
! [X2316,X2317,X2318,X2319,X2320] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2318,X2319),X2317),X2316))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2319,hAPP(X2317,X2320)),hAPP(X2316,X2320)))
| ~ class_Orderings_Oord(X2319) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2319,hAPP(X2317,esk35_4(X2316,X2317,X2318,X2319))),hAPP(X2316,esk35_4(X2316,X2317,X2318,X2319))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2318,X2319),X2317),X2316))
| ~ class_Orderings_Oord(X2319) ) ),
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_607,plain,
! [X2619,X2620,X2621,X2622,X2623,X2624,X2625,X2626] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2626,X2625,X2624,X2623,X2622,X2621)
| ~ c_Finite__Set_Ofinite(X2625,X2620)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2625,tc_HOL_Obool),X2619),X2620))
| hAPP(hAPP(X2624,hAPP(X2621,X2619)),hAPP(X2621,X2620)) = hAPP(X2621,X2620) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).
fof(i_0_608,plain,
! [X2729,X2730,X2731,X2732,X2733,X2734,X2735,X2736] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2736,X2735,X2734,X2733,X2732,X2731)
| ~ c_Finite__Set_Ofinite(X2735,X2730)
| ~ hBOOL(hAPP(hAPP(c_member(X2735),X2729),X2730))
| hAPP(hAPP(X2734,hAPP(X2732,X2729)),hAPP(X2731,X2730)) = hAPP(X2731,X2730) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).
fof(i_0_609,plain,
! [X2695,X2696,X2697,X2698,X2699,X2700,X2701] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(X2701,X2700,X2699,X2698,X2697,X2696)
| hAPP(hAPP(X2699,X2695),X2695) = X2695 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).
fof(i_0_610,plain,
! [X2073,X2074,X2075,X2076,X2077,X2078] :
( ( hBOOL(hAPP(hAPP(X2076,X2074),X2077))
| ~ hBOOL(hAPP(hAPP(c_member(X2078),X2077),c_SetInterval_Oord_OatLeastLessThan(X2078,X2076,X2075,X2074,X2073))) )
& ( hBOOL(hAPP(hAPP(X2075,X2077),X2073))
| ~ hBOOL(hAPP(hAPP(c_member(X2078),X2077),c_SetInterval_Oord_OatLeastLessThan(X2078,X2076,X2075,X2074,X2073))) )
& ( ~ hBOOL(hAPP(hAPP(X2076,X2074),X2077))
| ~ hBOOL(hAPP(hAPP(X2075,X2077),X2073))
| hBOOL(hAPP(hAPP(c_member(X2078),X2077),c_SetInterval_Oord_OatLeastLessThan(X2078,X2076,X2075,X2074,X2073))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])]) ).
fof(i_0_611,plain,
! [X2067,X2068,X2069,X2070,X2071,X2072] :
( ( hBOOL(hAPP(hAPP(X2069,X2068),X2071))
| ~ hBOOL(hAPP(hAPP(c_member(X2072),X2071),c_SetInterval_Oord_OgreaterThanAtMost(X2072,X2070,X2069,X2068,X2067))) )
& ( hBOOL(hAPP(hAPP(X2070,X2071),X2067))
| ~ hBOOL(hAPP(hAPP(c_member(X2072),X2071),c_SetInterval_Oord_OgreaterThanAtMost(X2072,X2070,X2069,X2068,X2067))) )
& ( ~ hBOOL(hAPP(hAPP(X2069,X2068),X2071))
| ~ hBOOL(hAPP(hAPP(X2070,X2071),X2067))
| hBOOL(hAPP(hAPP(c_member(X2072),X2071),c_SetInterval_Oord_OgreaterThanAtMost(X2072,X2070,X2069,X2068,X2067))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])]) ).
fof(i_0_612,plain,
! [X2481,X2482,X2483,X2484,X2485,X2486] :
( ~ c_Fun_Oinj__on(X2486,X2485,X2484,X2483)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2485,tc_HOL_Obool),c_Set_Oimage(X2486,X2485,X2484,X2483)),X2482))
| ~ c_Fun_Oinj__on(X2485,X2486,X2481,X2482)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2486,tc_HOL_Obool),c_Set_Oimage(X2485,X2486,X2481,X2482)),X2483))
| ~ c_Finite__Set_Ofinite(X2486,X2483)
| ~ c_Finite__Set_Ofinite(X2485,X2482)
| c_Finite__Set_Ocard(X2486,X2483) = c_Finite__Set_Ocard(X2485,X2482) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).
fof(i_0_613,plain,
! [X2124,X2125,X2126,X2127,X2129,X2133] :
( ( ~ c_Arrow__Order__Mirabelle_Ounanimity(X2124)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2125),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),X2126),X2127)),hAPP(X2125,esk28_4(X2124,X2125,X2126,X2127))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2126),X2127)),hAPP(X2124,X2125))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk29_1(X2129)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X2129) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk30_1(X2129)),esk31_1(X2129))),hAPP(esk29_1(X2129),X2133)))
| c_Arrow__Order__Mirabelle_Ounanimity(X2129) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk30_1(X2129)),esk31_1(X2129))),hAPP(X2129,esk29_1(X2129))))
| c_Arrow__Order__Mirabelle_Ounanimity(X2129) ) ),
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_614,plain,
! [X2173,X2174,X2175,X2176,X2177,X2178] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2178,X2177)),X2176),c_FuncSet_OPi(X2178,X2177,X2175,hAPP(c_COMBK(tc_fun(X2177,tc_HOL_Obool),X2178),X2174))))
| ~ c_Fun_Oinj__on(X2178,X2177,X2176,X2175)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2177,X2178)),X2173),c_FuncSet_OPi(X2177,X2178,X2174,hAPP(c_COMBK(tc_fun(X2178,tc_HOL_Obool),X2177),X2175))))
| ~ c_Fun_Oinj__on(X2177,X2178,X2173,X2174)
| ~ c_Finite__Set_Ofinite(X2178,X2175)
| ~ c_Finite__Set_Ofinite(X2177,X2174)
| c_Finite__Set_Ocard(X2178,X2175) = c_Finite__Set_Ocard(X2177,X2174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij])]) ).
fof(i_0_615,plain,
! [X2478,X2479,X2480] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2480,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2480,tc_fun(X2480,tc_HOL_Obool),tc_HOL_Obool),c_member(X2480)),X2479)),hAPP(hAPP(c_COMBC(X2480,tc_fun(X2480,tc_HOL_Obool),tc_HOL_Obool),c_member(X2480)),X2478)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2480,tc_HOL_Obool),X2479),X2478)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2480,tc_HOL_Obool),X2479),X2478))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2480,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2480,tc_fun(X2480,tc_HOL_Obool),tc_HOL_Obool),c_member(X2480)),X2479)),hAPP(hAPP(c_COMBC(X2480,tc_fun(X2480,tc_HOL_Obool),tc_HOL_Obool),c_member(X2480)),X2478))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).
fof(i_0_616,plain,
! [X1785,X1786,X1787,X1788] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X1788,c_Set_Oimage(X1787,X1788,X1786,X1785))),c_Finite__Set_Ocard(X1787,X1785)))
| ~ c_Fun_Oinj__on(X1787,X1788,X1786,X1785) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_524])]) ).
fof(i_0_617,plain,
! [X2186,X2187,X2188,X2189,X2190,X2191] :
( ~ c_Fun_Oinj__on(X2191,X2190,X2189,X2188)
| ~ hBOOL(hAPP(hAPP(c_member(X2190),X2187),c_Set_Oimage(X2191,X2190,X2189,X2188)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2191,tc_HOL_Obool),X2188),X2186))
| hBOOL(hAPP(hAPP(c_member(X2191),hAPP(c_Fun_Othe__inv__into(X2191,X2190,X2188,X2189),X2187)),X2186)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).
fof(i_0_618,plain,
! [X2991,X2992,X2993,X2994,X2995,X2997] :
( ( ~ c_Fun_Oinj__on(X2993,X2992,X2995,X2994)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2992,tc_HOL_Obool),c_Set_Oimage(X2993,X2992,X2995,X2994)),X2991))
| c_Set_Oimage(X2992,X2993,esk50_4(X2991,X2992,X2993,X2994),X2991) = X2994
| X2994 = c_Orderings_Obot__class_Obot(tc_fun(X2993,tc_HOL_Obool)) )
& ( c_Fun_Oinj__on(X2993,X2992,esk51_4(X2991,X2992,X2993,X2994),X2994)
| c_Set_Oimage(X2992,X2993,X2997,X2991) != X2994
| X2994 = c_Orderings_Obot__class_Obot(tc_fun(X2993,tc_HOL_Obool)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2992,tc_HOL_Obool),c_Set_Oimage(X2993,X2992,esk51_4(X2991,X2992,X2993,X2994),X2994)),X2991))
| c_Set_Oimage(X2992,X2993,X2997,X2991) != X2994
| X2994 = c_Orderings_Obot__class_Obot(tc_fun(X2993,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_inj__on__iff__surj])])])])]) ).
fof(i_0_619,plain,
! [X2552,X2553,X2554,X2555,X2556] :
( ( ~ c_Fun_Oinj__on(X2555,X2553,X2556,X2554)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2553,tc_HOL_Obool),c_Set_Oimage(X2555,X2553,X2556,X2554)),X2552))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2555,X2554)),c_Finite__Set_Ocard(X2553,X2552)))
| ~ c_Finite__Set_Ofinite(X2553,X2552)
| ~ c_Finite__Set_Ofinite(X2555,X2554) )
& ( c_Fun_Oinj__on(X2555,X2553,esk39_4(X2552,X2553,X2554,X2555),X2554)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2555,X2554)),c_Finite__Set_Ocard(X2553,X2552)))
| ~ c_Finite__Set_Ofinite(X2553,X2552)
| ~ c_Finite__Set_Ofinite(X2555,X2554) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2553,tc_HOL_Obool),c_Set_Oimage(X2555,X2553,esk39_4(X2552,X2553,X2554,X2555),X2554)),X2552))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2555,X2554)),c_Finite__Set_Ocard(X2553,X2552)))
| ~ c_Finite__Set_Ofinite(X2553,X2552)
| ~ c_Finite__Set_Ofinite(X2555,X2554) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le])])])])]) ).
fof(i_0_620,plain,
! [X1989,X1990,X1991,X1992,X1993] :
( ( X1990 != X1989
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1990 != X1992
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1993),X1989)),X1991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1989 != X1992
| X1990 = X1993
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1993)),X1991))
| X1990 = X1992
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1989 = X1992
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),X1991))
| X1990 = X1992
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1990 != X1992
| X1990 = X1992
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1989 != X1992
| X1989 = X1992
| X1990 = X1992
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),X1991))
| X1989 = X1992
| X1990 = X1992
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1989 != X1992
| X1990 != X1993
| X1990 = X1992
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),X1991))
| X1990 != X1993
| X1990 = X1992
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1989 != X1992
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1993)),X1991))
| X1990 = X1992
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),X1991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1993)),X1991))
| X1990 = X1992
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1990 != X1992
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1993),X1989)),X1991))
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1989 != X1992
| X1989 = X1992
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1993),X1989)),X1991))
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),X1991))
| X1989 = X1992
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1993),X1989)),X1991))
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1989 != X1992
| X1990 != X1993
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1993),X1989)),X1991))
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),X1991))
| X1990 != X1993
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1993),X1989)),X1991))
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( X1989 != X1992
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1993)),X1991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1993),X1989)),X1991))
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),X1991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1993)),X1991))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1993),X1989)),X1991))
| X1990 = X1989
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1990),X1989)),c_Arrow__Order__Mirabelle_Oabove(X1991,X1993,X1992)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1991),c_Arrow__Order__Mirabelle_OLin))
| X1993 = X1992 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__above])])]) ).
fof(i_0_621,plain,
! [X1994,X1995,X1996,X1997,X1998] :
( ( X1995 != X1994
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1994 != X1998
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1997)),X1996))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1995 != X1998
| X1994 = X1997
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1997),X1994)),X1996))
| X1994 = X1998
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1995 = X1998
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),X1996))
| X1994 = X1998
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1994 != X1998
| X1994 = X1998
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1995 != X1998
| X1995 = X1998
| X1994 = X1998
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),X1996))
| X1995 = X1998
| X1994 = X1998
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1995 != X1998
| X1994 != X1997
| X1994 = X1998
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),X1996))
| X1994 != X1997
| X1994 = X1998
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1995 != X1998
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1997),X1994)),X1996))
| X1994 = X1998
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),X1996))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1997),X1994)),X1996))
| X1994 = X1998
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1994 != X1998
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1997)),X1996))
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1995 != X1998
| X1995 = X1998
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1997)),X1996))
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),X1996))
| X1995 = X1998
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1997)),X1996))
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1995 != X1998
| X1994 != X1997
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1997)),X1996))
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),X1996))
| X1994 != X1997
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1997)),X1996))
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( X1995 != X1998
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1997),X1994)),X1996))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1997)),X1996))
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),X1996))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1997),X1994)),X1996))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1997)),X1996))
| X1995 = X1994
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1995),X1994)),c_Arrow__Order__Mirabelle_Obelow(X1996,X1998,X1997)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1996),c_Arrow__Order__Mirabelle_OLin))
| X1998 = X1997 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__below])])]) ).
fof(i_0_622,plain,
! [X2503,X2504,X2505,X2506,X2507] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2506,tc_HOL_Obool),c_Set_Oimage(X2507,X2506,X2505,X2504)),c_Set_Oimage(X2507,X2506,X2505,X2503)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2507,tc_HOL_Obool),X2504),X2503))
| ~ c_Fun_Oinj__on(X2507,X2506,X2505,c_Orderings_Otop__class_Otop(tc_fun(X2507,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2507,tc_HOL_Obool),X2504),X2503))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2506,tc_HOL_Obool),c_Set_Oimage(X2507,X2506,X2505,X2504)),c_Set_Oimage(X2507,X2506,X2505,X2503)))
| ~ c_Fun_Oinj__on(X2507,X2506,X2505,c_Orderings_Otop__class_Otop(tc_fun(X2507,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff])])]) ).
fof(i_0_623,plain,
! [X2544,X2545,X2546] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2546,tc_HOL_Obool)),X2545),X2544))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2546,tc_HOL_Obool),tc_fun(X2546,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2546,tc_HOL_Obool),tc_fun(X2546,tc_HOL_Obool)),X2545),X2544)),c_Wellfounded_Ofinite__psubset(X2546))) )
& ( c_Finite__Set_Ofinite(X2546,X2544)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2546,tc_HOL_Obool),tc_fun(X2546,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2546,tc_HOL_Obool),tc_fun(X2546,tc_HOL_Obool)),X2545),X2544)),c_Wellfounded_Ofinite__psubset(X2546))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2546,tc_HOL_Obool)),X2545),X2544))
| ~ c_Finite__Set_Ofinite(X2546,X2544)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2546,tc_HOL_Obool),tc_fun(X2546,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2546,tc_HOL_Obool),tc_fun(X2546,tc_HOL_Obool)),X2545),X2544)),c_Wellfounded_Ofinite__psubset(X2546))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).
fof(i_0_624,plain,
! [X2525,X2526,X2527,X2528,X2529] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2529,X2528)),X2527),c_FuncSet_OPi(X2529,X2528,X2526,hAPP(c_COMBK(tc_fun(X2528,tc_HOL_Obool),X2529),X2525))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2528,tc_HOL_Obool),c_Set_Oimage(X2529,X2528,X2527,X2526)),X2525)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__image])]) ).
fof(i_0_625,plain,
! [X1789,X1790,X1791,X1792,X1794,X1795] :
( ( X1789 = hAPP(X1790,esk3_4(X1789,X1790,X1791,X1792))
| ~ hBOOL(hAPP(hAPP(c_member(X1791),X1789),c_Set_Oimage(X1792,X1791,X1790,c_Orderings_Otop__class_Otop(tc_fun(X1792,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1792,X1791,X1790,c_Orderings_Otop__class_Otop(tc_fun(X1792,tc_HOL_Obool))) )
& ( X1789 != hAPP(X1790,X1794)
| X1794 = esk3_4(X1789,X1790,X1791,X1792)
| ~ hBOOL(hAPP(hAPP(c_member(X1791),X1789),c_Set_Oimage(X1792,X1791,X1790,c_Orderings_Otop__class_Otop(tc_fun(X1792,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1792,X1791,X1790,c_Orderings_Otop__class_Otop(tc_fun(X1792,tc_HOL_Obool))) )
& ( X1789 = hAPP(X1790,esk4_5(X1789,X1790,X1791,X1792,X1795))
| X1789 != hAPP(X1790,X1795)
| hBOOL(hAPP(hAPP(c_member(X1791),X1789),c_Set_Oimage(X1792,X1791,X1790,c_Orderings_Otop__class_Otop(tc_fun(X1792,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1792,X1791,X1790,c_Orderings_Otop__class_Otop(tc_fun(X1792,tc_HOL_Obool))) )
& ( esk4_5(X1789,X1790,X1791,X1792,X1795) != X1795
| X1789 != hAPP(X1790,X1795)
| hBOOL(hAPP(hAPP(c_member(X1791),X1789),c_Set_Oimage(X1792,X1791,X1790,c_Orderings_Otop__class_Otop(tc_fun(X1792,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X1792,X1791,X1790,c_Orderings_Otop__class_Otop(tc_fun(X1792,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_626,plain,
! [X2609,X2610,X2611,X2612] :
( ~ c_Finite__Set_Ofinite(X2612,X2611)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2610,c_Set_Oimage(X2612,X2610,X2609,X2611))),c_Finite__Set_Ocard(X2612,X2611))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).
fof(i_0_627,plain,
! [X1839,X1840,X1841,X1842,X1843] :
( ~ c_Fun_Oinj__on(X1843,X1842,X1841,X1840)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1843,tc_HOL_Obool)),X1839),X1840))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1842,tc_HOL_Obool)),c_Set_Oimage(X1843,X1842,X1841,X1839)),c_Set_Oimage(X1843,X1842,X1841,X1840))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).
fof(i_0_628,plain,
! [X2340,X2341,X2342] :
( ~ c_Finite__Set_Ofinite(X2342,X2341)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2342,tc_HOL_Obool),c_Set_Oimage(X2342,X2342,X2340,X2341)),X2341))
| ~ c_Fun_Oinj__on(X2342,X2342,X2340,X2341)
| c_Set_Oimage(X2342,X2342,X2340,X2341) = X2341 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).
fof(i_0_629,plain,
! [X2558,X2559,X2560,X2561,X2562] :
( ~ c_Fun_Oinj__on(X2562,X2561,X2560,X2559)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2561,tc_HOL_Obool),c_Set_Oimage(X2562,X2561,X2560,X2559)),X2558))
| ~ c_Finite__Set_Ofinite(X2561,X2558)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2562,X2559)),c_Finite__Set_Ocard(X2561,X2558))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).
fof(i_0_630,plain,
! [X1892,X1893,X1894,X1895,X1896,X1898,X1899,X1900,X1901,X1902,X1903] :
( ( hBOOL(hAPP(hAPP(c_member(X1894),esk11_4(X1892,X1893,X1894,X1895)),X1892))
| ~ hBOOL(hAPP(hAPP(c_member(X1896),X1895),c_Set_Oimage(X1894,X1896,X1893,X1892))) )
& ( X1895 = hAPP(X1893,esk11_4(X1892,X1893,X1894,X1895))
| ~ hBOOL(hAPP(hAPP(c_member(X1896),X1895),c_Set_Oimage(X1894,X1896,X1893,X1892))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X1900),X1902),X1898))
| X1901 != hAPP(X1899,X1902)
| hBOOL(hAPP(hAPP(c_member(X1903),X1901),c_Set_Oimage(X1900,X1903,X1899,X1898))) ) ),
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_631,plain,
! [X1999,X2000,X2001] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2000),X1999)),X2001))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1999),X2000)),X2001))
| X2000 = X1999
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2001),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),X1999),X2000)),X2001))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2000),X1999)),X2001))
| X2000 = X1999
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2001),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_525])])]) ).
fof(i_0_632,plain,
! [X2002,X2003,X2004] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2004),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),X2003),X2002)),X2004))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2002),X2003)),X2004)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_526])]) ).
fof(i_0_633,plain,
! [X2547,X2548,X2549,X2550,X2551] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2551,X2550)),X2549),c_FuncSet_OPi(X2551,X2550,X2548,hAPP(c_COMBK(tc_fun(X2550,tc_HOL_Obool),X2551),X2547))))
| ~ c_Fun_Oinj__on(X2551,X2550,X2549,X2548)
| ~ c_Finite__Set_Ofinite(X2550,X2547)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2551,X2548)),c_Finite__Set_Ocard(X2550,X2547))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj])]) ).
fof(i_0_634,plain,
! [X2332,X2333,X2334,X2335,X2336] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2336,tc_HOL_Obool),X2335),X2334))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X2336,X2333),tc_HOL_Obool),c_FuncSet_OPi(X2336,X2333,X2334,X2332)),c_FuncSet_OPi(X2336,X2333,X2335,X2332))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__anti__mono])]) ).
fof(i_0_635,plain,
! [X2498,X2499,X2500,X2501,X2502] :
( ~ c_Finite__Set_Ofinite(X2502,c_Set_Oimage(X2501,X2502,X2500,c_Orderings_Otop__class_Otop(tc_fun(X2501,tc_HOL_Obool))))
| c_Finite__Set_Ofinite(X2499,c_Set_Oimage(X2501,X2499,hAPP(c_COMBB(X2502,X2499,X2501,X2498),X2500),c_Orderings_Otop__class_Otop(tc_fun(X2501,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).
fof(i_0_636,plain,
! [X1696] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1696),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),X1696)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_const__Lin__Prof])]) ).
fof(i_0_637,plain,
! [X2056,X2057,X2058,X2059,X2060,X2061] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2061,X2060)),X2059),c_FuncSet_OPi(X2061,X2060,X2058,hAPP(c_COMBK(tc_fun(X2060,tc_HOL_Obool),X2061),X2057))))
| ~ hBOOL(hAPP(hAPP(c_member(X2061),X2056),X2058))
| hBOOL(hAPP(hAPP(c_member(X2060),hAPP(X2059,X2056)),X2057)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_funcset__mem])]) ).
fof(i_0_638,plain,
! [X2438,X2439,X2440,X2441,X2442] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2442,tc_HOL_Obool),X2441),X2440))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2439,tc_HOL_Obool),c_Set_Oimage(X2442,X2439,X2438,X2441)),c_Set_Oimage(X2442,X2439,X2438,X2440))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).
fof(i_0_639,plain,
! [X2594,X2595,X2596,X2597,X2598] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X2598,X2597)),hAPP(X2598,X2596)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2595,X2595)),hAPP(hAPP(c_Product__Type_OPair(X2595,X2595),X2597),X2596)),X2594))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2595,X2595)),hAPP(hAPP(c_Product__Type_OPair(X2595,X2595),X2597),X2596)),c_Wellfounded_Omlex__prod(X2595,X2598,X2594))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).
fof(i_0_640,plain,
! [X2145,X2146,X2147,X2148,X2149] :
( ~ c_Fun_Oinj__on(X2149,X2148,X2147,X2146)
| ~ hBOOL(hAPP(hAPP(c_member(X2148),X2145),c_Set_Oimage(X2149,X2148,X2147,X2146)))
| hAPP(X2147,hAPP(c_Fun_Othe__inv__into(X2149,X2148,X2146,X2147),X2145)) = X2145 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])]) ).
fof(i_0_641,plain,
! [X3271,X3272,X3273,X3274,X3275] :
( ~ class_Groups_Ocomm__monoid__add(X3275)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3275,X3274,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3273),X3272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3271),X3272))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3275,hAPP(c_COMBB(tc_Nat_Onat,X3275,tc_Nat_Onat,X3274),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X3272)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3273,X3271)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])]) ).
fof(i_0_642,plain,
! [X2140,X2141,X2142,X2143,X2144] :
( ( ~ c_FunDef_Oin__rel(X2144,X2143,X2142,X2141,X2140)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2144,X2143)),hAPP(hAPP(c_Product__Type_OPair(X2144,X2143),X2141),X2140)),X2142)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2144,X2143)),hAPP(hAPP(c_Product__Type_OPair(X2144,X2143),X2141),X2140)),X2142))
| c_FunDef_Oin__rel(X2144,X2143,X2142,X2141,X2140) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
fof(i_0_643,plain,
! [X3013,X3014,X3015,X3016] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3016,tc_fun(X3015,tc_HOL_Obool))),X3014),X3013))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3016,X3015)),hAPP(hAPP(c_Product__Type_OPair(X3016,X3015),X3014),X3013)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3016,X3015),tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3016,X3015)),hAPP(hAPP(c_Product__Type_OPair(X3016,X3015),X3014),X3013)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3016,X3015),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3016,tc_fun(X3015,tc_HOL_Obool))),X3014),X3013)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2])]) ).
fof(i_0_644,plain,
! [X3266,X3267,X3268,X3269,X3270] :
( ~ class_Groups_Ocomm__monoid__add(X3270)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3269),X3268))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3268),X3267))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3270),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3270,X3266,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3269,X3268))),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3270,X3266,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3268,X3267))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3270,X3266,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3269,X3267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])]) ).
fof(i_0_645,plain,
! [X2854,X2855,X2856,X2857,X2859,X2860,X2861,X2862,X2863] :
( ( hBOOL(hAPP(hAPP(c_member(X2857),esk46_4(X2854,X2855,X2856,X2857)),X2855))
| c_FuncSet_OPi(X2857,X2856,X2855,X2854) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2857,X2856),tc_HOL_Obool)) )
& ( hAPP(X2854,esk46_4(X2854,X2855,X2856,X2857)) = c_Orderings_Obot__class_Obot(tc_fun(X2856,tc_HOL_Obool))
| c_FuncSet_OPi(X2857,X2856,X2855,X2854) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2857,X2856),tc_HOL_Obool)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2862),X2863),X2860))
| hAPP(X2859,X2863) != c_Orderings_Obot__class_Obot(tc_fun(X2861,tc_HOL_Obool))
| c_FuncSet_OPi(X2862,X2861,X2860,X2859) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2862,X2861),tc_HOL_Obool)) ) ),
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_Pi__eq__empty])])])])])]) ).
fof(i_0_646,plain,
! [X3332,X3333,X3334,X3335,X3336,X3337] : hAPP(c_COMBS(X3337,X3336,X3335,X3334,X3333),X3332) = hAPP(hAPP(X3334,X3332),hAPP(X3333,X3332)),
inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).
fof(i_0_647,plain,
! [X2050,X2051,X2052,X2053,X2054,X2055] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2055,X2054)),X2053),c_FuncSet_OPi(X2055,X2054,X2052,X2051)))
| ~ hBOOL(hAPP(hAPP(c_member(X2055),X2050),X2052))
| hBOOL(hAPP(hAPP(c_member(X2054),hAPP(X2053,X2050)),hAPP(X2051,X2050))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pi__mem])]) ).
fof(i_0_648,plain,
! [X2039,X2040,X2041,X2042,X2043,X2044] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X2044,X2043)),X2042),c_FuncSet_OPi(X2044,X2043,X2041,X2040)))
| hBOOL(hAPP(hAPP(c_member(X2043),hAPP(X2042,X2039)),hAPP(X2040,X2039)))
| ~ hBOOL(hAPP(hAPP(c_member(X2044),X2039),X2041)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_527])]) ).
fof(i_0_649,plain,
! [X1797,X1798,X1799,X1800,X1801] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1800),hAPP(X1799,X1798)),c_Set_Oimage(X1801,X1800,X1799,X1797)))
| hBOOL(hAPP(hAPP(c_member(X1801),X1798),X1797))
| ~ c_Fun_Oinj__on(X1801,X1800,X1799,c_Orderings_Otop__class_Otop(tc_fun(X1801,tc_HOL_Obool))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X1801),X1798),X1797))
| hBOOL(hAPP(hAPP(c_member(X1800),hAPP(X1799,X1798)),c_Set_Oimage(X1801,X1800,X1799,X1797)))
| ~ c_Fun_Oinj__on(X1801,X1800,X1799,c_Orderings_Otop__class_Otop(tc_fun(X1801,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff])])]) ).
fof(i_0_650,plain,
! [X1977,X1978,X1979,X1980] :
( ( X1979 != X1977
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Omkbot(X1978,X1977))) )
& ( X1980 != X1977
| X1980 != X1979
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Omkbot(X1978,X1977))) )
& ( X1980 = X1977
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1978))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Omkbot(X1978,X1977))) )
& ( X1980 != X1977
| X1980 = X1977
| X1979 = X1977
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Omkbot(X1978,X1977))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1978))
| X1980 = X1977
| X1979 = X1977
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Omkbot(X1978,X1977))) )
& ( X1980 != X1977
| X1980 = X1979
| X1979 = X1977
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Omkbot(X1978,X1977))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),X1978))
| X1980 = X1979
| X1979 = X1977
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1980),X1979)),c_Arrow__Order__Mirabelle_Omkbot(X1978,X1977))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mkbot])])]) ).
fof(i_0_651,plain,
! [X1981,X1982,X1983,X1984] :
( ( X1984 != X1981
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),c_Arrow__Order__Mirabelle_Omktop(X1982,X1981))) )
& ( X1983 != X1981
| X1984 != X1983
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),c_Arrow__Order__Mirabelle_Omktop(X1982,X1981))) )
& ( X1983 = X1981
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),X1982))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),c_Arrow__Order__Mirabelle_Omktop(X1982,X1981))) )
& ( X1983 != X1981
| X1983 = X1981
| X1984 = X1981
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),c_Arrow__Order__Mirabelle_Omktop(X1982,X1981))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),X1982))
| X1983 = X1981
| X1984 = X1981
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),c_Arrow__Order__Mirabelle_Omktop(X1982,X1981))) )
& ( X1983 != X1981
| X1984 = X1983
| X1984 = X1981
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),c_Arrow__Order__Mirabelle_Omktop(X1982,X1981))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),X1982))
| X1984 = X1983
| X1984 = X1981
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1984),X1983)),c_Arrow__Order__Mirabelle_Omktop(X1982,X1981))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mktop])])]) ).
fof(i_0_652,plain,
! [X1859,X1860,X1861,X1862,X1863,X1864,X1865,X1866,X1867,X1868] :
( ( ~ c_Fun_Oinj__on(X1862,X1861,X1860,X1859)
| ~ hBOOL(hAPP(hAPP(c_member(X1862),X1863),X1859))
| ~ hBOOL(hAPP(hAPP(c_member(X1862),X1864),X1859))
| hAPP(X1860,X1863) != hAPP(X1860,X1864)
| X1863 = X1864 )
& ( hBOOL(hAPP(hAPP(c_member(X1868),esk9_4(X1865,X1866,X1867,X1868)),X1865))
| c_Fun_Oinj__on(X1868,X1867,X1866,X1865) )
& ( hBOOL(hAPP(hAPP(c_member(X1868),esk10_4(X1865,X1866,X1867,X1868)),X1865))
| c_Fun_Oinj__on(X1868,X1867,X1866,X1865) )
& ( hAPP(X1866,esk9_4(X1865,X1866,X1867,X1868)) = hAPP(X1866,esk10_4(X1865,X1866,X1867,X1868))
| c_Fun_Oinj__on(X1868,X1867,X1866,X1865) )
& ( esk9_4(X1865,X1866,X1867,X1868) != esk10_4(X1865,X1866,X1867,X1868)
| c_Fun_Oinj__on(X1868,X1867,X1866,X1865) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__def])])])])])]) ).
fof(i_0_653,plain,
! [X1932,X1933,X1934,X1935,X1936] : c_Set_Oimage(X1936,X1935,hAPP(c_COMBB(X1934,X1935,X1936,X1933),X1932),c_Orderings_Otop__class_Otop(tc_fun(X1936,tc_HOL_Obool))) = c_Set_Oimage(X1934,X1935,X1933,c_Set_Oimage(X1936,X1934,X1932,c_Orderings_Otop__class_Otop(tc_fun(X1936,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_range__composition]) ).
fof(i_0_654,plain,
! [X2337,X2338,X2339] :
( ~ c_Finite__Set_Ofinite(X2339,X2338)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2339,tc_HOL_Obool),X2338),c_Set_Oimage(X2339,X2339,X2337,X2338)))
| c_Fun_Oinj__on(X2339,X2339,X2337,X2338) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).
fof(i_0_655,plain,
! [X2097,X2098,X2099,X2100,X2101] :
( ( ~ c_Arrow__Order__Mirabelle_Odictator(X2098,X2097)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2099),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X2098,X2099) = hAPP(X2099,X2097) )
& ( hBOOL(hAPP(hAPP(c_member(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_2(X2100,X2101)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2101,X2100) )
& ( hAPP(X2101,esk22_2(X2100,X2101)) != hAPP(esk22_2(X2100,X2101),X2100)
| c_Arrow__Order__Mirabelle_Odictator(X2101,X2100) ) ),
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_656,plain,
! [X1937,X1938,X1939,X1940] :
( ~ c_Fun_Oinj__on(X1940,X1939,X1938,c_Orderings_Otop__class_Otop(tc_fun(X1940,tc_HOL_Obool)))
| c_Fun_Oinj__on(X1940,tc_fun(X1937,X1939),hAPP(c_COMBB(X1939,tc_fun(X1937,X1939),X1940,c_COMBK(X1939,X1937)),X1938),c_Orderings_Otop__class_Otop(tc_fun(X1940,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).
fof(i_0_657,plain,
! [X2045,X2046] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2046,X2046)),c_COMBI(X2046)),c_FuncSet_OPi(X2046,X2046,X2045,hAPP(c_COMBK(tc_fun(X2046,tc_HOL_Obool),X2046),X2045)))),
inference(variable_rename,[status(thm)],[fact_funcset__id]) ).
fof(i_0_658,plain,
! [X1873,X1874,X1875,X1876,X1877,X1878] : c_Set_Oimage(X1878,X1877,X1876,c_Set_Oimage(X1875,X1878,X1874,X1873)) = c_Set_Oimage(X1875,X1877,hAPP(c_COMBB(X1878,X1877,X1875,X1876),X1874),X1873),
inference(variable_rename,[status(thm)],[fact_image__image]) ).
fof(i_0_659,plain,
! [X1953,X1954,X1955] :
( X1955 = X1954
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1953),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_Oabove(X1953,X1955,X1954)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_above__Lin])]) ).
fof(i_0_660,plain,
! [X1950,X1951,X1952] :
( X1952 = X1951
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1950),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(X1950,X1952,X1951)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_below__Lin])]) ).
fof(i_0_661,plain,
! [X3262,X3263,X3264,X3265] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3264),X3263))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3265,X3262,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3263,hAPP(c_Nat_OSuc,X3264))) = c_Groups_Ozero__class_Ozero(X3265)
| ~ class_Groups_Ocomm__monoid__add(X3265) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3264),X3263))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3265,X3262,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3263,hAPP(c_Nat_OSuc,X3264))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3265),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3265,X3262,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3263,X3264))),hAPP(X3262,X3264))
| ~ class_Groups_Ocomm__monoid__add(X3265) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_528])])]) ).
fof(i_0_662,plain,
! [X2192,X2193,X2194,X2195] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2195,X2195)),hAPP(hAPP(c_Product__Type_OPair(X2195,X2195),X2194),X2193)),c_Wellfounded_Omeasure(X2195,X2192)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2192,X2194)),hAPP(X2192,X2193))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2192,X2194)),hAPP(X2192,X2193)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2195,X2195)),hAPP(hAPP(c_Product__Type_OPair(X2195,X2195),X2194),X2193)),c_Wellfounded_Omeasure(X2195,X2192))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).
fof(i_0_663,plain,
! [X2220,X2221,X2222,X2223,X2224] :
( ~ c_Finite__Set_Ofinite(X2224,X2223)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2222,tc_HOL_Obool),X2221),c_Set_Oimage(X2224,X2222,X2220,X2223)))
| c_Finite__Set_Ofinite(X2222,X2221) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
fof(i_0_664,plain,
! [X2084,X2085,X2086,X2087,X2088] :
( ( hBOOL(hAPP(hAPP(X2086,X2085),X2087))
| ~ hBOOL(hAPP(hAPP(c_member(X2088),X2087),c_SetInterval_Oord_OatLeastAtMost(X2088,X2086,X2085,X2084))) )
& ( hBOOL(hAPP(hAPP(X2086,X2087),X2084))
| ~ hBOOL(hAPP(hAPP(c_member(X2088),X2087),c_SetInterval_Oord_OatLeastAtMost(X2088,X2086,X2085,X2084))) )
& ( ~ hBOOL(hAPP(hAPP(X2086,X2085),X2087))
| ~ hBOOL(hAPP(hAPP(X2086,X2087),X2084))
| hBOOL(hAPP(hAPP(c_member(X2088),X2087),c_SetInterval_Oord_OatLeastAtMost(X2088,X2086,X2085,X2084))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])]) ).
fof(i_0_665,plain,
! [X2079,X2080,X2081,X2082,X2083] :
( ( hBOOL(hAPP(hAPP(X2081,X2080),X2082))
| ~ hBOOL(hAPP(hAPP(c_member(X2083),X2082),c_SetInterval_Oord_OgreaterThanLessThan(X2083,X2081,X2080,X2079))) )
& ( hBOOL(hAPP(hAPP(X2081,X2082),X2079))
| ~ hBOOL(hAPP(hAPP(c_member(X2083),X2082),c_SetInterval_Oord_OgreaterThanLessThan(X2083,X2081,X2080,X2079))) )
& ( ~ hBOOL(hAPP(hAPP(X2081,X2080),X2082))
| ~ hBOOL(hAPP(hAPP(X2081,X2082),X2079))
| hBOOL(hAPP(hAPP(c_member(X2083),X2082),c_SetInterval_Oord_OgreaterThanLessThan(X2083,X2081,X2080,X2079))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])]) ).
fof(i_0_666,plain,
! [X3276,X3277,X3278,X3279] :
( ~ class_Groups_Ocomm__monoid__add(X3279)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3279,X3278,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3277),hAPP(c_Nat_OSuc,X3276))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3279,hAPP(c_COMBB(tc_Nat_Onat,X3279,tc_Nat_Onat,X3278),c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3277,X3276)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])]) ).
fof(i_0_667,plain,
! [X1948,X1949] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1949),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_Omkbot(X1949,X1948)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mkbot__Lin])]) ).
fof(i_0_668,plain,
! [X1946,X1947] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1947),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_Omktop(X1947,X1946)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mktop__Lin])]) ).
fof(i_0_669,plain,
! [X2539,X2540,X2541,X2542,X2543] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2543,X2542)),hAPP(X2543,X2541)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2540,X2540)),hAPP(hAPP(c_Product__Type_OPair(X2540,X2540),X2542),X2541)),c_Wellfounded_Omlex__prod(X2540,X2543,X2539))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).
fof(i_0_670,plain,
! [X2165,X2166,X2167,X2168] :
( ~ c_Fun_Oinj__on(X2168,X2167,X2166,X2165)
| c_Set_Oimage(X2167,X2168,c_Fun_Othe__inv__into(X2168,X2167,X2165,X2166),c_Set_Oimage(X2168,X2167,X2166,X2165)) = X2165 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).
fof(i_0_671,plain,
! [X2842,X2843] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X2843),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2842,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2842),c_Finite__Set_Ocard(tc_Nat_Onat,X2843)))))
| X2843 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2842,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2842),c_Finite__Set_Ocard(tc_Nat_Onat,X2843))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).
fof(i_0_672,plain,
! [X2169,X2170,X2171,X2172] :
( ~ c_Fun_Oinj__on(X2172,X2171,X2170,X2169)
| c_Fun_Oinj__on(X2171,X2172,c_Fun_Othe__inv__into(X2172,X2171,X2169,X2170),c_Set_Oimage(X2172,X2171,X2170,X2169)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).
fof(i_0_673,plain,
! [X2322,X2323,X2324,X2325,X2326] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2326,X2323),X2325))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2326,X2324),X2325))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2326,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X2326,X2325,X2324)),c_SetInterval_Oord__class_OatLeastLessThan(X2326,X2323,X2322)))
| ~ class_Orderings_Olinorder(X2326) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2326,X2324),X2322))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2326,X2324),X2325))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2326,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X2326,X2325,X2324)),c_SetInterval_Oord__class_OatLeastLessThan(X2326,X2323,X2322)))
| ~ class_Orderings_Olinorder(X2326) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).
fof(i_0_674,plain,
! [X1827,X1828,X1829,X1830] : hBOOL(hAPP(hAPP(c_member(X1830),hAPP(X1829,X1828)),c_Set_Oimage(X1827,X1830,X1829,c_Orderings_Otop__class_Otop(tc_fun(X1827,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[fact_rangeI]) ).
fof(i_0_675,plain,
! [X3283,X3284,X3285,X3286] :
( ~ class_Groups_Ocomm__monoid__add(X3286)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3285),X3284))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3286,X3283,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3285,X3284)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3286),hAPP(X3283,X3285)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3286,X3283,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3285),X3284))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc])]) ).
fof(i_0_676,plain,
! [X1887,X1888,X1889,X1890,X1891] :
( ~ hBOOL(hAPP(hAPP(c_member(X1891),X1890),X1889))
| hBOOL(hAPP(hAPP(c_member(X1888),hAPP(X1887,X1890)),c_Set_Oimage(X1891,X1888,X1887,X1889))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).
fof(i_0_677,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
inference(fof_simplification,[status(thm)],[fact__096_Ib_M_Aa_J_A_126_058_ALab_096]) ).
fof(i_0_678,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_679,plain,
! [X1941,X1942,X1943,X1944,X1945] :
( X1945 != hAPP(X1944,X1943)
| hBOOL(hAPP(hAPP(c_member(X1942),X1945),c_Set_Oimage(X1941,X1942,X1944,c_Orderings_Otop__class_Otop(tc_fun(X1941,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).
fof(i_0_680,plain,
! [X1777,X1778,X1779,X1780,X1781,X1782] :
( X1782 != hAPP(X1781,X1780)
| ~ hBOOL(hAPP(hAPP(c_member(X1779),X1780),X1778))
| hBOOL(hAPP(hAPP(c_member(X1777),X1782),c_Set_Oimage(X1779,X1777,X1781,X1778))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).
fof(i_0_681,plain,
! [X1881,X1882,X1883,X1884,X1885,X1886] :
( ~ hBOOL(hAPP(hAPP(c_member(X1886),X1885),X1884))
| X1883 != hAPP(X1882,X1885)
| hBOOL(hAPP(hAPP(c_member(X1881),X1883),c_Set_Oimage(X1886,X1881,X1882,X1884))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).
fof(i_0_682,plain,
! [X1822,X1823,X1824,X1825,X1826] :
( ( c_Set_Oimage(X1826,X1825,X1824,X1823) != c_Set_Oimage(X1826,X1825,X1824,X1822)
| X1823 = X1822
| ~ c_Fun_Oinj__on(X1826,X1825,X1824,c_Orderings_Otop__class_Otop(tc_fun(X1826,tc_HOL_Obool))) )
& ( X1823 != X1822
| c_Set_Oimage(X1826,X1825,X1824,X1823) = c_Set_Oimage(X1826,X1825,X1824,X1822)
| ~ c_Fun_Oinj__on(X1826,X1825,X1824,c_Orderings_Otop__class_Otop(tc_fun(X1826,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_683,plain,
! [X3103,X3104,X3105,X3106] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3106)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3106),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3106),X3105),X3104)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3106),X3103),X3104)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3106),X3105),X3103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_684,plain,
! [X3082,X3083,X3084,X3085] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3085),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3085),X3084),X3083)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3085),X3082),X3083)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3085),X3084),X3082))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3085) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3085),X3084),X3082))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3085),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3085),X3084),X3083)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3085),X3082),X3083)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3085) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_685,plain,
! [X3107,X3108,X3109,X3110] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3110)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3110),X3109),X3108)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3110),X3109),X3107)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3110),X3108),X3107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_686,plain,
! [X3086,X3087,X3088,X3089] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3089),X3088),X3087)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3089),X3088),X3086)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3089),X3087),X3086))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3089) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3089),X3087),X3086))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3089),X3088),X3087)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3089),X3088),X3086)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3089) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_687,plain,
! [X2492,X2493,X2494,X2495] :
( ~ c_Finite__Set_Ofinite(X2495,c_Set_Oimage(X2494,X2495,X2493,X2492))
| ~ c_Fun_Oinj__on(X2494,X2495,X2493,X2492)
| c_Finite__Set_Ofinite(X2494,X2492) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).
fof(i_0_688,plain,
! [X1985,X1986,X1987,X1988] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1988,tc_HOL_Obool)),X1987),X1986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1988,tc_HOL_Obool)),X1986),X1985))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1988,tc_HOL_Obool)),X1987),X1985)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).
fof(i_0_689,plain,
! [X3068,X3069,X3070,X3071] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3071,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3071),X3070),X3069)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3071),X3068),X3069)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3071,X3070),X3068))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3071) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3071,X3070),X3068))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3071,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3071),X3070),X3069)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3071),X3068),X3069)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3071) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_690,plain,
! [X3047,X3048,X3049,X3050] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3050)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3050,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3050),X3049),X3048)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3050),X3047),X3048)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3050,X3049),X3047)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_691,plain,
! [X3064,X3065,X3066,X3067] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3067,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3067),X3066),X3065)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3067),X3066),X3064)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3067,X3065),X3064))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3067) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3067,X3065),X3064))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3067,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3067),X3066),X3065)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3067),X3066),X3064)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3067) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_692,plain,
! [X3043,X3044,X3045,X3046] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3046)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3046,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3046),X3045),X3044)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3046),X3045),X3043)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3046,X3044),X3043)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_693,plain,
! [X2161,X2162,X2163,X2164] :
( ~ c_Fun_Oinj__on(X2164,X2163,X2162,c_Orderings_Otop__class_Otop(tc_fun(X2164,tc_HOL_Obool)))
| hAPP(c_Fun_Othe__inv__into(X2164,X2163,c_Orderings_Otop__class_Otop(tc_fun(X2164,tc_HOL_Obool)),X2162),hAPP(X2162,X2161)) = X2161 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])]) ).
fof(i_0_694,plain,
! [X1693,X1694,X1695] :
( ( hAPP(hAPP(c_COMBC(X1695,tc_fun(X1695,tc_HOL_Obool),tc_HOL_Obool),c_member(X1695)),X1694) != hAPP(hAPP(c_COMBC(X1695,tc_fun(X1695,tc_HOL_Obool),tc_HOL_Obool),c_member(X1695)),X1693)
| X1694 = X1693 )
& ( X1694 != X1693
| hAPP(hAPP(c_COMBC(X1695,tc_fun(X1695,tc_HOL_Obool),tc_HOL_Obool),c_member(X1695)),X1694) = hAPP(hAPP(c_COMBC(X1695,tc_fun(X1695,tc_HOL_Obool),tc_HOL_Obool),c_member(X1695)),X1693) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).
fof(i_0_695,plain,
! [X2924,X2925,X2926] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2926),X2925)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2926),X2924)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2925),X2924)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2925),X2924))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2926),X2925)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2926),X2924))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_696,plain,
! [X2156,X2157,X2158,X2159,X2160] :
( ~ c_Fun_Oinj__on(X2160,X2159,X2158,X2157)
| ~ hBOOL(hAPP(hAPP(c_member(X2160),X2156),X2157))
| hAPP(c_Fun_Othe__inv__into(X2160,X2159,X2157,X2158),hAPP(X2158,X2156)) = X2156 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).
fof(i_0_697,plain,
! [X2150,X2151,X2152,X2153,X2154,X2155] :
( ~ c_Fun_Oinj__on(X2155,X2154,X2153,X2152)
| hAPP(X2153,X2151) != X2150
| ~ hBOOL(hAPP(hAPP(c_member(X2155),X2151),X2152))
| hAPP(c_Fun_Othe__inv__into(X2155,X2154,X2152,X2153),X2150) = X2151 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).
fof(i_0_698,plain,
! [X2518,X2519,X2520,X2521] :
( ~ c_Finite__Set_Ofinite(X2521,X2520)
| c_Finite__Set_Ocard(X2519,c_Set_Oimage(X2521,X2519,X2518,X2520)) != c_Finite__Set_Ocard(X2521,X2520)
| c_Fun_Oinj__on(X2521,X2519,X2518,X2520) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).
fof(i_0_699,plain,
! [X2514,X2515,X2516,X2517] :
( ( ~ c_Fun_Oinj__on(X2517,X2515,X2514,X2516)
| c_Finite__Set_Ocard(X2515,c_Set_Oimage(X2517,X2515,X2514,X2516)) = c_Finite__Set_Ocard(X2517,X2516)
| ~ c_Finite__Set_Ofinite(X2517,X2516) )
& ( c_Finite__Set_Ocard(X2515,c_Set_Oimage(X2517,X2515,X2514,X2516)) != c_Finite__Set_Ocard(X2517,X2516)
| c_Fun_Oinj__on(X2517,X2515,X2514,X2516)
| ~ c_Finite__Set_Ofinite(X2517,X2516) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).
fof(i_0_700,plain,
! [X3168,X3169,X3170,X3171] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3171,tc_fun(X3170,tc_HOL_Obool))),X3169),X3168)),
inference(variable_rename,[status(thm)],[i_0_529]) ).
fof(i_0_701,plain,
! [X3320,X3321,X3322,X3323,X3324,X3325] : hAPP(hAPP(c_COMBB(X3325,X3324,X3323,X3322),X3321),X3320) = hAPP(X3322,hAPP(X3321,X3320)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
fof(i_0_702,plain,
! [X3098,X3099,X3100,X3101,X3102] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3102)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3102),X3101),X3100))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3102),X3099),X3098))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3102),X3101),X3099)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3102),X3100),X3098))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_703,plain,
! [X2986,X2987,X2988] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2988),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2987,X2986)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2987),X2988),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2986),X2988)),
inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).
fof(i_0_704,plain,
! [X2826,X2827,X2828] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2828),X2827)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2828),X2826)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2827),X2826)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2827),X2826))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2828),X2827)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2828),X2826))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_705,plain,
! [X3137,X3138,X3139,X3140,X3141] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3141)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3141,X3140),X3139))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3141),X3138),X3137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3141),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3141),X3140),X3138)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3141),X3139),X3137))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_706,plain,
! [X3132,X3133,X3134,X3135,X3136] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3136)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3136),X3135),X3134))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3136,X3133),X3132))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3136),X3135),X3133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3136),X3134),X3132))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_707,plain,
! [X2461,X2462,X2463,X2464] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2464,tc_HOL_Obool),X2463),X2462))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2464,tc_HOL_Obool)),X2462),X2461))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2464,tc_HOL_Obool)),X2463),X2461)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).
fof(i_0_708,plain,
! [X2465,X2466,X2467,X2468] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2468,tc_HOL_Obool)),X2467),X2466))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2468,tc_HOL_Obool),X2466),X2465))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2468,tc_HOL_Obool)),X2467),X2465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).
fof(i_0_709,plain,
! [X2737,X2738] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2738)),X2737))
| hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2738),X2737)) )
& ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2738),X2737))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2738)),X2737)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_710,plain,
! [X2487,X2488,X2489] :
( ~ c_Finite__Set_Ofinite(X2489,X2488)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2489,tc_HOL_Obool),X2487),X2488))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2489,X2487)),c_Finite__Set_Ocard(X2489,X2488)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2489,tc_HOL_Obool)),X2487),X2488)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).
fof(i_0_711,plain,
! [X3051,X3052,X3053,X3054,X3055] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3055)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3055,X3054),X3053))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3055,X3052),X3051))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3055,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3055),X3054),X3052)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3055),X3053),X3051))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_712,plain,
! [X3166,X3167] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3167),X3166),X3166)),c_Groups_Ozero__class_Ozero(X3167)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3167),X3166),c_Groups_Ozero__class_Ozero(X3167)))
| ~ class_Rings_Olinordered__idom(X3167) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3167),X3166),c_Groups_Ozero__class_Ozero(X3167)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3167),X3166),X3166)),c_Groups_Ozero__class_Ozero(X3167)))
| ~ class_Rings_Olinordered__idom(X3167) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_713,plain,
! [X3148,X3149] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3149),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3149),X3148),X3148)),c_Groups_Ozero__class_Ozero(X3149)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3149),X3148),c_Groups_Ozero__class_Ozero(X3149)))
| ~ class_Groups_Olinordered__ab__group__add(X3149) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3149),X3148),c_Groups_Ozero__class_Ozero(X3149)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3149),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3149),X3148),X3148)),c_Groups_Ozero__class_Ozero(X3149)))
| ~ class_Groups_Olinordered__ab__group__add(X3149) ) ),
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_714,plain,
! [X2202,X2203] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk34_2(X2202,X2203)),c_Arrow__Order__Mirabelle_OLin))
| X2203 = X2202 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2203),X2202)),esk34_2(X2202,X2203)))
| X2203 = X2202 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_complete__Lin])])])]) ).
fof(i_0_715,plain,
! [X2911,X2912,X2913,X2914] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2914),X2913))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2912),X2911))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2914),X2912)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2913),X2911))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_716,plain,
! [X2512,X2513] :
( ~ c_Finite__Set_Ofinite(X2513,c_Orderings_Otop__class_Otop(tc_fun(X2513,tc_HOL_Obool)))
| c_Set_Oimage(X2513,X2513,X2512,c_Orderings_Otop__class_Otop(tc_fun(X2513,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2513,tc_HOL_Obool))
| c_Fun_Oinj__on(X2513,X2513,X2512,c_Orderings_Otop__class_Otop(tc_fun(X2513,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).
fof(i_0_717,plain,
! [X2445,X2446,X2447,X2448,X2449] :
( ~ c_Fun_Oinj__on(X2449,X2448,X2447,X2446)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2449,tc_HOL_Obool),X2445),X2446))
| c_Fun_Oinj__on(X2449,X2448,X2447,X2445) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).
fof(i_0_718,plain,
! [X1818,X1819,X1820,X1821] :
( ~ c_Fun_Oinj__on(X1821,X1820,X1819,X1818)
| c_Finite__Set_Ocard(X1820,c_Set_Oimage(X1821,X1820,X1819,X1818)) = c_Finite__Set_Ocard(X1821,X1818) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).
fof(i_0_719,plain,
! [X3142,X3143,X3144] :
( ~ class_Groups_Oordered__comm__monoid__add(X3144)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3144),X3143),c_Groups_Ozero__class_Ozero(X3144)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3144),X3142),c_Groups_Ozero__class_Ozero(X3144)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3144),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3144),X3143),X3142)),c_Groups_Ozero__class_Ozero(X3144))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_720,plain,
! [X2510,X2511] :
( ~ c_Finite__Set_Ofinite(X2511,c_Orderings_Otop__class_Otop(tc_fun(X2511,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(X2511,X2511,X2510,c_Orderings_Otop__class_Otop(tc_fun(X2511,tc_HOL_Obool)))
| c_Set_Oimage(X2511,X2511,X2510,c_Orderings_Otop__class_Otop(tc_fun(X2511,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2511,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).
fof(i_0_721,plain,
! [X3090,X3091,X3092,X3093] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3093)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3093),X3092),X3091))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3093),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3093),X3092),X3090)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3093),X3091),X3090))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_722,plain,
! [X3094,X3095,X3096,X3097] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3097)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3097),X3096),X3095))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3097),X3094),X3096)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3097),X3094),X3095))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_723,plain,
! [X3128,X3129] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3129,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3129),X3128),X3128)),c_Groups_Ozero__class_Ozero(X3129)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3129,X3128),c_Groups_Ozero__class_Ozero(X3129)))
| ~ class_Groups_Olinordered__ab__group__add(X3129) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3129,X3128),c_Groups_Ozero__class_Ozero(X3129)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3129,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3129),X3128),X3128)),c_Groups_Ozero__class_Ozero(X3129)))
| ~ class_Groups_Olinordered__ab__group__add(X3129) ) ),
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_724,plain,
! [X3003,X3004,X3005] :
( ~ class_Groups_Oordered__comm__monoid__add(X3005)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3005,X3004),c_Groups_Ozero__class_Ozero(X3005)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3005),X3003),c_Groups_Ozero__class_Ozero(X3005)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3005),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3005),X3004),X3003)),c_Groups_Ozero__class_Ozero(X3005))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_725,plain,
! [X3006,X3007,X3008] :
( ~ class_Groups_Oordered__comm__monoid__add(X3008)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3008),X3007),c_Groups_Ozero__class_Ozero(X3008)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3008,X3006),c_Groups_Ozero__class_Ozero(X3008)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3008),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3008),X3007),X3006)),c_Groups_Ozero__class_Ozero(X3008))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_726,plain,
! [X2813,X2814,X2815,X2816] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2816),X2815))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2814),X2813))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2816),X2814)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2815),X2813))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_727,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),esk13_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk13_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_530])])]) ).
fof(i_0_728,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),esk12_0))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk12_0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_531])])]) ).
fof(i_0_729,plain,
! [X2750,X2751,X2752,X2753] :
( ( c_Finite__Set_Ofinite(X2753,X2751)
| ~ c_Finite__Set_Ofinite(tc_sum(X2753,X2752),c_Sum__Type_OPlus(X2753,X2752,X2751,X2750)) )
& ( c_Finite__Set_Ofinite(X2752,X2750)
| ~ c_Finite__Set_Ofinite(tc_sum(X2753,X2752),c_Sum__Type_OPlus(X2753,X2752,X2751,X2750)) )
& ( ~ c_Finite__Set_Ofinite(X2753,X2751)
| ~ c_Finite__Set_Ofinite(X2752,X2750)
| c_Finite__Set_Ofinite(tc_sum(X2753,X2752),c_Sum__Type_OPlus(X2753,X2752,X2751,X2750)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).
fof(i_0_730,plain,
! [X2771,X2772,X2773,X2774] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2774,X2773),c_Sum__Type_OPlus(X2774,X2773,X2772,X2771))
| c_Finite__Set_Ofinite(X2774,X2772) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).
fof(i_0_731,plain,
! [X2767,X2768,X2769,X2770] :
( ~ c_Finite__Set_Ofinite(tc_sum(X2770,X2769),c_Sum__Type_OPlus(X2770,X2769,X2768,X2767))
| c_Finite__Set_Ofinite(X2769,X2767) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).
fof(i_0_732,plain,
! [X3060,X3061,X3062,X3063] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3063)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3063,X3062),X3061))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3063,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3063),X3062),X3060)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3063),X3061),X3060))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_733,plain,
! [X3056,X3057,X3058,X3059] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3059)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3059,X3058),X3057))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3059,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3059),X3056),X3058)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3059),X3056),X3057))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_734,plain,
! [X2904,X2905,X2906] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2906),X2905)),X2904))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2906),X2904)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_735,plain,
! [X3111,X3112,X3113] :
( ~ class_Groups_Oordered__comm__monoid__add(X3113)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3113,X3112),c_Groups_Ozero__class_Ozero(X3113)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3113,X3111),c_Groups_Ozero__class_Ozero(X3113)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3113,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3113),X3112),X3111)),c_Groups_Ozero__class_Ozero(X3113))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_736,plain,
! [X3280,X3281,X3282] :
( ~ class_Groups_Ocomm__monoid__add(X3282)
| hAPP(X3281,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X3282)
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3282,X3281,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3280)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3282,X3281,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])]) ).
fof(i_0_737,plain,
! [X2457,X2458,X2459,X2460] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2459,X2460),X2458),X2457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2459,X2460)),X2458),X2457))
| ~ class_Orderings_Oord(X2460) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2459,X2460),X2457),X2458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2459,X2460)),X2458),X2457))
| ~ class_Orderings_Oord(X2460) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2459,X2460),X2458),X2457))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2459,X2460),X2457),X2458))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2459,X2460)),X2458),X2457))
| ~ class_Orderings_Oord(X2460) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_532])])]) ).
fof(i_0_738,plain,
! [X2643,X2644,X2645,X2646,X2647,X2648] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2648,tc_fun(X2647,tc_HOL_Obool)),X2646),X2645))
| ~ hBOOL(hAPP(hAPP(X2646,X2644),X2643))
| hBOOL(hAPP(hAPP(X2645,X2644),X2643)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).
fof(i_0_739,plain,
! [X2633,X2634,X2635,X2636,X2637,X2638] :
( ~ hBOOL(hAPP(hAPP(X2638,X2637),X2636))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2635,tc_fun(X2634,tc_HOL_Obool)),X2638),X2633))
| hBOOL(hAPP(hAPP(X2633,X2637),X2636)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).
fof(i_0_740,plain,
! [X2915,X2916,X2917] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2917),X2916))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2917),X2915)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2916),X2915))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_741,plain,
! [X1910,X1911,X1912,X1913,X1914,X1915] :
( ( hAPP(X1913,X1911) != hAPP(X1913,X1910)
| X1911 = X1910
| ~ hBOOL(hAPP(hAPP(c_member(X1915),X1910),X1912))
| ~ hBOOL(hAPP(hAPP(c_member(X1915),X1911),X1912))
| ~ c_Fun_Oinj__on(X1915,X1914,X1913,X1912) )
& ( X1911 != X1910
| hAPP(X1913,X1911) = hAPP(X1913,X1910)
| ~ hBOOL(hAPP(hAPP(c_member(X1915),X1910),X1912))
| ~ hBOOL(hAPP(hAPP(c_member(X1915),X1911),X1912))
| ~ c_Fun_Oinj__on(X1915,X1914,X1913,X1912) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).
fof(i_0_742,plain,
! [X1916,X1917,X1918,X1919,X1920,X1921] :
( ~ c_Fun_Oinj__on(X1921,X1920,X1919,X1918)
| X1917 = X1916
| ~ hBOOL(hAPP(hAPP(c_member(X1921),X1917),X1918))
| ~ hBOOL(hAPP(hAPP(c_member(X1921),X1916),X1918))
| hAPP(X1919,X1917) != hAPP(X1919,X1916) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).
fof(i_0_743,plain,
! [X1904,X1905,X1906,X1907,X1908,X1909] :
( ~ c_Fun_Oinj__on(X1909,X1908,X1907,X1906)
| hAPP(X1907,X1905) != hAPP(X1907,X1904)
| ~ hBOOL(hAPP(hAPP(c_member(X1909),X1905),X1906))
| ~ hBOOL(hAPP(hAPP(c_member(X1909),X1904),X1906))
| X1905 = X1904 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).
fof(i_0_744,plain,
! [X2804,X2805,X2806] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2806),X2804))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2806),X2805)),X2804)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2805),X2804))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2806),X2805)),X2804)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_533])])]) ).
fof(i_0_745,plain,
! [X2807,X2808,X2809] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2809),X2808)),X2807))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2809),X2807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_746,plain,
! [X2810,X2811,X2812] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2812),X2811)),X2810))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2811),X2810)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_747,plain,
! [X3145,X3146,X3147] :
( ~ class_Groups_Oordered__comm__monoid__add(X3147)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3147),c_Groups_Ozero__class_Ozero(X3147)),X3146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3147),c_Groups_Ozero__class_Ozero(X3147)),X3145))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3147),c_Groups_Ozero__class_Ozero(X3147)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3147),X3146),X3145))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_748,plain,
! [X1802,X1803,X1804,X1806,X1807,X1808] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk5_2(X1802,X1803)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1804),X1803))
| ~ hBOOL(hAPP(X1802,X1804)) )
& ( hBOOL(hAPP(X1802,esk5_2(X1802,X1803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1804),X1803))
| ~ hBOOL(hAPP(X1802,X1804)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk6_2(X1806,X1807)),X1807))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1808),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1807)))
| ~ hBOOL(hAPP(X1806,X1808)) )
& ( hBOOL(hAPP(X1806,esk6_2(X1806,X1807)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1808),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1807)))
| ~ hBOOL(hAPP(X1806,X1808)) ) ),
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_749,plain,
! [X2817,X2818,X2819] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2819),X2818))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2819),X2817)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2818),X2817))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_750,plain,
! [X1835,X1836,X1837,X1838] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1838,tc_HOL_Obool)),X1837),X1836))
| ~ hBOOL(hAPP(hAPP(c_member(X1838),X1835),X1837))
| hBOOL(hAPP(hAPP(c_member(X1838),X1835),X1836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).
fof(i_0_751,plain,
! [X2522,X2523,X2524] :
( ~ c_Finite__Set_Ofinite(X2524,X2523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2524,tc_HOL_Obool)),X2522),X2523))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X2524,X2522)),c_Finite__Set_Ocard(X2524,X2523))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).
fof(i_0_752,plain,
! [X2980,X2981] : 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)),X2981),X2980),
inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).
fof(i_0_753,plain,
! [X3204,X3205,X3206,X3207,X3208] :
( ~ class_Rings_Ocomm__semiring__1(X3208)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3208),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3208),X3207),X3206)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3208),X3205),X3204)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3208),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3208),X3207),X3205)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3208),X3206),X3204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_754,plain,
! [X1810,X1811,X1813,X1814,X1815,X1817] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk7_2(X1810,X1811)),X1811))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1813),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1811)))
| hBOOL(hAPP(X1810,X1813)) )
& ( ~ hBOOL(hAPP(X1810,esk7_2(X1810,X1811)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1813),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1811)))
| hBOOL(hAPP(X1810,X1813)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk8_2(X1814,X1815)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1815)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1817),X1815))
| hBOOL(hAPP(X1814,X1817)) )
& ( ~ hBOOL(hAPP(X1814,esk8_2(X1814,X1815)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1817),X1815))
| hBOOL(hAPP(X1814,X1817)) ) ),
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_755,plain,
! [X2228,X2229,X2230,X2231] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2231,tc_HOL_Obool),X2230),X2229))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2231,tc_HOL_Obool),X2229),X2228))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2231,tc_HOL_Obool),X2230),X2228)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).
fof(i_0_756,plain,
! [X3155,X3156,X3157] :
( ~ class_Groups_Oordered__comm__monoid__add(X3157)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3157,c_Groups_Ozero__class_Ozero(X3157)),X3156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3157),c_Groups_Ozero__class_Ozero(X3157)),X3155))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3157),c_Groups_Ozero__class_Ozero(X3157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3157),X3156),X3155))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_757,plain,
! [X3152,X3153,X3154] :
( ~ class_Groups_Oordered__comm__monoid__add(X3154)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3154),c_Groups_Ozero__class_Ozero(X3154)),X3153))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3154,c_Groups_Ozero__class_Ozero(X3154)),X3152))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3154),c_Groups_Ozero__class_Ozero(X3154)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3154),X3153),X3152))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_758,plain,
! [X2929,X2930] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2930),X2929)),X2930)),
inference(variable_rename,[status(thm)],[i_0_534]) ).
fof(i_0_759,plain,
! [X2927,X2928] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2928),X2927)),X2927)),
inference(variable_rename,[status(thm)],[i_0_535]) ).
fof(i_0_760,plain,
! [X2999,X3000,X3001,X3002] :
( ~ c_Finite__Set_Ofinite(X3002,X3001)
| ~ c_Finite__Set_Ofinite(X3000,X2999)
| c_Finite__Set_Ocard(tc_sum(X3002,X3000),c_Sum__Type_OPlus(X3002,X3000,X3001,X2999)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X3002,X3001)),c_Finite__Set_Ocard(X3000,X2999)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).
fof(i_0_761,plain,
! [X2777,X2778,X2779,X2780] :
( ( ~ c_Finite__Set_Ofinite(X2780,X2779)
| ~ c_Finite__Set_Ofinite(X2778,X2777)
| c_Finite__Set_Ocard(tc_sum(X2780,X2778),c_Sum__Type_OPlus(X2780,X2778,X2779,X2777)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X2780,X2779)),c_Finite__Set_Ocard(X2778,X2777)) )
& ( c_Finite__Set_Ofinite(X2780,X2779)
| c_Finite__Set_Ocard(tc_sum(X2780,X2778),c_Sum__Type_OPlus(X2780,X2778,X2779,X2777)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X2778,X2777)
| c_Finite__Set_Ocard(tc_sum(X2780,X2778),c_Sum__Type_OPlus(X2780,X2778,X2779,X2777)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if])])]) ).
fof(i_0_762,plain,
! [X3162,X3163,X3164,X3165] :
( ~ class_Rings_Olinordered__semidom(X3165)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3165),c_Groups_Ozero__class_Ozero(X3165)),X3164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3165),X3163),X3162))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3165),X3163),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3165),X3164),X3162))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_763,plain,
! [X3150,X3151] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3151),c_Groups_Ozero__class_Ozero(X3151)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3151),X3150),X3150)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3151),c_Groups_Ozero__class_Ozero(X3151)),X3150))
| ~ class_Groups_Olinordered__ab__group__add(X3151) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3151),c_Groups_Ozero__class_Ozero(X3151)),X3150))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3151),c_Groups_Ozero__class_Ozero(X3151)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3151),X3150),X3150)))
| ~ class_Groups_Olinordered__ab__group__add(X3151) ) ),
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,
! [X2958,X2959] :
( ( ~ 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),X2959),X2958)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2959))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2958)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2959))
| 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),X2959),X2958))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2958))
| 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),X2959),X2958))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_765,plain,
! [X2606,X2607,X2608] :
( ~ c_Finite__Set_Ofinite(X2608,X2607)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2608,tc_HOL_Obool),X2606),X2607))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2608,X2607)),c_Finite__Set_Ocard(X2608,X2606)))
| X2606 = X2607 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).
fof(i_0_766,plain,
! [X3009,X3010,X3011,X3012] :
( ~ class_Groups_Oordered__comm__monoid__add(X3012)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3012,c_Groups_Ozero__class_Ozero(X3012)),X3011))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3012),X3010),X3009))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3012),X3010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3012),X3011),X3009))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_767,plain,
! [X3158,X3159,X3160,X3161] :
( ~ class_Groups_Oordered__comm__monoid__add(X3161)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3161),c_Groups_Ozero__class_Ozero(X3161)),X3160))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3161,X3159),X3158))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3161),X3159),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3161),X3160),X3158))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_768,plain,
! [X3125,X3126,X3127] :
( ~ class_Groups_Oordered__comm__monoid__add(X3127)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3127,c_Groups_Ozero__class_Ozero(X3127)),X3126))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3127,c_Groups_Ozero__class_Ozero(X3127)),X3125))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3127,c_Groups_Ozero__class_Ozero(X3127)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3127),X3126),X3125))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_769,negated_conjecture,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))
& v_Lba____ != v_Lab____ ),
inference(fof_nnf,[status(thm)],[i_0_536]) ).
fof(i_0_770,plain,
! [X2475,X2476,X2477] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2477,tc_HOL_Obool),X2476),X2475))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2477,tc_HOL_Obool)),X2476),X2475)) )
& ( X2476 != X2475
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2477,tc_HOL_Obool)),X2476),X2475)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2477,tc_HOL_Obool),X2476),X2475))
| X2476 = X2475
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2477,tc_HOL_Obool)),X2476),X2475)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).
fof(i_0_771,plain,
! [X2472,X2473,X2474] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2474,tc_HOL_Obool),X2473),X2472))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2474,tc_HOL_Obool)),X2473),X2472))
| X2473 = X2472 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2474,tc_HOL_Obool)),X2473),X2472))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2474,tc_HOL_Obool),X2473),X2472)) )
& ( X2473 != X2472
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2474,tc_HOL_Obool),X2473),X2472)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).
fof(i_0_772,plain,
! [X2469,X2470,X2471] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2471,tc_HOL_Obool)),X2470),X2469))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2471,tc_HOL_Obool),X2470),X2469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).
fof(i_0_773,plain,
! [X2884,X2885] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2885,tc_HOL_Obool)),X2884),c_Orderings_Obot__class_Obot(tc_fun(X2885,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_537]) ).
fof(i_0_774,plain,
! [X2764,X2765,X2766] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2766,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X2766,X2765)),c_SetInterval_Oord__class_OgreaterThan(X2766,X2764)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2766,X2764),X2765))
| ~ class_Orderings_Olinorder(X2766) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2766,X2764),X2765))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2766,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X2766,X2765)),c_SetInterval_Oord__class_OgreaterThan(X2766,X2764)))
| ~ class_Orderings_Olinorder(X2766) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])]) ).
fof(i_0_775,plain,
! [X3130,X3131] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3131,c_Groups_Ozero__class_Ozero(X3131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3131),X3130),X3130)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3131,c_Groups_Ozero__class_Ozero(X3131)),X3130))
| ~ class_Groups_Olinordered__ab__group__add(X3131) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3131,c_Groups_Ozero__class_Ozero(X3131)),X3130))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3131,c_Groups_Ozero__class_Ozero(X3131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3131),X3130),X3130)))
| ~ class_Groups_Olinordered__ab__group__add(X3131) ) ),
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_776,plain,
! [X2047,X2048,X2049] : c_FuncSet_OPi(X2049,X2048,X2047,hAPP(c_COMBK(tc_fun(X2048,tc_HOL_Obool),X2049),c_Orderings_Otop__class_Otop(tc_fun(X2048,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2049,X2048),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pi__UNIV]) ).
fof(i_0_777,plain,
! [X3118,X3119,X3120,X3121] :
( ~ class_Groups_Oordered__comm__monoid__add(X3121)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3121,c_Groups_Ozero__class_Ozero(X3121)),X3120))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3121,X3119),X3118))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3121,X3119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3121),X3120),X3118))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_778,plain,
! [X3114,X3115,X3116,X3117] :
( ~ class_Groups_Oordered__comm__monoid__add(X3117)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3117,c_Groups_Ozero__class_Ozero(X3117)),X3116))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3117,X3115),X3114))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3117,X3115),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3117),X3114),X3116))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_779,plain,
! [X2103,X2104,X2105,X2106] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2106),X2105),c_SetInterval_Oord_OatMost(X2106,X2104,X2103)))
| hBOOL(hAPP(hAPP(X2104,X2105),X2103)) )
& ( ~ hBOOL(hAPP(hAPP(X2104,X2105),X2103))
| hBOOL(hAPP(hAPP(c_member(X2106),X2105),c_SetInterval_Oord_OatMost(X2106,X2104,X2103))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])]) ).
fof(i_0_780,plain,
! [X2093,X2094,X2095,X2096] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2096),X2095),c_SetInterval_Oord_OlessThan(X2096,X2094,X2093)))
| hBOOL(hAPP(hAPP(X2094,X2095),X2093)) )
& ( ~ hBOOL(hAPP(hAPP(X2094,X2095),X2093))
| hBOOL(hAPP(hAPP(c_member(X2096),X2095),c_SetInterval_Oord_OlessThan(X2096,X2094,X2093))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])]) ).
fof(i_0_781,plain,
! [X2107,X2108,X2109,X2110] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2110),X2109),c_SetInterval_Oord_OatLeast(X2110,X2108,X2107)))
| hBOOL(hAPP(hAPP(X2108,X2107),X2109)) )
& ( ~ hBOOL(hAPP(hAPP(X2108,X2107),X2109))
| hBOOL(hAPP(hAPP(c_member(X2110),X2109),c_SetInterval_Oord_OatLeast(X2110,X2108,X2107))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])]) ).
fof(i_0_782,plain,
! [X2089,X2090,X2091,X2092] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2092),X2091),c_SetInterval_Oord_OgreaterThan(X2092,X2090,X2089)))
| hBOOL(hAPP(hAPP(X2090,X2089),X2091)) )
& ( ~ hBOOL(hAPP(hAPP(X2090,X2089),X2091))
| hBOOL(hAPP(hAPP(c_member(X2092),X2091),c_SetInterval_Oord_OgreaterThan(X2092,X2090,X2089))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])]) ).
fof(i_0_783,plain,
! [X2754,X2755,X2756,X2757] :
( ~ c_Finite__Set_Ofinite(X2757,X2756)
| ~ c_Finite__Set_Ofinite(X2755,X2754)
| c_Finite__Set_Ofinite(tc_sum(X2757,X2755),c_Sum__Type_OPlus(X2757,X2755,X2756,X2754)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).
fof(i_0_784,plain,
! [X3326,X3327,X3328,X3329,X3330,X3331] : hAPP(hAPP(hAPP(c_COMBC(X3331,X3330,X3329),X3328),X3327),X3326) = hAPP(hAPP(X3328,X3326),X3327),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
fof(i_0_785,plain,
! [X2244,X2245,X2246] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2244,tc_HOL_Obool),X2246),X2245))
| X2246 != X2245 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2244,tc_HOL_Obool),X2245),X2246))
| X2246 != X2245 )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2244,tc_HOL_Obool),X2246),X2245))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2244,tc_HOL_Obool),X2245),X2246))
| X2246 = X2245 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).
fof(i_0_786,plain,
! [X2207,X2208,X2209] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2209,tc_HOL_Obool),X2208),X2207))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2209,tc_HOL_Obool),X2207),X2208))
| X2208 = X2207 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).
fof(i_0_787,plain,
! [X2414,X2415,X2416,X2417] :
( ~ hBOOL(hAPP(hAPP(c_member(X2417),X2416),X2415))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2417,tc_HOL_Obool),X2415),X2414))
| hBOOL(hAPP(hAPP(c_member(X2417),X2416),X2414)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).
fof(i_0_788,plain,
! [X2418,X2419,X2420,X2421] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2421,tc_HOL_Obool),X2420),X2419))
| ~ hBOOL(hAPP(hAPP(c_member(X2421),X2418),X2420))
| hBOOL(hAPP(hAPP(c_member(X2421),X2418),X2419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).
fof(i_0_789,plain,
! [X2410,X2411,X2412,X2413] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2413,tc_HOL_Obool),X2412),X2411))
| ~ hBOOL(hAPP(hAPP(c_member(X2413),X2410),X2412))
| hBOOL(hAPP(hAPP(c_member(X2413),X2410),X2411)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).
fof(i_0_790,plain,
! [X2212,X2213,X2214,X2215] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2215,tc_HOL_Obool),X2214),X2213))
| ~ hBOOL(hAPP(hAPP(c_member(X2215),X2212),X2214))
| hBOOL(hAPP(hAPP(c_member(X2215),X2212),X2213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).
fof(i_0_791,plain,
! [X3211,X3212,X3213,X3214,X3215] :
( ~ c_Finite__Set_Ofolding__one__idem(X3215,X3214,X3213)
| ~ c_Finite__Set_Ofinite(X3215,X3212)
| X3211 = c_Orderings_Obot__class_Obot(tc_fun(X3215,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3215,tc_HOL_Obool),X3211),X3212))
| hAPP(hAPP(X3214,hAPP(X3213,X3211)),hAPP(X3213,X3212)) = hAPP(X3213,X3212) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem])]) ).
fof(i_0_792,plain,
! [X2791,X2792,X2793,X2794] :
( ( X2792 = c_Orderings_Obot__class_Obot(tc_fun(X2794,tc_HOL_Obool))
| c_Sum__Type_OPlus(X2794,X2793,X2792,X2791) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2794,X2793),tc_HOL_Obool)) )
& ( X2791 = c_Orderings_Obot__class_Obot(tc_fun(X2793,tc_HOL_Obool))
| c_Sum__Type_OPlus(X2794,X2793,X2792,X2791) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2794,X2793),tc_HOL_Obool)) )
& ( X2792 != c_Orderings_Obot__class_Obot(tc_fun(X2794,tc_HOL_Obool))
| X2791 != c_Orderings_Obot__class_Obot(tc_fun(X2793,tc_HOL_Obool))
| c_Sum__Type_OPlus(X2794,X2793,X2792,X2791) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2794,X2793),tc_HOL_Obool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv])])]) ).
fof(i_0_793,plain,
! [X2298,X2299,X2300,X2301,X2302] :
( ~ class_Orderings_Oord(X2302)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2301,X2302),X2300),X2299))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2302,hAPP(X2300,X2298)),hAPP(X2299,X2298))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_794,plain,
! [X2256,X2257,X2258,X2259,X2260] :
( ~ class_Orderings_Oord(X2260)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2259,X2260),X2258),X2257))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2260,hAPP(X2258,X2256)),hAPP(X2257,X2256))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_795,plain,
! [X2216,X2217,X2218,X2219] :
( ~ c_Finite__Set_Ofinite(X2219,X2218)
| c_Finite__Set_Ofinite(X2217,c_Set_Oimage(X2219,X2217,X2216,X2218)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).
fof(i_0_796,plain,
! [X2603,X2604,X2605] :
( ~ c_Finite__Set_Ofinite(X2605,X2604)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2605,tc_HOL_Obool),X2603),X2604))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2605,X2603)),c_Finite__Set_Ocard(X2605,X2604))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).
fof(i_0_797,plain,
! [X3200,X3201,X3202,X3203] :
( ~ class_Rings_Ocomm__semiring__1(X3203)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3203),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3203),X3202),X3201)),X3200) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3203),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3203),X3202),X3200)),X3201) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_798,plain,
! [X1922,X1923,X1924,X1925,X1926] :
( ( hAPP(X1924,X1923) != hAPP(X1924,X1922)
| X1923 = X1922
| ~ c_Fun_Oinj__on(X1926,X1925,X1924,c_Orderings_Otop__class_Otop(tc_fun(X1926,tc_HOL_Obool))) )
& ( X1923 != X1922
| hAPP(X1924,X1923) = hAPP(X1924,X1922)
| ~ c_Fun_Oinj__on(X1926,X1925,X1924,c_Orderings_Otop__class_Otop(tc_fun(X1926,tc_HOL_Obool))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).
fof(i_0_799,plain,
! [X1927,X1928,X1929,X1930,X1931] :
( ~ c_Fun_Oinj__on(X1931,X1930,X1929,c_Orderings_Otop__class_Otop(tc_fun(X1931,tc_HOL_Obool)))
| hAPP(X1929,X1928) != hAPP(X1929,X1927)
| X1928 = X1927 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).
fof(i_0_800,plain,
! [X1956,X1957,X1958,X1959,X1960] :
( ( X1959 = X1957
| c_SetInterval_Oord__class_OatLeastLessThan(X1960,X1959,X1958) != c_SetInterval_Oord__class_OatLeastLessThan(X1960,X1957,X1956)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1960),X1957),X1956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1960),X1959),X1958))
| ~ class_Orderings_Olinorder(X1960) )
& ( X1958 = X1956
| c_SetInterval_Oord__class_OatLeastLessThan(X1960,X1959,X1958) != c_SetInterval_Oord__class_OatLeastLessThan(X1960,X1957,X1956)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1960),X1957),X1956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1960),X1959),X1958))
| ~ class_Orderings_Olinorder(X1960) )
& ( X1959 != X1957
| X1958 != X1956
| c_SetInterval_Oord__class_OatLeastLessThan(X1960,X1959,X1958) = c_SetInterval_Oord__class_OatLeastLessThan(X1960,X1957,X1956)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1960),X1957),X1956))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1960),X1959),X1958))
| ~ class_Orderings_Olinorder(X1960) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).
fof(i_0_801,plain,
! [X1961,X1962,X1963,X1964,X1965] :
( ~ class_Orderings_Olinorder(X1965)
| c_SetInterval_Oord__class_OatLeastLessThan(X1965,X1964,X1963) != c_SetInterval_Oord__class_OatLeastLessThan(X1965,X1962,X1961)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1965),X1964),X1963))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1965),X1962),X1961))
| X1964 = X1962 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).
fof(i_0_802,plain,
! [X1966,X1967,X1968,X1969,X1970] :
( ~ class_Orderings_Olinorder(X1970)
| c_SetInterval_Oord__class_OatLeastLessThan(X1970,X1969,X1968) != c_SetInterval_Oord__class_OatLeastLessThan(X1970,X1967,X1966)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1970),X1969),X1968))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1970),X1967),X1966))
| X1968 = X1966 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).
fof(i_0_803,plain,
! [X2801,X2802,X2803] :
( X2803 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2802,X2802),tc_HOL_Obool))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2802,X2802),tc_HOL_Obool),X2803),X2801)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__by__empty])]) ).
fof(i_0_804,plain,
! [X2960,X2961] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2961),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2961),X2960)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_805,plain,
! [X2962,X2963] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2963),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2962),X2963)))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_806,plain,
! [X2678,X2679,X2680] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2680),X2679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2679),X2678))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2680)),X2678)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_807,plain,
! [X2530] :
( ~ c_Finite__Set_Ofinite(X2530,c_Orderings_Otop__class_Otop(tc_fun(X2530,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(X2530,c_Orderings_Otop__class_Otop(tc_fun(X2530,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).
fof(i_0_808,plain,
! [X2850,X2851] :
( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2851,tc_HOL_Obool)),X2850))
| hBOOL(hAPP(hAPP(c_member(X2851),X2850),c_Orderings_Obot__class_Obot(tc_fun(X2851,tc_HOL_Obool)))) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X2851),X2850),c_Orderings_Obot__class_Obot(tc_fun(X2851,tc_HOL_Obool))))
| hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2851,tc_HOL_Obool)),X2850)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).
fof(i_0_809,plain,
! [X2839,X2840] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2840,tc_HOL_Obool),X2839),c_Orderings_Obot__class_Obot(tc_fun(X2840,tc_HOL_Obool))))
| X2839 = c_Orderings_Obot__class_Obot(tc_fun(X2840,tc_HOL_Obool)) )
& ( X2839 != c_Orderings_Obot__class_Obot(tc_fun(X2840,tc_HOL_Obool))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2840,tc_HOL_Obool),X2839),c_Orderings_Obot__class_Obot(tc_fun(X2840,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).
fof(i_0_810,plain,
! [X2950,X2951,X2952,X2953] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2953,tc_HOL_Obool)) != c_Set_Oimage(X2952,X2953,X2951,X2950)
| X2950 = c_Orderings_Obot__class_Obot(tc_fun(X2952,tc_HOL_Obool)) )
& ( X2950 != c_Orderings_Obot__class_Obot(tc_fun(X2952,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X2953,tc_HOL_Obool)) = c_Set_Oimage(X2952,X2953,X2951,X2950) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).
fof(i_0_811,plain,
! [X2943,X2944,X2945,X2946] :
( ( c_Set_Oimage(X2946,X2945,X2944,X2943) != c_Orderings_Obot__class_Obot(tc_fun(X2945,tc_HOL_Obool))
| X2943 = c_Orderings_Obot__class_Obot(tc_fun(X2946,tc_HOL_Obool)) )
& ( X2943 != c_Orderings_Obot__class_Obot(tc_fun(X2946,tc_HOL_Obool))
| c_Set_Oimage(X2946,X2945,X2944,X2943) = c_Orderings_Obot__class_Obot(tc_fun(X2945,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).
fof(i_0_812,plain,
( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
& c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_1230_O_O_060N_125_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096])])]) ).
fof(i_0_813,plain,
! [X2685,X2686] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2686)),hAPP(c_Nat_OSuc,X2685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2686),X2685)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_814,plain,
! [X2668,X2669] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2669)),hAPP(c_Nat_OSuc,X2668)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2669),X2668)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2669),X2668))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2669)),hAPP(c_Nat_OSuc,X2668))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_815,plain,
! [X2627,X2628] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2628,X2627),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2628,X2627),tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2627,c_Orderings_Otop__class_Otop(tc_fun(X2627,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Finite__Set_Ofinite(X2628,c_Orderings_Otop__class_Otop(tc_fun(X2628,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).
fof(i_0_816,plain,
! [X1713,X1714,X1715,X1716] :
( ~ class_Orderings_Opreorder(X1716)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1716),X1715),X1714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1716),X1714),X1713))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1716),X1715),X1713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_817,plain,
! [X1709,X1710,X1711,X1712] :
( ~ class_Orderings_Oorder(X1712)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1712),X1711),X1710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1712),X1709),X1711))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1712),X1709),X1710)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_818,plain,
! [X2687,X2688] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2688,X2687)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2688),hAPP(c_Nat_OSuc,X2687)),
inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).
fof(i_0_819,plain,
! [X3122,X3123,X3124] :
( ( X3123 = c_Groups_Ozero__class_Ozero(X3124)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3124),X3123),X3122) != c_Groups_Ozero__class_Ozero(X3124)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3124,c_Groups_Ozero__class_Ozero(X3124)),X3122))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3124,c_Groups_Ozero__class_Ozero(X3124)),X3123))
| ~ class_Groups_Oordered__comm__monoid__add(X3124) )
& ( X3122 = c_Groups_Ozero__class_Ozero(X3124)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3124),X3123),X3122) != c_Groups_Ozero__class_Ozero(X3124)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3124,c_Groups_Ozero__class_Ozero(X3124)),X3122))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3124,c_Groups_Ozero__class_Ozero(X3124)),X3123))
| ~ class_Groups_Oordered__comm__monoid__add(X3124) )
& ( X3123 != c_Groups_Ozero__class_Ozero(X3124)
| X3122 != c_Groups_Ozero__class_Ozero(X3124)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3124),X3123),X3122) = c_Groups_Ozero__class_Ozero(X3124)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3124,c_Groups_Ozero__class_Ozero(X3124)),X3122))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3124,c_Groups_Ozero__class_Ozero(X3124)),X3123))
| ~ class_Groups_Oordered__comm__monoid__add(X3124) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_820,plain,
! [X2775,X2776] : c_Sum__Type_OPlus(X2776,X2775,c_Orderings_Otop__class_Otop(tc_fun(X2776,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2775,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2776,X2775),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(i_0_821,plain,
! [X2931,X2932,X2933] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2933),X2932))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2933),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2932),X2931))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_822,plain,
! [X2921,X2922,X2923] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2923),X2922))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2923),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2922),X2921))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_823,plain,
! [X2934,X2935,X2936] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2936),X2935))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2934),X2935))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_824,plain,
! [X2918,X2919,X2920] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2920),X2919))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2918),X2919))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_825,plain,
! [X2708,X2709,X2711,X2712,X2713] :
( ( X2709 = hAPP(c_Nat_OSuc,esk44_2(X2708,X2709))
| X2709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2709),hAPP(c_Nat_OSuc,X2708))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk44_2(X2708,X2709)),X2708))
| X2709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2709),hAPP(c_Nat_OSuc,X2708))) )
& ( X2712 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2712),hAPP(c_Nat_OSuc,X2711))) )
& ( X2712 != hAPP(c_Nat_OSuc,X2713)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2713),X2711))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2712),hAPP(c_Nat_OSuc,X2711))) ) ),
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_826,plain,
! [X3196,X3197,X3198,X3199] :
( ~ class_Rings_Ocomm__semiring__1(X3199)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3199),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3199),X3198),X3197)),X3196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3199),X3198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3199),X3197),X3196)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_827,plain,
! [X3019,X3020,X3021,X3022] :
( ~ class_Groups_Oab__semigroup__add(X3022)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3022),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3022),X3021),X3020)),X3019) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3022),X3021),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3022),X3020),X3019)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_828,plain,
! [X3192,X3193,X3194,X3195] :
( ~ class_Rings_Ocomm__semiring__1(X3195)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3195),X3194),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3195),X3193),X3192)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3195),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3195),X3194),X3193)),X3192) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_829,plain,
! [X2651,X2652] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2652)),hAPP(c_Nat_OSuc,X2651)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2652),X2651)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2652),X2651))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2652)),hAPP(c_Nat_OSuc,X2651))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_830,plain,
! [X2347,X2348,X2349,X2350] :
( ~ class_Orderings_Opreorder(X2350)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2350,X2349),X2348))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2350),X2348),X2347))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2350),X2349),X2347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_831,plain,
! [X2355,X2356,X2357,X2358] :
( ~ class_Orderings_Opreorder(X2358)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2358),X2357),X2356))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2358,X2356),X2355))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2358),X2357),X2355)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_832,plain,
! [X2343,X2344,X2345,X2346] :
( ~ class_Orderings_Oorder(X2346)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2346,X2345),X2344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2346),X2343),X2345))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2346),X2343),X2344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_833,plain,
! [X2351,X2352,X2353,X2354] :
( ~ class_Orderings_Oorder(X2354)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2354),X2353),X2352))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2354,X2351),X2353))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2354),X2351),X2352)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_834,plain,
! [X2329,X2330] :
( ( c_Finite__Set_Ofinite(X2330,c_Orderings_Otop__class_Otop(tc_fun(X2330,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2330,X2329),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2330,X2329),tc_HOL_Obool))) )
& ( c_Finite__Set_Ofinite(X2329,c_Orderings_Otop__class_Otop(tc_fun(X2329,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(tc_sum(X2330,X2329),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2330,X2329),tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2330,c_Orderings_Otop__class_Otop(tc_fun(X2330,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2329,c_Orderings_Otop__class_Otop(tc_fun(X2329,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_sum(X2330,X2329),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X2330,X2329),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_835,plain,
! [X2327,X2328] :
( ~ c_Finite__Set_Ofinite(X2328,c_Orderings_Otop__class_Otop(tc_fun(X2328,tc_HOL_Obool)))
| ~ c_Finite__Set_Ofinite(X2327,c_Orderings_Otop__class_Otop(tc_fun(X2327,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_prod(X2328,X2327),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X2328,X2327),tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).
fof(i_0_836,plain,
! [X2907,X2908,X2909,X2910] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2910),X2909))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2908),X2909) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2910),X2907)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2908),X2907)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_837,plain,
! [X2683,X2684] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2684)),X2683))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2684),X2683)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_838,plain,
! [X2655,X2656] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2656),X2655))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2655)),X2656)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2655)),X2656))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2656),X2655)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_538])]) ).
fof(i_0_839,plain,
! [X2786,X2787] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2787,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X2787,tc_HOL_Obool))),X2786)),
inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).
fof(i_0_840,plain,
! [X2630,X2631] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2631),X2630))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2631)),hAPP(c_Nat_OSuc,X2630))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_841,plain,
! [X2983,X2984,X2985] : c_FuncSet_OPi(X2985,X2984,c_Orderings_Obot__class_Obot(tc_fun(X2985,tc_HOL_Obool)),X2983) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2985,X2984),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Pi__empty]) ).
fof(i_0_842,plain,
! [X2823,X2824,X2825] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2825),X2824))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2825),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2824),X2823))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_843,plain,
! [X2798,X2799,X2800] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2800),X2799))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2800),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2799),X2798))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_844,plain,
! [X2820,X2821,X2822] :
( ~ 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2820),X2821))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_845,plain,
! [X2795,X2796,X2797] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2797),X2796))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2797),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2795),X2796))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_846,plain,
! [X2443,X2444] :
( ~ c_Finite__Set_Ofinite(tc_fun(X2444,X2443),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X2444,X2443),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2443,c_Orderings_Otop__class_Otop(tc_fun(X2443,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).
fof(i_0_847,plain,
! [X2664,X2665] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2665),X2664))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2664),hAPP(c_Nat_OSuc,X2665))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2664),hAPP(c_Nat_OSuc,X2665)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2665),X2664)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_539])]) ).
fof(i_0_848,plain,
! [X2761,X2762,X2763] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2763),X2762),c_SetInterval_Oord__class_OgreaterThan(X2763,X2761)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2763),X2761),X2762))
| ~ class_Orderings_Oord(X2763) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2763),X2761),X2762))
| hBOOL(hAPP(hAPP(c_member(X2763),X2762),c_SetInterval_Oord__class_OgreaterThan(X2763,X2761)))
| ~ class_Orderings_Oord(X2763) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).
fof(i_0_849,plain,
! [X2875,X2876,X2877] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2877),X2876)),X2875) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2877),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2876),X2875)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_850,plain,
! [X2726,X2727] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2727),X2726))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2727)),X2726)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2727)),X2726))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2727),X2726)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_851,plain,
! [X2722,X2723] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2723)),X2722))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2723),X2722)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2723),X2722))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2723)),X2722)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_852,plain,
! [X2714,X2715] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2715)),X2714))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2715),X2714)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_853,plain,
! [X3232,X3233,X3234,X3235,X3236] :
( ~ c_Finite__Set_Ofolding__one__idem(X3236,X3235,X3234)
| ~ c_Finite__Set_Ofinite(X3236,X3233)
| ~ hBOOL(hAPP(hAPP(c_member(X3236),X3232),X3233))
| hAPP(hAPP(X3235,X3232),hAPP(X3234,X3233)) = hAPP(X3234,X3233) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])]) ).
fof(i_0_854,plain,
! [X2291,X2292,X2293,X2294] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2294,tc_HOL_Obool),X2293),X2292))
| ~ hBOOL(hAPP(X2293,X2291))
| hBOOL(hAPP(X2292,X2291)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).
fof(i_0_855,plain,
! [X2306,X2307,X2308,X2309] :
( ~ hBOOL(hAPP(X2309,X2308))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2307,tc_HOL_Obool),X2309),X2306))
| hBOOL(hAPP(X2306,X2308)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).
fof(i_0_856,plain,
! [X2268,X2269,X2270,X2271] :
( ~ class_Orderings_Opreorder(X2271)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2271,X2270),X2269))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2271,X2269),X2268))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2271,X2270),X2268)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_857,plain,
! [X2261,X2262,X2263,X2264] :
( ~ class_Orderings_Oorder(X2264)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2264,X2263),X2262))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2264,X2261),X2263))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2264,X2261),X2262)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_858,plain,
! [X2676,X2677] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2677),X2676))
| hAPP(c_Nat_OSuc,X2677) = X2676
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2677)),X2676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_859,plain,
! [X1733,X1734,X1735] :
( ~ class_Orderings_Oorder(X1735)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1735),X1734),X1733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1735),X1733),X1734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_540])]) ).
fof(i_0_860,plain,
! [X1748,X1749,X1750] :
( ~ class_Orderings_Opreorder(X1750)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1750),X1749),X1748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1750),X1748),X1749)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_541])]) ).
fof(i_0_861,plain,
! [X1745,X1746,X1747] :
( ~ class_Orderings_Opreorder(X1747)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1747),X1746),X1745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1747),X1745),X1746)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_542])]) ).
fof(i_0_862,plain,
! [X1736,X1737,X1738] :
( ~ class_Orderings_Opreorder(X1738)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1738),X1737),X1736))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1738),X1736),X1737)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_543])]) ).
fof(i_0_863,plain,
! [X1706,X1707,X1708] :
( ~ class_Orderings_Opreorder(X1708)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1708),X1707),X1706))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1708),X1706),X1707)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_544])]) ).
fof(i_0_864,plain,
! [X1763,X1764,X1765] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1765),X1764),X1763))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1765),X1763),X1764))
| X1764 = X1763
| ~ class_Orderings_Olinorder(X1765) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1765),X1763),X1764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1765),X1764),X1763))
| ~ class_Orderings_Olinorder(X1765) )
& ( X1764 != X1763
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1765),X1764),X1763))
| ~ class_Orderings_Olinorder(X1765) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_545])])]) ).
fof(i_0_865,plain,
! [X2716,X2717] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2716),hAPP(c_Nat_OSuc,X2717)))
| X2716 = X2717
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2717),X2716)) )
& ( X2716 != X2717
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2716),hAPP(c_Nat_OSuc,X2717)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2717),X2716)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_866,plain,
! [X2639,X2640] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2640)),X2639))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2640),X2639)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_867,plain,
! [X2899,X2900] : ~ hBOOL(hAPP(hAPP(c_member(X2900),X2899),c_Orderings_Obot__class_Obot(tc_fun(X2900,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_546]) ).
fof(i_0_868,plain,
! [X2783,X2784] : ~ hBOOL(hAPP(hAPP(c_member(X2784),X2783),c_Orderings_Obot__class_Obot(tc_fun(X2784,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[i_0_547]) ).
fof(i_0_869,plain,
! [X2947,X2948,X2949] : c_Set_Oimage(X2949,X2948,X2947,c_Orderings_Obot__class_Obot(tc_fun(X2949,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2948,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_image__empty]) ).
fof(i_0_870,plain,
! [X2395,X2396,X2397] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2397,X2396),X2395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2397),X2396),X2395))
| ~ class_Orderings_Opreorder(X2397) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2397,X2395),X2396))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2397),X2396),X2395))
| ~ class_Orderings_Opreorder(X2397) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2397,X2396),X2395))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2397,X2395),X2396))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2397),X2396),X2395))
| ~ class_Orderings_Opreorder(X2397) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_548])])]) ).
fof(i_0_871,plain,
! [X2450,X2452,X2453,X2454] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2450)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2452),X2450))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2452),esk37_1(X2450))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk38_2(X2453,X2454)),X2453))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X2453) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk38_2(X2453,X2454)),X2454))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X2453) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded])])])])])]) ).
fof(i_0_872,plain,
! [X2681,X2682] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2682),hAPP(c_Nat_OSuc,X2681)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2682),X2681))
| X2682 = X2681 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_549])]) ).
fof(i_0_873,plain,
! [X2672,X2673] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2673),X2672))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2673),hAPP(c_Nat_OSuc,X2672)))
| X2672 = X2673 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_550])]) ).
fof(i_0_874,plain,
! [X2670,X2671] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2671),hAPP(c_Nat_OSuc,X2670)))
| X2671 = X2670
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2671),X2670)) )
& ( X2671 != X2670
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2671),hAPP(c_Nat_OSuc,X2670)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2671),X2670)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_551])])]) ).
fof(i_0_875,plain,
! [X2666,X2667] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2667),hAPP(c_Nat_OSuc,X2666)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2667),X2666))
| X2667 = X2666 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2667),X2666))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2667),hAPP(c_Nat_OSuc,X2666))) )
& ( X2667 != X2666
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2667),hAPP(c_Nat_OSuc,X2666))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_876,plain,
! [X2718,X2719] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2719),X2718))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2719)),X2718)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_877,plain,
! [X3188,X3189,X3190,X3191] :
( ~ class_Rings_Ocomm__semiring__1(X3191)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3191),X3190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3191),X3189),X3188)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3191),X3189),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3191),X3190),X3188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_878,plain,
! [X2566,X2567,X2568] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2568),X2567))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2567),X2566))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2568),X2566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_879,plain,
! [X2232,X2233,X2234] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2234,tc_HOL_Obool),X2233),X2232))
| ~ c_Finite__Set_Ofinite(X2234,X2232)
| c_Finite__Set_Ofinite(X2234,X2233) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).
fof(i_0_880,plain,
! [X2241,X2242,X2243] :
( ~ c_Finite__Set_Ofinite(X2243,X2242)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2243,tc_HOL_Obool),X2241),X2242))
| c_Finite__Set_Ofinite(X2243,X2241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).
fof(i_0_881,plain,
! [X2368,X2369,X2370] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2370),X2369),X2368))
| X2369 = X2368
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2370,X2369),X2368))
| ~ class_Orderings_Olinorder(X2370) )
& ( X2369 != X2368
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2370),X2369),X2368))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2370,X2369),X2368))
| ~ class_Orderings_Olinorder(X2370) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_552])])]) ).
fof(i_0_882,plain,
! [X2407,X2408,X2409] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2409),X2408),X2407))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2409,X2407),X2408))
| ~ class_Orderings_Olinorder(X2409) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2409,X2407),X2408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2409),X2408),X2407))
| ~ class_Orderings_Olinorder(X2409) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_553])])]) ).
fof(i_0_883,plain,
! [X2374,X2375,X2376] :
( ~ class_Orderings_Olinorder(X2376)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2376,X2375),X2374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2376),X2374),X2375)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_554])]) ).
fof(i_0_884,plain,
! [X2404,X2405,X2406] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2406,X2405),X2404))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2406),X2404),X2405))
| ~ class_Orderings_Olinorder(X2406) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2406),X2404),X2405))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2406,X2405),X2404))
| ~ class_Orderings_Olinorder(X2406) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_555])])]) ).
fof(i_0_885,plain,
! [X2964,X2965,X2967,X2968,X2969] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2965),X2964))
| X2964 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2965),esk49_2(X2964,X2965))) )
& ( X2967 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2968),X2969))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2968),X2967)) ) ),
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_886,plain,
! [X2977,X2978,X2979] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2979,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastLessThan(X2979,X2978,X2977)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2979),X2978),X2977))
| ~ class_Orderings_Oorder(X2979) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2979),X2978),X2977))
| c_Orderings_Obot__class_Obot(tc_fun(X2979,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X2979,X2978,X2977)
| ~ class_Orderings_Oorder(X2979) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_556])])]) ).
fof(i_0_887,plain,
! [X2974,X2975,X2976] :
( ( c_SetInterval_Oord__class_OatLeastLessThan(X2976,X2975,X2974) != c_Orderings_Obot__class_Obot(tc_fun(X2976,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2976),X2975),X2974))
| ~ class_Orderings_Oorder(X2976) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2976),X2975),X2974))
| c_SetInterval_Oord__class_OatLeastLessThan(X2976,X2975,X2974) = c_Orderings_Obot__class_Obot(tc_fun(X2976,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X2976) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_557])])]) ).
fof(i_0_888,plain,
! [X2788,X2789,X2790] : c_Fun_Oinj__on(X2790,X2789,X2788,c_Orderings_Obot__class_Obot(tc_fun(X2790,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).
fof(i_0_889,plain,
! [X2724,X2725] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2725),hAPP(c_Nat_OSuc,X2724)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2725),X2724)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2725),X2724))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2725),hAPP(c_Nat_OSuc,X2724))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_890,plain,
! [X2574,X2576,X2577,X2578] :
( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2574)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2576),X2574))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2576),esk40_1(X2574))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk41_2(X2577,X2578)),X2577))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X2577) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk41_2(X2577,X2578)),X2578))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X2577) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded__le])])])])])]) ).
fof(i_0_891,plain,
! [X2781,X2782] :
( ( X2781 != c_Orderings_Obot__class_Obot(tc_fun(X2782,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(X2782,X2781))) )
& ( c_Finite__Set_Ofinite(X2782,X2781)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2782,X2781))) )
& ( X2781 = c_Orderings_Obot__class_Obot(tc_fun(X2782,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X2782,X2781)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2782,X2781))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).
fof(i_0_892,plain,
! [X2674,X2675] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2675),X2674))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2675),hAPP(c_Nat_OSuc,X2674))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_893,plain,
! [X2746,X2747,X2748,X2749] : c_Nat_Onat_Onat__case(X2749,X2748,X2747,hAPP(c_Nat_OSuc,X2746)) = hAPP(X2747,X2746),
inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).
fof(i_0_894,plain,
! [X2653,X2654] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2654),hAPP(c_Nat_OSuc,X2653)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2654),X2653))
| X2654 = hAPP(c_Nat_OSuc,X2653) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2654),X2653))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2654),hAPP(c_Nat_OSuc,X2653))) )
& ( X2654 != hAPP(c_Nat_OSuc,X2653)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2654),hAPP(c_Nat_OSuc,X2653))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_895,plain,
! [X2641,X2642] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2642),hAPP(c_Nat_OSuc,X2641)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2642),X2641))
| X2642 = hAPP(c_Nat_OSuc,X2641) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_558])]) ).
fof(i_0_896,plain,
! [X2424,X2425] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2425,tc_HOL_Obool),X2424),c_Orderings_Otop__class_Otop(tc_fun(X2425,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).
fof(i_0_897,plain,
! [X1771,X1772,X1773] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1772),X1773))
| hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| X1773 = X1772
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1773),X1772)) )
& ( ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| X1773 = X1772
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1773),X1772)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1772),X1773))
| hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1773),X1772)) )
& ( ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1773),X1772)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1772),X1773))
| hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| X1773 = X1772
| ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773)) )
& ( ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| X1773 = X1772
| ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1772),X1773))
| hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773)) )
& ( ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773))
| ~ hBOOL(hAPP(hAPP(X1771,X1772),X1773)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_898,plain,
! [X2872,X2873,X2874] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2874),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2873),X2872)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2873),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2874),X2872)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_899,plain,
! [X2310,X2311,X2312] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2312,X2311),X2310))
| X2311 != X2310
| ~ class_Orderings_Oorder(X2312) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2312,X2310),X2311))
| X2311 != X2310
| ~ class_Orderings_Oorder(X2312) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2312,X2311),X2310))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2312,X2310),X2311))
| X2311 = X2310
| ~ class_Orderings_Oorder(X2312) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_900,plain,
! [X2295,X2296,X2297] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2297,X2295),X2296))
| X2295 = X2296
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2297,X2296),X2295))
| ~ class_Orderings_Oorder(X2297) )
& ( X2295 != X2296
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2297,X2295),X2296))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2297,X2296),X2295))
| ~ class_Orderings_Oorder(X2297) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_901,plain,
! [X2272,X2273,X2274] :
( ~ class_Orderings_Oorder(X2274)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2274,X2273),X2272))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2274,X2272),X2273))
| X2273 = X2272 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_902,plain,
! [X2265,X2266,X2267] :
( ~ class_Orderings_Oorder(X2267)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2267,X2266),X2265))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2267,X2265),X2266))
| X2265 = X2266 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_903,plain,
! [X2508,X2509] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Finite__Set_Ocard(X2509,X2508)))
| c_Finite__Set_Ofinite(X2509,X2508) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).
fof(i_0_904,plain,
! [X2657] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2657)),X2657)),
inference(variable_rename,[status(thm)],[i_0_559]) ).
fof(i_0_905,plain,
! [X2720,X2721] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2721),X2720))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2721),hAPP(c_Nat_OSuc,X2720))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_906,plain,
! [X2496,X2497] :
( ~ c_Finite__Set_Ofinite(X2497,c_Orderings_Otop__class_Otop(tc_fun(X2497,tc_HOL_Obool)))
| c_Finite__Set_Ocard(X2497,X2496) != c_Finite__Set_Ocard(X2497,c_Orderings_Otop__class_Otop(tc_fun(X2497,tc_HOL_Obool)))
| X2496 = c_Orderings_Otop__class_Otop(tc_fun(X2497,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
fof(i_0_907,plain,
! [X2398,X2399,X2400] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2400,X2399),X2398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2400),X2399),X2398))
| ~ class_Orderings_Oorder(X2400) )
& ( X2399 != X2398
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2400),X2399),X2398))
| ~ class_Orderings_Oorder(X2400) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2400,X2399),X2398))
| X2399 = X2398
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2400),X2399),X2398))
| ~ class_Orderings_Oorder(X2400) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_908,plain,
! [X2392,X2393,X2394] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2394,X2393),X2392))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2394),X2393),X2392))
| X2393 = X2392
| ~ class_Orderings_Oorder(X2394) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2394),X2393),X2392))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2394,X2393),X2392))
| ~ class_Orderings_Oorder(X2394) )
& ( X2393 != X2392
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2394,X2393),X2392))
| ~ class_Orderings_Oorder(X2394) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_909,plain,
! [X2371,X2372,X2373] :
( ~ class_Orderings_Opreorder(X2373)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2373),X2372),X2371))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2373,X2372),X2371)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_910,plain,
! [X2835,X2836] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2836),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2836),X2835))),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_911,plain,
! [X2837,X2838] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2837),X2838))),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_912,plain,
! [X1871,X1872] : c_Set_Oimage(X1872,X1872,c_COMBI(X1872),X1871) = X1871,
inference(variable_rename,[status(thm)],[fact_image__ident]) ).
fof(i_0_913,plain,
! [X1879,X1880] : c_Fun_Oinj__on(X1880,X1880,c_COMBI(X1880),X1879),
inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).
fof(i_0_914,plain,
! [X2743,X2744,X2745] : c_Nat_Onat_Onat__case(X2745,X2744,X2743,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2744,
inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).
fof(i_0_915,plain,
! [X2380,X2381,X2382] :
( ~ class_Orderings_Oorder(X2382)
| X2381 = X2380
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2382,X2381),X2380))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2382),X2381),X2380)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_916,plain,
! [X2365,X2366,X2367] :
( ~ class_Orderings_Oorder(X2367)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2367,X2366),X2365))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2367),X2366),X2365))
| X2366 = X2365 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_917,plain,
! [X2362,X2363,X2364] :
( ~ class_Orderings_Oorder(X2364)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2364,X2363),X2362))
| X2363 = X2362
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2364),X2363),X2362)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_918,plain,
! [X2359,X2360,X2361] :
( ~ class_Orderings_Oorder(X2361)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2361,X2360),X2359))
| X2359 = X2360
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2361),X2360),X2359)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_919,plain,
! [X2383,X2384,X2385] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2385,X2384),X2383))
| X2384 = X2383
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2385),X2384),X2383))
| ~ class_Orderings_Olinorder(X2385) )
& ( X2384 != X2383
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2385,X2384),X2383))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2385),X2384),X2383))
| ~ class_Orderings_Olinorder(X2385) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_560])])]) ).
fof(i_0_920,plain,
! [X2377,X2378,X2379] :
( ~ class_Orderings_Oorder(X2379)
| X2378 = X2377
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2379,X2377),X2378))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2379),X2377),X2378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_921,plain,
! [X2707] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2707),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X2707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2707 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2707),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_922,plain,
! [X2702] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X2702),
inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).
fof(i_0_923,plain,
! [X2564,X2565] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2565),X2564))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2564),X2565))
| X2565 = X2564 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_924,plain,
! [X1690,X1691,X1692] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1692),X1691),hAPP(c_fequal,X1690)))
| X1691 = X1690 )
& ( X1691 != X1690
| hBOOL(hAPP(hAPP(c_member(X1692),X1691),hAPP(c_fequal,X1690))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).
fof(i_0_925,plain,
! [X2649,X2650] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2650),X2649))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2650),hAPP(c_Nat_OSuc,X2649))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_926,plain,
! [X2893,X2894,X2895,X2896,X2897] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2894),X2895),X2893))
| X2893 != c_Orderings_Obot__class_Obot(tc_fun(X2894,tc_HOL_Obool)) )
& ( X2896 = c_Orderings_Obot__class_Obot(tc_fun(X2897,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X2897),esk48_2(X2896,X2897)),X2896)) ) ),
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__in__conv])])])])]) ).
fof(i_0_927,plain,
! [X2887,X2888,X2890,X2891,X2892] :
( ( hBOOL(hAPP(hAPP(c_member(X2888),esk47_2(X2887,X2888)),X2887))
| X2887 = c_Orderings_Obot__class_Obot(tc_fun(X2888,tc_HOL_Obool)) )
& ( X2890 != c_Orderings_Obot__class_Obot(tc_fun(X2891,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2891),X2892),X2890)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_561])])])])]) ).
fof(i_0_928,plain,
! [X2592,X2593] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2593),X2592))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2593),X2592)) )
& ( X2593 != X2592
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2593),X2592)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_929,plain,
! [X2588,X2589] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2589),X2588))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2589),X2588)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_930,plain,
! [X2586,X2587] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2587),X2586))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2587),X2586))
| X2587 = X2586 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2587),X2586))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2587),X2586)) )
& ( X2587 != X2586
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2587),X2586)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_931,plain,
! [X2584,X2585] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2585),X2584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2585),X2584)) )
& ( X2585 != X2584
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2585),X2584)) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2585),X2584))
| X2585 = X2584
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2585),X2584)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_932,plain,
! [X2582,X2583] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2583),X2582))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2583),X2582)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_933,plain,
! [X1766,X1767,X1768] :
( ( X1767 = X1766
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1768),X1767),X1766))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1768),X1766),X1767))
| ~ class_Orderings_Olinorder(X1768) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1768),X1767),X1766))
| X1767 != X1766
| ~ class_Orderings_Olinorder(X1768) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1768),X1766),X1767))
| X1767 != X1766
| ~ class_Orderings_Olinorder(X1768) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_934,plain,
! [X3172,X3173,X3174] :
( ~ class_Rings_Olinordered__idom(X3174)
| X3173 = X3172
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3174),X3173),X3172))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3174),X3172),X3173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_562])]) ).
fof(i_0_935,plain,
! [X1760,X1761,X1762] :
( ~ class_Orderings_Olinorder(X1762)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1762),X1761),X1760))
| X1761 = X1760
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1762),X1760),X1761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_936,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_563])])]) ).
fof(i_0_937,plain,
! [X1754,X1755,X1756] :
( ~ class_Orderings_Olinorder(X1756)
| X1755 = X1754
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1756),X1755),X1754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1756),X1754),X1755)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_564])]) ).
fof(i_0_938,plain,
! [X1703,X1704,X1705] :
( ~ class_Orderings_Olinorder(X1705)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1705),X1704),X1703))
| X1704 = X1703
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1705),X1703),X1704)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_565])]) ).
fof(i_0_939,plain,
! [X2331] :
( ( ~ c_Finite__Set_Ofinite(tc_Option_Ooption(X2331),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2331),tc_HOL_Obool)))
| c_Finite__Set_Ofinite(X2331,c_Orderings_Otop__class_Otop(tc_fun(X2331,tc_HOL_Obool))) )
& ( ~ c_Finite__Set_Ofinite(X2331,c_Orderings_Otop__class_Otop(tc_fun(X2331,tc_HOL_Obool)))
| c_Finite__Set_Ofinite(tc_Option_Ooption(X2331),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X2331),tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).
fof(i_0_940,plain,
! [X2970,X2971,X2972] :
( ~ class_Orderings_Oorder(X2972)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2972,X2971),X2970))
| c_SetInterval_Oord__class_OatLeastLessThan(X2972,X2970,X2971) = c_Orderings_Obot__class_Obot(tc_fun(X2972,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty])]) ).
fof(i_0_941,plain,
! [X2590,X2591] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2591),X2590))
| X2591 = X2590
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2591),X2590)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_942,plain,
! [X2901,X2902,X2903] :
( X2903 != c_Orderings_Obot__class_Obot(tc_fun(X2902,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2902),X2901),X2903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_566])]) ).
fof(i_0_943,plain,
! [X1971,X1972] : hBOOL(hAPP(hAPP(c_member(X1972),X1971),c_Orderings_Otop__class_Otop(tc_fun(X1972,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(i_0_944,plain,
! [X1783,X1784] : hBOOL(hAPP(hAPP(c_member(X1784),X1783),c_Orderings_Otop__class_Otop(tc_fun(X1784,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).
fof(i_0_945,plain,
! [X1856,X1857,X1858] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X1858),X1857),X1856))
| hBOOL(hAPP(X1856,X1857)) )
& ( ~ hBOOL(hAPP(X1856,X1857))
| hBOOL(hAPP(hAPP(c_member(X1858),X1857),X1856)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
fof(i_0_946,plain,
! [X2401,X2402,X2403] :
( ~ class_Orderings_Olinorder(X2403)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2403,X2402),X2401))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2403),X2401),X2402)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_947,plain,
! [X2386,X2387,X2388] :
( ~ class_Orderings_Olinorder(X2388)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2388,X2387),X2386))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2388),X2386),X2387)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_567])]) ).
fof(i_0_948,plain,
! [X2389,X2390,X2391] :
( ~ class_Orderings_Olinorder(X2391)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2391),X2390),X2389))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2391,X2389),X2390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_949,plain,
! [X2846,X2847] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2847)),X2846) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2847),X2846)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_950,plain,
! [X2829,X2830,X2832,X2833,X2834] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2830),X2829))
| X2829 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2830),esk45_2(X2829,X2830)) )
& ( X2832 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2833),X2834)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2833),X2832)) ) ),
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_951,plain,
! [X1684,X1685] :
( X1685 = X1684
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1685),X1684))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1684),X1685)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_569])]) ).
fof(i_0_952,plain,
! [X1682,X1683] :
( ( X1683 = X1682
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1683),X1682))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1682),X1683)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1683),X1682))
| X1683 != X1682 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1682),X1683))
| X1683 != X1682 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_953,plain,
! [X2703,X2705,X2706] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2703))
| X2703 = hAPP(c_Nat_OSuc,esk43_1(X2703)) )
& ( X2705 != hAPP(c_Nat_OSuc,X2706)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2705)) ) ),
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_954,plain,
! [X1751,X1752,X1753] :
( ~ class_Orderings_Oorder(X1753)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1753),X1752),X1751))
| X1752 != X1751 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_955,plain,
! [X1742,X1743,X1744] :
( ~ class_Orderings_Oorder(X1744)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1744),X1743),X1742))
| X1743 != X1742 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_956,plain,
! [X1739,X1740,X1741] :
( ~ class_Orderings_Oorder(X1741)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1741),X1740),X1739))
| X1739 != X1740 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_957,plain,
! [X2225,X2226,X2227] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2225,tc_HOL_Obool),X2227),X2226))
| X2227 != X2226 )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2225,tc_HOL_Obool),X2226),X2227))
| X2227 != X2226 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_570])])]) ).
fof(i_0_958,plain,
! [X2238,X2239,X2240] :
( X2240 != X2239
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2238,tc_HOL_Obool),X2240),X2239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).
fof(i_0_959,plain,
! [X2235,X2236,X2237] :
( X2237 != X2236
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2235,tc_HOL_Obool),X2236),X2237)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).
fof(i_0_960,plain,
! [X1769,X1770] :
( ~ class_Orderings_Opreorder(X1770)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1770),X1769),X1769)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_571])]) ).
fof(i_0_961,plain,
! [X2249,X2250] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2250,tc_HOL_Obool),X2249),X2249)),
inference(variable_rename,[status(thm)],[fact_subset__refl]) ).
fof(i_0_962,plain,
! [X1701] :
( ( X1701 = 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)),X1701)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1701))
| X1701 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_963,plain,
! [X3039,X3040,X3041,X3042] :
( ~ class_Groups_Ocancel__semigroup__add(X3042)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3042),X3041),X3040) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3042),X3039),X3040)
| X3041 = X3039 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_964,plain,
! [X3027,X3028,X3029,X3030] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3030),X3029),X3028) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3030),X3027),X3028)
| X3029 = X3027
| ~ class_Groups_Ocancel__semigroup__add(X3030) )
& ( X3029 != X3027
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3030),X3029),X3028) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3030),X3027),X3028)
| ~ class_Groups_Ocancel__semigroup__add(X3030) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_965,plain,
! [X3035,X3036,X3037,X3038] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3038)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3038),X3037),X3036) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3038),X3037),X3035)
| X3036 = X3035 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_966,plain,
! [X3031,X3032,X3033,X3034] :
( ~ class_Groups_Ocancel__semigroup__add(X3034)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3034),X3033),X3032) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3034),X3033),X3031)
| X3032 = X3031 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_967,plain,
! [X3023,X3024,X3025,X3026] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3026),X3025),X3024) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3026),X3025),X3023)
| X3024 = X3023
| ~ class_Groups_Ocancel__semigroup__add(X3026) )
& ( X3024 != X3023
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3026),X3025),X3024) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3026),X3025),X3023)
| ~ class_Groups_Ocancel__semigroup__add(X3026) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_968,plain,
! [X2313,X2314,X2315] :
( ~ class_Orderings_Olinorder(X2315)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2315,X2314),X2313))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2315,X2313),X2314)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_969,plain,
! [X2253,X2254,X2255] :
( ~ class_Orderings_Olinorder(X2255)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2255,X2254),X2253))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2255,X2253),X2254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_572])]) ).
fof(i_0_970,plain,
! [X2848,X2849] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2849),hAPP(c_Nat_OSuc,X2848)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2849),X2848)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_971,plain,
! [X2844,X2845] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2845)),X2844) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2845),hAPP(c_Nat_OSuc,X2844)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_972,plain,
! [X1702] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1702),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_573]) ).
fof(i_0_973,plain,
! [X1700] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1700),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_574]) ).
fof(i_0_974,plain,
! [X1689] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1689),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[i_0_575]) ).
fof(i_0_975,plain,
! [X3178] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3178)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,X3178)),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_976,plain,
! [X1698,X1699] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1699),X1698))
| X1698 != 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_977,plain,
! [X2571,X2572] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2572),X2571))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2571),X2572)) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_978,plain,
! [X2632] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2632))),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_979,plain,
! [X1774,X1775] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1775),X1774))
| X1775 != X1774 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_980,plain,
! [X1687,X1688] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1688),X1687))
| X1687 != X1688 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_981,plain,
! [X1686] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1686),X1686)),
inference(variable_rename,[status(thm)],[i_0_576]) ).
fof(i_0_982,plain,
! [X1681] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1681),X1681)),
inference(variable_rename,[status(thm)],[i_0_577]) ).
fof(i_0_983,plain,
! [X2881,X2882,X2883] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2883),X2882) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2881),X2882)
| X2883 = X2881 )
& ( X2883 != X2881
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2883),X2882) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2881),X2882) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_984,plain,
! [X2878,X2879,X2880] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2880),X2879) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2880),X2878)
| X2879 = X2878 )
& ( X2879 != X2878
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2880),X2879) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2880),X2878) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_985,plain,
! [X2629] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2629),hAPP(c_Nat_OSuc,X2629))),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_986,plain,
! [X1674,X1675] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1675,tc_HOL_Obool)),X1674)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(i_0_987,plain,
! [X2580] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2580),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X2580 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2580 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2580),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).
fof(i_0_988,plain,
! [X2956,X2957] :
( ( X2957 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2957 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2957),X2956) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2956 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2957 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2957),X2956) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2957 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2956 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2957),X2956) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2956 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2956 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2957),X2956) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2957 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2956 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2957),X2956) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2957 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2956 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2957),X2956) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])]) ).
fof(i_0_989,plain,
! [X2954,X2955] :
( ( X2955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2955 = 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),X2955),X2954) )
& ( X2954 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2955 = 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),X2955),X2954) )
& ( X2955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2954 = 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),X2955),X2954) )
& ( X2954 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2954 = 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),X2955),X2954) )
& ( X2955 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2954 != 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),X2955),X2954) )
& ( X2955 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2954 != 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),X2955),X2954) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_990,plain,
! [X1671,X1672] :
( hAPP(X1672,esk1_2(X1671,X1672)) != hAPP(X1671,esk1_2(X1671,X1672))
| X1672 = X1671 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_991,plain,
! [X3228,X3229,X3230,X3231] :
( ~ c_Finite__Set_Ofolding__one__idem(X3231,X3230,X3229)
| hAPP(hAPP(X3230,X3228),X3228) = X3228 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])]) ).
fof(i_0_992,plain,
! [X3338,X3339] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X3339),X3338))
| X3339 = X3338 ),
inference(variable_rename,[status(thm)],[i_0_578]) ).
fof(i_0_993,plain,
! [X2210,X2211] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2211,X2210)),
inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).
fof(i_0_994,plain,
! [X3177] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X3177)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X3177)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[fact_nat_Osize_I2_J]) ).
fof(i_0_995,plain,
! [X2852,X2853] :
( ~ class_Orderings_Obot(X2853)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2853,c_Orderings_Obot__class_Obot(X2853)),X2852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).
fof(i_0_996,plain,
! [X3185,X3186,X3187] :
( ~ class_Rings_Ocomm__semiring__1(X3187)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3187),X3186),X3185) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3187),X3185),X3186) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_997,plain,
! [X1697] :
( X1697 = 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)),X1697)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_998,plain,
! [X2422,X2423] :
( ~ class_Orderings_Otop(X2423)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2423,X2422),c_Orderings_Otop__class_Otop(X2423))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).
fof(i_0_999,plain,
! [X3175,X3176] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3176),X3175),X3175) != c_Groups_Ozero__class_Ozero(X3176)
| X3175 = c_Groups_Ozero__class_Ozero(X3176)
| ~ class_Groups_Olinordered__ab__group__add(X3176) )
& ( X3175 != c_Groups_Ozero__class_Ozero(X3176)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3176),X3175),X3175) = c_Groups_Ozero__class_Ozero(X3176)
| ~ class_Groups_Olinordered__ab__group__add(X3176) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_1000,plain,
! [X3076,X3077] :
( ( c_Groups_Ozero__class_Ozero(X3077) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3077),X3076),X3076)
| X3076 = c_Groups_Ozero__class_Ozero(X3077)
| ~ class_Groups_Olinordered__ab__group__add(X3077) )
& ( X3076 != c_Groups_Ozero__class_Ozero(X3077)
| c_Groups_Ozero__class_Ozero(X3077) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3077),X3076),X3076)
| ~ class_Groups_Olinordered__ab__group__add(X3077) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_1001,plain,
! [X3180,X3181,X3182] :
( ( X3181 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3182),X3181),X3180)
| X3180 = c_Groups_Ozero__class_Ozero(X3182)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3182) )
& ( X3180 != c_Groups_Ozero__class_Ozero(X3182)
| X3181 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3182),X3181),X3180)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3182) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_1002,plain,
! [X2303,X2304,X2305] :
( ~ class_Orderings_Opreorder(X2305)
| X2304 != X2303
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2305,X2304),X2303)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_1003,plain,
! [X3316,X3317,X3318,X3319] : hAPP(hAPP(c_COMBK(X3319,X3318),X3317),X3316) = X3317,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(i_0_1004,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__nat]) ).
fof(i_0_1005,plain,
! [X2870,X2871] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2871),X2870) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2870),X2871),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_1006,plain,
! [X2205,X2206] :
( ~ class_Orderings_Opreorder(X2206)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2206,X2205),X2205)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_1007,plain,
! [X2581] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2581)),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_1008,plain,
! [X2563] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2563)),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_1009,plain,
! [X2841] : c_Orderings_Otop__class_Otop(tc_fun(X2841,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X2841,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_UNIV__not__empty]) ).
fof(i_0_1010,plain,
! [X2867,X2868,X2869] :
( ~ class_Orderings_Obot(X2869)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2868,X2869)),X2867) = c_Orderings_Obot__class_Obot(X2869) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).
fof(i_0_1011,plain,
! [X2864,X2865,X2866] :
( ~ class_Orderings_Obot(X2866)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2865,X2866)),X2864) = c_Orderings_Obot__class_Obot(X2866) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).
fof(i_0_1012,plain,
! [X1677,X1678,X1679] :
( ~ class_Orderings_Otop(X1679)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1678,X1679)),X1677) = c_Orderings_Otop__class_Otop(X1679) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).
fof(i_0_1013,plain,
! [X2939,X2940] :
( ( X2940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2940),X2939) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2940),X2939) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2940 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2939 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2940),X2939) = 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_1014,plain,
! [X2982] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2982,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan0]) ).
fof(i_0_1015,plain,
! [X2569,X2570] :
( X2570 != X2569
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2570),X2569)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_1016,plain,
! [X3340,X3341] :
( X3341 != X3340
| hBOOL(hAPP(hAPP(c_fequal,X3341),X3340)) ),
inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).
fof(i_0_1017,plain,
! [X2941,X2942] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2942),X2941) != X2942
| X2941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])]) ).
fof(i_0_1018,plain,
! [X2989,X2990] :
( ( c_Finite__Set_Ocard(X2990,X2989) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2989 = c_Orderings_Obot__class_Obot(tc_fun(X2990,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X2990,X2989) )
& ( X2989 != c_Orderings_Obot__class_Obot(tc_fun(X2990,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2990,X2989) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Finite__Set_Ofinite(X2990,X2989)
| c_Finite__Set_Ocard(X2990,X2989) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_579])])]) ).
fof(i_0_1019,plain,
! [X2573] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2573),X2573)),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_1020,plain,
! [X2456] :
( ~ class_Finite__Set_Ofinite(X2456)
| c_Finite__Set_Ofinite(X2456,c_Orderings_Otop__class_Otop(tc_fun(X2456,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).
fof(i_0_1021,plain,
! [X3209,X3210] :
( ~ class_Rings_Ocomm__semiring__1(X3210)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3210),c_Groups_Ozero__class_Ozero(X3210)),X3209) = X3209 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_1022,plain,
! [X3080,X3081] :
( ~ class_Groups_Omonoid__add(X3081)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3081),c_Groups_Ozero__class_Ozero(X3081)),X3080) = X3080 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_1023,plain,
! [X3078,X3079] :
( ~ class_Groups_Ocomm__monoid__add(X3079)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3079),c_Groups_Ozero__class_Ozero(X3079)),X3078) = X3078 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_1024,plain,
! [X2973] : c_Finite__Set_Ocard(X2973,c_Orderings_Obot__class_Obot(tc_fun(X2973,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_card_Oempty]) ).
fof(i_0_1025,plain,
! [X3183,X3184] :
( ~ class_Rings_Ocomm__semiring__1(X3184)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3184),X3183),c_Groups_Ozero__class_Ozero(X3184)) = X3183 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_1026,plain,
! [X3074,X3075] :
( ~ class_Groups_Omonoid__add(X3075)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3075),X3074),c_Groups_Ozero__class_Ozero(X3075)) = X3074 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_1027,plain,
! [X3072,X3073] :
( ~ class_Groups_Ocomm__monoid__add(X3073)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3073),X3072),c_Groups_Ozero__class_Ozero(X3073)) = X3072 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_1028,plain,
! [X2886] : c_Finite__Set_Ofinite(X2886,c_Orderings_Obot__class_Obot(tc_fun(X2886,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J]) ).
fof(i_0_1029,plain,
! [X2785] : c_Finite__Set_Ofinite(X2785,c_Orderings_Obot__class_Obot(tc_fun(X2785,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_finite_OemptyI]) ).
fof(i_0_1030,plain,
! [X2758,X2759,X2760] :
( ( c_SetInterval_Oord__class_OgreaterThan(X2760,X2759) != c_SetInterval_Oord__class_OgreaterThan(X2760,X2758)
| X2759 = X2758
| ~ class_Orderings_Olinorder(X2760) )
& ( X2759 != X2758
| c_SetInterval_Oord__class_OgreaterThan(X2760,X2759) = c_SetInterval_Oord__class_OgreaterThan(X2760,X2758)
| ~ class_Orderings_Olinorder(X2760) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])]) ).
fof(i_0_1031,plain,
! [X2937] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2937) = X2937,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_1032,plain,
! [X2728] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2728) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2728)),
inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(i_0_1033,plain,
! [X2938] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2938),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2938,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_1034,plain,
! [X3309,X3310] :
( ~ class_Finite__Set_Ofinite(X3310)
| ~ class_Finite__Set_Ofinite(X3309)
| class_Finite__Set_Ofinite(tc_sum(X3310,X3309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).
fof(i_0_1035,plain,
! [X3312,X3313] :
( ~ class_Finite__Set_Ofinite(X3313)
| ~ class_Finite__Set_Ofinite(X3312)
| class_Finite__Set_Ofinite(tc_prod(X3313,X3312)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).
fof(i_0_1036,plain,
! [X3299,X3300] :
( ~ class_Finite__Set_Ofinite(X3300)
| ~ class_Finite__Set_Ofinite(X3299)
| class_Finite__Set_Ofinite(tc_fun(X3300,X3299)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).
fof(i_0_1037,plain,
! [X2691,X2692] :
( ( hAPP(c_Nat_OSuc,X2692) != hAPP(c_Nat_OSuc,X2691)
| X2692 = X2691 )
& ( X2692 != X2691
| hAPP(c_Nat_OSuc,X2692) = hAPP(c_Nat_OSuc,X2691) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1038,plain,
! [X2689,X2690] :
( hAPP(c_Nat_OSuc,X2690) != hAPP(c_Nat_OSuc,X2689)
| X2690 = X2689 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1039,plain,
! [X3307,X3308] :
( ~ class_Orderings_Obot(X3308)
| class_Orderings_Obot(tc_fun(X3307,X3308)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).
fof(i_0_1040,plain,
! [X3305,X3306] :
( ~ class_Orderings_Oord(X3306)
| class_Orderings_Oord(tc_fun(X3305,X3306)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_1041,plain,
! [X3301,X3302] :
( ~ class_Orderings_Oorder(X3302)
| class_Orderings_Oorder(tc_fun(X3301,X3302)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_1042,plain,
! [X3297,X3298] :
( ~ class_Orderings_Opreorder(X3298)
| class_Orderings_Opreorder(tc_fun(X3297,X3298)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_1043,plain,
! [X3303,X3304] :
( ~ class_Orderings_Otop(X3304)
| class_Orderings_Otop(tc_fun(X3303,X3304)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).
fof(i_0_1044,plain,
! [X2490,X2491] :
( c_Finite__Set_Ofinite(X2491,X2490)
| c_Finite__Set_Ocard(X2491,X2490) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_580])]) ).
fof(i_0_1045,plain,
! [X2661] : hAPP(c_Nat_OSuc,X2661) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1046,plain,
! [X2660] : hAPP(c_Nat_OSuc,X2660) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1047,plain,
! [X2658] : hAPP(c_Nat_OSuc,X2658) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1048,plain,
! [X2663] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2663),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1049,plain,
! [X2662] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2662),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1050,plain,
! [X2659] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2659),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1051,plain,
! [X2251,X2252] :
( ~ class_Finite__Set_Ofinite(X2252)
| c_Finite__Set_Ofinite(X2252,X2251) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).
fof(i_0_1052,plain,
! [X2247,X2248] :
( ~ class_Finite__Set_Ofinite(X2248)
| c_Finite__Set_Ofinite(X2248,X2247) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).
fof(i_0_1053,plain,
! [X2693] : hAPP(c_Nat_OSuc,X2693) != X2693,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1054,plain,
! [X2694] : X2694 != hAPP(c_Nat_OSuc,X2694),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1055,plain,
! [X3314,X3315] : hAPP(c_COMBI(X3315),X3314) = X3314,
inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).
fof(i_0_1056,plain,
! [X3311] :
( ~ class_Finite__Set_Ofinite(X3311)
| class_Finite__Set_Ofinite(tc_Option_Ooption(X3311)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).
fof(i_0_1057,plain,
! [X3179] : c_Nat_Osize__class_Osize(tc_Nat_Onat,X3179) = X3179,
inference(variable_rename,[status(thm)],[fact_nat__size]) ).
fof(i_0_1058,plain,
~ hBOOL(c_fFalse),
inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).
cnf(i_0_1059,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),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____))),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_581]),
[final] ).
cnf(i_0_1060,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_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____)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_Lab____)),v_Lba____)))),
inference(split_conjunct,[status(thm)],[i_0_582]),
[final] ).
cnf(i_0_1061,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_583]),
[final] ).
cnf(i_0_1062,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_584]),
[final] ).
cnf(i_0_1063,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_584]),
[final] ).
cnf(i_0_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)))
| 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,esk14_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk14_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_585]),
[final] ).
cnf(i_0_1065,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk14_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk14_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_585]),
[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),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_586]),
[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)))
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk17_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk17_6(X3,X6,X2,X1,X5,X4))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_587]),
[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)))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk17_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk17_6(X6,X3,X5,X4,X2,X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_587]),
[final] ).
cnf(i_0_1069,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X4)),c_Wellfounded_Omax__ext(X1,X2)))
| ~ c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1,c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X2),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1070,plain,
( X3 = X4
| hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X3) != hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4) ),
inference(split_conjunct,[status(thm)],[i_0_589]),
[final] ).
cnf(i_0_1071,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk14_6(X3,X6,X2,X1,X5,X4))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk14_6(X3,X6,X2,X1,X5,X4))))
| X5 = X1
| X4 = X2
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_585]),
[final] ).
cnf(i_0_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),X4),X5)),hAPP(v_F,X6)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk14_6(X6,X3,X5,X4,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk14_6(X6,X3,X5,X4,X2,X1))))
| X2 = X4
| X1 = X5
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_585]),
[final] ).
cnf(i_0_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),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_586]),
[final] ).
cnf(i_0_1074,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(v_F,X6)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk17_6(X3,X6,X2,X1,X5,X4))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk17_6(X3,X6,X2,X1,X5,X4))))
| X1 = X2
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_587]),
[final] ).
cnf(i_0_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),X4),X5)),hAPP(v_F,X6)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk17_6(X6,X3,X5,X4,X2,X1))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X5)),hAPP(X6,esk17_6(X6,X3,X5,X4,X2,X1))))
| X4 = X5
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X6),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X3),c_Arrow__Order__Mirabelle_OProf)) ),
inference(split_conjunct,[status(thm)],[i_0_587]),
[final] ).
cnf(i_0_1076,plain,
( c_Wellfounded_Omax__extp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1,c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X4),X2,X3)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_588]),
[final] ).
cnf(i_0_1077,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,esk42_5(X3,X2,X1,X4,X5))),hAPP(X3,esk42_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[final] ).
cnf(i_0_1078,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk32_5(X3,X2,X1,X4,X5))),hAPP(X3,esk32_5(X3,X2,X1,X4,X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1079,plain,
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(X4,hAPP(X3,X5)) = hAPP(X3,c_Set_Oimage(X1,X1,X4,X5))
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| hAPP(X4,hAPP(hAPP(X2,esk55_5(X5,X4,X3,X2,X1)),esk56_5(X5,X4,X3,X2,X1))) != hAPP(hAPP(X2,hAPP(X4,esk55_5(X5,X4,X3,X2,X1))),hAPP(X4,esk56_5(X5,X4,X3,X2,X1)))
| ~ c_Finite__Set_Ofinite(X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_592]),
[final] ).
cnf(i_0_1080,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk23_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,esk23_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_593]),
[final] ).
cnf(i_0_1081,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk23_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,esk23_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_593]),
[final] ).
cnf(i_0_1082,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk16_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,esk16_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_594]),
[final] ).
cnf(i_0_1083,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),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,esk16_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,esk16_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_594]),
[final] ).
cnf(i_0_1084,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X1)),X2),c_FuncSet_OPi(X5,X1,X4,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X5),X3))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,esk33_5(X3,X2,X1,X4,X5))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[final] ).
cnf(i_0_1085,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4,hAPP(hAPP(c_COMBC(X1,X4,X4),c_COMBS(X1,X4,tc_fun(X4,X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1,c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)),X5)),c_Groups_Ozero__class_Ozero(X4)),X3) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1086,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4,hAPP(hAPP(c_COMBC(X1,X4,X4),c_COMBS(X1,X4,tc_fun(X4,X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1,c_If(X4)),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)),X5)),c_Groups_Ozero__class_Ozero(X4)),X3) = c_Groups_Ozero__class_Ozero(X4)
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1087,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,X5)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X4,esk23_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,esk23_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_593]),
[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),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,esk23_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,esk23_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_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),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,esk16_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,esk16_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_594]),
[final] ).
cnf(i_0_1090,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk16_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,esk16_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_594]),
[final] ).
cnf(i_0_1091,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk57_5(X3,X4,X5,X1,X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ 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)),X5),X4)),c_Wellfounded_Omax__ext(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1092,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4,hAPP(hAPP(c_COMBC(X1,X4,X4),c_COMBS(X1,X4,tc_fun(X4,X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1,c_If(X4)),hAPP(c_fequal,X2)),X5)),c_Groups_Ozero__class_Ozero(X4)),X3) = hAPP(X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1093,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X4,hAPP(hAPP(c_COMBC(X1,X4,X4),c_COMBS(X1,X4,tc_fun(X4,X4),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X4,tc_fun(X4,X4)),X1,c_If(X4)),hAPP(c_fequal,X2)),X5)),c_Groups_Ozero__class_Ozero(X4)),X3) = c_Groups_Ozero__class_Ozero(X4)
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(split_conjunct,[status(thm)],[i_0_598]),
[final] ).
cnf(i_0_1094,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_2(X1,X2)),esk21_2(X1,X2))),hAPP(X2,esk19_2(X1,X2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1095,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk20_2(X1,X2)),esk21_2(X1,X2))),hAPP(esk19_2(X1,X2),X1)))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1096,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk19_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1097,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| 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)),X5),X3)),c_Wellfounded_Omax__ext(X1,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk58_4(X4,X3,X5,X1)),X2)),X4))
| ~ c_Finite__Set_Ofinite(X1,X5)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1098,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)),X5),X3)),c_Wellfounded_Omax__ext(X1,X4)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk54_4(X4,X3,X5,X1)),X2)),X4))
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_600]),
[final] ).
cnf(i_0_1099,plain,
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| esk20_2(X1,X2) != esk21_2(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(split_conjunct,[status(thm)],[i_0_599]),
[final] ).
cnf(i_0_1100,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_601]),
[final] ).
cnf(i_0_1101,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk18_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,esk18_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_602]),
[final] ).
cnf(i_0_1102,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,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,esk18_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,esk18_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_602]),
[final] ).
cnf(i_0_1103,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk57_5(X2,X3,X4,X1,X5)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ 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)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1104,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_601]),
[final] ).
cnf(i_0_1105,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk42_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X5,X3)),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_590]),
[final] ).
cnf(i_0_1106,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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,esk18_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,esk18_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_602]),
[final] ).
cnf(i_0_1107,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),hAPP(v_F,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X3,esk18_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,esk18_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_602]),
[final] ).
cnf(i_0_1108,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk33_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_595]),
[final] ).
cnf(i_0_1109,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),esk36_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_603]),
[final] ).
cnf(i_0_1110,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk32_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_591]),
[final] ).
cnf(i_0_1111,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Recdef_Osame__fst(X7,X3,X1,X6)))
| ~ hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),hAPP(X6,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1112,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OLin)))),
inference(split_conjunct,[status(thm)],[fact_assms_I1_J]),
[final] ).
cnf(i_0_1113,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X7,X3),tc_prod(X7,X3))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X7,X3),tc_prod(X7,X3)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X1),X4)),hAPP(hAPP(c_Product__Type_OPair(X7,X3),X2),X5))),c_Wellfounded_Olex__prod(X7,X3,X8,X6)))
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X4),X5)),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1114,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X5),tc_prod(X1,X5))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X5),tc_prod(X1,X5)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X2),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X5),X3),X7))),c_Wellfounded_Olex__prod(X1,X5,X4,X8)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_601]),
[final] ).
cnf(i_0_1115,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk52_5(X2,X3,X4,X1,X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X3))
| ~ c_Wellfounded_Omax__extp(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1116,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,esk35_4(X3,X2,X4,X1))),hAPP(X3,esk35_4(X3,X2,X4,X1))))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1117,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_607]),
[final] ).
cnf(i_0_1118,plain,
( hAPP(hAPP(X3,hAPP(X5,X8)),hAPP(X6,X7)) = hAPP(X6,X7)
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6)
| ~ c_Finite__Set_Ofinite(X2,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X8),X7)) ),
inference(split_conjunct,[status(thm)],[i_0_608]),
[final] ).
cnf(i_0_1119,plain,
( hAPP(hAPP(X3,X7),X7) = X7
| ~ c_Finite__Set_Ofolding__image__simple__idem(X1,X2,X3,X4,X5,X6) ),
inference(split_conjunct,[status(thm)],[i_0_609]),
[final] ).
cnf(i_0_1120,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastLessThan(X4,X5,X1,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1121,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanAtMost(X4,X1,X5,X6,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1122,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastLessThan(X4,X1,X5,X2,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1123,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanAtMost(X4,X5,X1,X2,X6))) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1124,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_612]),
[final] ).
cnf(i_0_1125,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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,esk28_4(X1,X2,X3,X4)))) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1126,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_614]),
[final] ).
cnf(i_0_1127,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_615]),
[final] ).
cnf(i_0_1128,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(X1,c_Set_Oimage(X2,X1,X3,X4))),c_Finite__Set_Ocard(X2,X4)))
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_616]),
[final] ).
cnf(i_0_1129,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)),X6))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),c_Set_Oimage(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X4),X6)) ),
inference(split_conjunct,[status(thm)],[i_0_617]),
[final] ).
cnf(i_0_1130,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk51_4(X3,X1,X2,X4),X4)),X3))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X1,X2,X5,X3) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1131,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk39_4(X3,X1,X4,X2),X4)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2,X4)),c_Finite__Set_Ocard(X1,X3)))
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1132,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),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_620]),
[final] ).
cnf(i_0_1133,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Obelow(X3,X5,X4)))
| X5 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_621]),
[final] ).
cnf(i_0_1134,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X4),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),c_Set_Oimage(X2,X1,X3,X5)))
| ~ c_Fun_Oinj__on(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_622]),
[final] ).
cnf(i_0_1135,plain,
( hBOOL(hAPP(hAPP(X1,X2),esk52_5(X3,X4,X1,X5,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X2),X4))
| ~ c_Wellfounded_Omax__extp(X5,X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1136,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk58_4(X2,X3,X4,X1)),X4))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| 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)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))
| ~ c_Finite__Set_Ofinite(X1,X4)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1137,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk54_4(X2,X3,X4,X1)),X4))
| 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)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_600]),
[final] ).
cnf(i_0_1138,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_623]),
[final] ).
cnf(i_0_1139,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5)))) ),
inference(split_conjunct,[status(thm)],[i_0_624]),
[final] ).
cnf(i_0_1140,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X3),X1)),c_Wellfounded_Omax__ext(X2,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1141,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)),X2),X3)),c_Wellfounded_Omax__ext(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1142,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_Omax__ext(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_597]),
[final] ).
cnf(i_0_1143,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X6,X1,X4,X2,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_610]),
[final] ).
cnf(i_0_1144,plain,
( hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X6,X4,X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_611]),
[final] ).
cnf(i_0_1145,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_623]),
[final] ).
cnf(i_0_1146,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_621]),
[final] ).
cnf(i_0_1147,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_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_620]),
[final] ).
cnf(i_0_1148,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_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_620]),
[final] ).
cnf(i_0_1149,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_621]),
[final] ).
cnf(i_0_1150,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_621]),
[final] ).
cnf(i_0_1151,plain,
( X1 = X5
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),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_620]),
[final] ).
cnf(i_0_1152,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)),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_620]),
[final] ).
cnf(i_0_1153,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_621]),
[final] ).
cnf(i_0_1154,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_615]),
[final] ).
cnf(i_0_1155,plain,
( c_Set_Oimage(X2,X1,esk50_4(X5,X2,X1,X4),X5) = X4
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ 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)) ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1156,plain,
( X1 = c_Set_Oimage(X2,X3,X4,esk36_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_603]),
[final] ).
cnf(i_0_1157,plain,
( X1 = hAPP(X2,esk4_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_625]),
[final] ).
cnf(i_0_1158,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_626]),
[final] ).
cnf(i_0_1159,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_627]),
[final] ).
cnf(i_0_1160,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X5)))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5))
| ~ c_Finite__Set_Ofinite(X2,X5)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1161,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_628]),
[final] ).
cnf(i_0_1162,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_629]),
[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))
| ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_622]),
[final] ).
cnf(i_0_1164,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk11_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_630]),
[final] ).
cnf(i_0_1165,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_631]),
[final] ).
cnf(i_0_1166,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_632]),
[final] ).
cnf(i_0_1167,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_633]),
[final] ).
cnf(i_0_1168,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_623]),
[final] ).
cnf(i_0_1169,plain,
( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X1,X4,X5,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,esk53_4(X3,X5,X4,X1)),X2))
| ~ c_Finite__Set_Ofinite(X1,X5)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1170,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)))))
| esk4_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_625]),
[final] ).
cnf(i_0_1171,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_634]),
[final] ).
cnf(i_0_1172,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)),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_620]),
[final] ).
cnf(i_0_1173,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_621]),
[final] ).
cnf(i_0_1174,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_635]),
[final] ).
cnf(i_0_1175,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_621]),
[final] ).
cnf(i_0_1176,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)),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_620]),
[final] ).
cnf(i_0_1177,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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)),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_620]),
[final] ).
cnf(i_0_1178,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__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_621]),
[final] ).
cnf(i_0_1179,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_636]),
[final] ).
cnf(i_0_1180,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),esk26_1(X1)),esk27_1(X1))),hAPP(X1,esk24_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),esk26_1(X1)),esk27_1(X1))),hAPP(X1,esk25_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1181,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_637]),
[final] ).
cnf(i_0_1182,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_621]),
[final] ).
cnf(i_0_1183,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_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_620]),
[final] ).
cnf(i_0_1184,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)),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_620]),
[final] ).
cnf(i_0_1185,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_621]),
[final] ).
cnf(i_0_1186,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)),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_620]),
[final] ).
cnf(i_0_1187,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_621]),
[final] ).
cnf(i_0_1188,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)),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_620]),
[final] ).
cnf(i_0_1189,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_621]),
[final] ).
cnf(i_0_1190,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_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_620]),
[final] ).
cnf(i_0_1191,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_621]),
[final] ).
cnf(i_0_1192,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_638]),
[final] ).
cnf(i_0_1193,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_639]),
[final] ).
cnf(i_0_1194,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,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),v_Lba____))),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[fact__096F_A_I_Fi_O_ALba_J_A_058_ALin_096]),
[final] ).
cnf(i_0_1195,plain,
( hAPP(X3,hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X5)) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),c_Set_Oimage(X1,X2,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_640]),
[final] ).
cnf(i_0_1196,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5),X4))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X4)),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X5))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_641]),
[final] ).
cnf(i_0_1197,plain,
( X1 = hAPP(X2,esk3_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_625]),
[final] ).
cnf(i_0_1198,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_642]),
[final] ).
cnf(i_0_1199,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X1)),esk27_1(X1))),hAPP(esk25_1(X1),X2)))
| c_Arrow__Order__Mirabelle_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),esk26_1(X1)),esk27_1(X1))),hAPP(esk24_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1200,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X1)),esk27_1(X1))),hAPP(esk24_1(X1),X2)))
| c_Arrow__Order__Mirabelle_OIIA(X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X1)),esk27_1(X1))),hAPP(esk25_1(X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1201,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_642]),
[final] ).
cnf(i_0_1202,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1203,plain,
( X3 = esk3_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_625]),
[final] ).
cnf(i_0_1204,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X3))),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X4))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_644]),
[final] ).
cnf(i_0_1205,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),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_631]),
[final] ).
cnf(i_0_1206,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_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_620]),
[final] ).
cnf(i_0_1207,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_621]),
[final] ).
cnf(i_0_1208,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk46_4(X2,X3,X4,X1)),X3))
| c_FuncSet_OPi(X1,X4,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X4),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1209,plain,
hAPP(c_COMBS(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X4,X6),hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_646]),
[final] ).
cnf(i_0_1210,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_647]),
[final] ).
cnf(i_0_1211,plain,
( hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),hAPP(X5,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_648]),
[final] ).
cnf(i_0_1212,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X3),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,X5)))
| ~ c_Fun_Oinj__on(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_649]),
[final] ).
cnf(i_0_1213,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_643]),
[final] ).
cnf(i_0_1214,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk53_4(X2,X3,X4,X1)),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X1,X4,X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1215,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)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1216,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)),c_Arrow__Order__Mirabelle_Omktop(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1217,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)),c_Arrow__Order__Mirabelle_Omktop(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1218,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)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1219,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)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1220,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)),c_Arrow__Order__Mirabelle_Omktop(X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1221,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk10_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1222,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk9_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1223,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk26_1(X1)),esk27_1(X1))),hAPP(X1,esk24_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),esk26_1(X1)),esk27_1(X1))),hAPP(X1,esk25_1(X1))))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1224,plain,
( X1 = hAPP(X2,esk11_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_630]),
[final] ).
cnf(i_0_1225,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_653]),
[final] ).
cnf(i_0_1226,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_654]),
[final] ).
cnf(i_0_1227,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_655]),
[final] ).
cnf(i_0_1228,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_621]),
[final] ).
cnf(i_0_1229,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)),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_620]),
[final] ).
cnf(i_0_1230,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_656]),
[final] ).
cnf(i_0_1231,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_657]),
[final] ).
cnf(i_0_1232,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_658]),
[final] ).
cnf(i_0_1233,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_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_659]),
[final] ).
cnf(i_0_1234,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X3,X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X3),c_Arrow__Order__Mirabelle_OLin)) ),
inference(split_conjunct,[status(thm)],[i_0_660]),
[final] ).
cnf(i_0_1235,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X1))),hAPP(X4,X1))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_661]),
[final] ).
cnf(i_0_1236,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_662]),
[final] ).
cnf(i_0_1237,plain,
( c_Finite__Set_Ofinite(X3,X4)
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X4),c_Set_Oimage(X1,X3,X5,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_663]),
[final] ).
cnf(i_0_1238,plain,
( hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_649]),
[final] ).
cnf(i_0_1239,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_603]),
[final] ).
cnf(i_0_1240,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X5,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1241,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X5,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_665]),
[final] ).
cnf(i_0_1242,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeastAtMost(X4,X1,X2,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1243,plain,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThanLessThan(X4,X1,X2,X5))) ),
inference(split_conjunct,[status(thm)],[i_0_665]),
[final] ).
cnf(i_0_1244,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X3),hAPP(c_Nat_OSuc,X4))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,hAPP(c_COMBB(tc_Nat_Onat,X1,tc_Nat_Onat,X2),c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X3,X4))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_666]),
[final] ).
cnf(i_0_1245,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),esk30_1(X1)),esk31_1(X1))),hAPP(X1,esk29_1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1246,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_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_667]),
[final] ).
cnf(i_0_1247,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_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_668]),
[final] ).
cnf(i_0_1248,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_669]),
[final] ).
cnf(i_0_1249,plain,
( c_Set_Oimage(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X4)) = X4
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_670]),
[final] ).
cnf(i_0_1250,plain,
( X1 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Finite__Set_Ocard(tc_Nat_Onat,X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X1),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Finite__Set_Ocard(tc_Nat_Onat,X1))))) ),
inference(split_conjunct,[status(thm)],[i_0_671]),
[final] ).
cnf(i_0_1251,plain,
( c_Fun_Oinj__on(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),c_Set_Oimage(X1,X2,X3,X4))
| ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_672]),
[final] ).
cnf(i_0_1252,plain,
( X1 != X2
| X1 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1253,plain,
( X1 != X2
| X3 != X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1254,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)),c_Arrow__Order__Mirabelle_Omktop(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1255,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1256,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_662]),
[final] ).
cnf(i_0_1257,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X2)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X5,X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_673]),
[final] ).
cnf(i_0_1258,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4)),c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X5)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_673]),
[final] ).
cnf(i_0_1259,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk22_2(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_655]),
[final] ).
cnf(i_0_1260,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_674]),
[final] ).
cnf(i_0_1261,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X3)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(X4,X2)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),X3)))
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_675]),
[final] ).
cnf(i_0_1262,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_676]),
[final] ).
cnf(i_0_1263,plain,
( hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X5,X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_664]),
[final] ).
cnf(i_0_1264,plain,
( hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X5,X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_665]),
[final] ).
cnf(i_0_1265,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),v_Lab____)),
inference(split_conjunct,[status(thm)],[i_0_677]),
[final] ).
cnf(i_0_1266,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_678]),
[final] ).
cnf(i_0_1267,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_679]),
[final] ).
cnf(i_0_1268,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk25_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1269,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),esk24_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_OIIA(X1) ),
inference(split_conjunct,[status(thm)],[i_0_593]),
[final] ).
cnf(i_0_1270,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))),esk29_1(X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1271,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_680]),
[final] ).
cnf(i_0_1272,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_630]),
[final] ).
cnf(i_0_1273,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_681]),
[final] ).
cnf(i_0_1274,plain,
( hAPP(X1,esk9_4(X2,X1,X3,X4)) = hAPP(X1,esk10_4(X2,X1,X3,X4))
| c_Fun_Oinj__on(X4,X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1275,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_682]),
[final] ).
cnf(i_0_1276,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_683]),
[final] ).
cnf(i_0_1277,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_684]),
[final] ).
cnf(i_0_1278,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4))) ),
inference(split_conjunct,[status(thm)],[i_0_685]),
[final] ).
cnf(i_0_1279,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_686]),
[final] ).
cnf(i_0_1280,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_687]),
[final] ).
cnf(i_0_1281,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_688]),
[final] ).
cnf(i_0_1282,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1283,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_690]),
[final] ).
cnf(i_0_1284,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_1285,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_692]),
[final] ).
cnf(i_0_1286,plain,
( c_Fun_Oinj__on(X1,X2,esk51_4(X3,X2,X1,X4),X4)
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Set_Oimage(X2,X1,X5,X3) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_618]),
[final] ).
cnf(i_0_1287,plain,
( c_Fun_Oinj__on(X1,X2,esk39_4(X3,X2,X4,X1),X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X4)),c_Finite__Set_Ocard(X2,X3)))
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_619]),
[final] ).
cnf(i_0_1288,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),esk30_1(X1)),esk31_1(X1))),hAPP(esk29_1(X1),X2)))
| c_Arrow__Order__Mirabelle_Ounanimity(X1) ),
inference(split_conjunct,[status(thm)],[i_0_613]),
[final] ).
cnf(i_0_1289,plain,
( hAPP(c_Fun_Othe__inv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(X3,X4)) = X4
| ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(split_conjunct,[status(thm)],[i_0_693]),
[final] ).
cnf(i_0_1290,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_694]),
[final] ).
cnf(i_0_1291,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_695]),
[final] ).
cnf(i_0_1292,plain,
( hAPP(c_Fun_Othe__inv__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_696]),
[final] ).
cnf(i_0_1293,plain,
( hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),X6) = X5
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(X3,X5) != X6
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_697]),
[final] ).
cnf(i_0_1294,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_698]),
[final] ).
cnf(i_0_1295,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_699]),
[final] ).
cnf(i_0_1296,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
inference(split_conjunct,[status(thm)],[i_0_700]),
[final] ).
cnf(i_0_1297,plain,
hAPP(hAPP(c_COMBB(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[i_0_701]),
[final] ).
cnf(i_0_1298,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X5)))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ hBOOL(hAPP(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_702]),
[final] ).
cnf(i_0_1299,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X3)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X1)),
inference(split_conjunct,[status(thm)],[i_0_703]),
[final] ).
cnf(i_0_1300,plain,
( hAPP(X1,esk46_4(X1,X2,X3,X4)) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| c_FuncSet_OPi(X4,X3,X2,X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1301,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_704]),
[final] ).
cnf(i_0_1302,plain,
( c_Fun_Oinj__on(X4,X3,X2,X1)
| esk9_4(X1,X2,X3,X4) != esk10_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1303,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_705]),
[final] ).
cnf(i_0_1304,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_706]),
[final] ).
cnf(i_0_1305,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_707]),
[final] ).
cnf(i_0_1306,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_708]),
[final] ).
cnf(i_0_1307,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_1308,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1309,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_710]),
[final] ).
cnf(i_0_1310,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_711]),
[final] ).
cnf(i_0_1311,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_712]),
[final] ).
cnf(i_0_1312,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_713]),
[final] ).
cnf(i_0_1313,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)),c_Arrow__Order__Mirabelle_Omkbot(X4,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_650]),
[final] ).
cnf(i_0_1314,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)),c_Arrow__Order__Mirabelle_Omktop(X4,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_651]),
[final] ).
cnf(i_0_1315,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),esk34_2(X2,X1)))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_714]),
[final] ).
cnf(i_0_1316,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_699]),
[final] ).
cnf(i_0_1317,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_715]),
[final] ).
cnf(i_0_1318,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_716]),
[final] ).
cnf(i_0_1319,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_717]),
[final] ).
cnf(i_0_1320,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_718]),
[final] ).
cnf(i_0_1321,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_719]),
[final] ).
cnf(i_0_1322,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_720]),
[final] ).
cnf(i_0_1323,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_721]),
[final] ).
cnf(i_0_1324,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_684]),
[final] ).
cnf(i_0_1325,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_722]),
[final] ).
cnf(i_0_1326,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_686]),
[final] ).
cnf(i_0_1327,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_723]),
[final] ).
cnf(i_0_1328,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_724]),
[final] ).
cnf(i_0_1329,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_725]),
[final] ).
cnf(i_0_1330,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_726]),
[final] ).
cnf(i_0_1331,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),esk13_0)),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_1332,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1333,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),esk12_0)),
inference(split_conjunct,[status(thm)],[i_0_728]),
[final] ).
cnf(i_0_1334,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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_1335,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_729]),
[final] ).
cnf(i_0_1336,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_729]),
[final] ).
cnf(i_0_1337,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_730]),
[final] ).
cnf(i_0_1338,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_731]),
[final] ).
cnf(i_0_1339,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_732]),
[final] ).
cnf(i_0_1340,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_689]),
[final] ).
cnf(i_0_1341,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_733]),
[final] ).
cnf(i_0_1342,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_691]),
[final] ).
cnf(i_0_1343,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_734]),
[final] ).
cnf(i_0_1344,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_735]),
[final] ).
cnf(i_0_1345,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X1,X2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3))
| ~ class_Groups_Ocomm__monoid__add(X1)
| hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1346,plain,
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1347,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_737]),
[final] ).
cnf(i_0_1348,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_737]),
[final] ).
cnf(i_0_1349,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_738]),
[final] ).
cnf(i_0_1350,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_739]),
[final] ).
cnf(i_0_1351,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_740]),
[final] ).
cnf(i_0_1352,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_695]),
[final] ).
cnf(i_0_1353,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_741]),
[final] ).
cnf(i_0_1354,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_742]),
[final] ).
cnf(i_0_1355,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_743]),
[final] ).
cnf(i_0_1356,plain,
( X5 = X6
| ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| hAPP(X3,X5) != hAPP(X3,X6) ),
inference(split_conjunct,[status(thm)],[i_0_652]),
[final] ).
cnf(i_0_1357,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_744]),
[final] ).
cnf(i_0_1358,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_744]),
[final] ).
cnf(i_0_1359,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_745]),
[final] ).
cnf(i_0_1360,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_746]),
[final] ).
cnf(i_0_1361,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1362,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk6_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_748]),
[final] ).
cnf(i_0_1363,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_749]),
[final] ).
cnf(i_0_1364,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_704]),
[final] ).
cnf(i_0_1365,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_750]),
[final] ).
cnf(i_0_1366,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_751]),
[final] ).
cnf(i_0_1367,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_752]),
[final] ).
cnf(i_0_1368,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_753]),
[final] ).
cnf(i_0_1369,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk7_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_754]),
[final] ).
cnf(i_0_1370,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_712]),
[final] ).
cnf(i_0_1371,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_713]),
[final] ).
cnf(i_0_1372,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_755]),
[final] ).
cnf(i_0_1373,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_756]),
[final] ).
cnf(i_0_1374,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_757]),
[final] ).
cnf(i_0_1375,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_758]),
[final] ).
cnf(i_0_1376,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_759]),
[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)),esk34_2(X1,X2)),c_Arrow__Order__Mirabelle_OLin))
| X2 = X1 ),
inference(split_conjunct,[status(thm)],[i_0_714]),
[final] ).
cnf(i_0_1378,plain,
( c_Finite__Set_Ocard(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_760]),
[final] ).
cnf(i_0_1379,plain,
( c_Finite__Set_Ocard(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X3,X4))
| ~ c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_761]),
[final] ).
cnf(i_0_1380,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_762]),
[final] ).
cnf(i_0_1381,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_737]),
[final] ).
cnf(i_0_1382,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_1383,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_1384,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_1385,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_723]),
[final] ).
cnf(i_0_1386,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_766]),
[final] ).
cnf(i_0_1387,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_767]),
[final] ).
cnf(i_0_1388,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_768]),
[final] ).
cnf(i_0_1389,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk7_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_754]),
[final] ).
cnf(i_0_1390,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),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_769]),
[final] ).
cnf(i_0_1391,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_770]),
[final] ).
cnf(i_0_1392,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_1393,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_1394,plain,
( hBOOL(hAPP(X1,esk6_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_748]),
[final] ).
cnf(i_0_1395,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_773]),
[final] ).
cnf(i_0_1396,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk5_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_748]),
[final] ).
cnf(i_0_1397,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X1,X2)),c_SetInterval_Oord__class_OgreaterThan(X1,X3)))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_774]),
[final] ).
cnf(i_0_1398,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_775]),
[final] ).
cnf(i_0_1399,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_776]),
[final] ).
cnf(i_0_1400,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk13_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_727]),
[final] ).
cnf(i_0_1401,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),esk12_0),c_Arrow__Order__Mirabelle_OLin)),
inference(split_conjunct,[status(thm)],[i_0_728]),
[final] ).
cnf(i_0_1402,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_1403,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_1404,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk8_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_754]),
[final] ).
cnf(i_0_1405,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_777]),
[final] ).
cnf(i_0_1406,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_778]),
[final] ).
cnf(i_0_1407,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatMost(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_779]),
[final] ).
cnf(i_0_1408,plain,
( hBOOL(hAPP(hAPP(X3,X2),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OlessThan(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1409,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeast(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_781]),
[final] ).
cnf(i_0_1410,plain,
( hBOOL(hAPP(hAPP(X3,X4),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThan(X1,X3,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_782]),
[final] ).
cnf(i_0_1411,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_783]),
[final] ).
cnf(i_0_1412,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_729]),
[final] ).
cnf(i_0_1413,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_770]),
[final] ).
cnf(i_0_1414,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_771]),
[final] ).
cnf(i_0_1415,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[i_0_784]),
[final] ).
cnf(i_0_1416,plain,
( c_FuncSet_OPi(X1,X5,X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X5),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(X4,X2) != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_645]),
[final] ).
cnf(i_0_1417,plain,
( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = c_Groups_Ozero__class_Ozero(X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_661]),
[final] ).
cnf(i_0_1418,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(tc_sum(X1,X3),c_Sum__Type_OPlus(X1,X3,X2,X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_761]),
[final] ).
cnf(i_0_1419,plain,
( c_Finite__Set_Ofinite(X1,X2)
| c_Finite__Set_Ocard(tc_sum(X3,X1),c_Sum__Type_OPlus(X3,X1,X4,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_761]),
[final] ).
cnf(i_0_1420,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_1421,plain,
( X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_785]),
[final] ).
cnf(i_0_1422,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_786]),
[final] ).
cnf(i_0_1423,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_787]),
[final] ).
cnf(i_0_1424,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_788]),
[final] ).
cnf(i_0_1425,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_789]),
[final] ).
cnf(i_0_1426,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_790]),
[final] ).
cnf(i_0_1427,plain,
( X5 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hAPP(hAPP(X2,hAPP(X3,X5)),hAPP(X3,X4)) = hAPP(X3,X4)
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X4)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_791]),
[final] ).
cnf(i_0_1428,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Sum__Type_OPlus(X2,X3,X1,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X3),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1429,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Sum__Type_OPlus(X3,X2,X4,X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X2),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1430,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_793]),
[final] ).
cnf(i_0_1431,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_794]),
[final] ).
cnf(i_0_1432,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_606]),
[final] ).
cnf(i_0_1433,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_795]),
[final] ).
cnf(i_0_1434,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_796]),
[final] ).
cnf(i_0_1435,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_797]),
[final] ).
cnf(i_0_1436,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_798]),
[final] ).
cnf(i_0_1437,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_799]),
[final] ).
cnf(i_0_1438,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) != c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X5))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X4))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1439,plain,
( X1 = X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) != c_SetInterval_Oord__class_OatLeastLessThan(X3,X5,X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X4),X1))
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_800]),
[final] ).
cnf(i_0_1440,plain,
( X2 = X4
| ~ class_Orderings_Olinorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_801]),
[final] ).
cnf(i_0_1441,plain,
( X3 = X5
| ~ class_Orderings_Olinorder(X1)
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_802]),
[final] ).
cnf(i_0_1442,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1),X3))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_803]),
[final] ).
cnf(i_0_1443,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_804]),
[final] ).
cnf(i_0_1444,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_805]),
[final] ).
cnf(i_0_1445,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_775]),
[final] ).
cnf(i_0_1446,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_806]),
[final] ).
cnf(i_0_1447,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_807]),
[final] ).
cnf(i_0_1448,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(X1,X3)),c_SetInterval_Oord__class_OgreaterThan(X1,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_774]),
[final] ).
cnf(i_0_1449,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1450,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1451,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_Set_Oimage(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_810]),
[final] ).
cnf(i_0_1452,plain,
( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Set_Oimage(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1453,plain,
c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_812]),
[final] ).
cnf(i_0_1454,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_1455,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_770]),
[final] ).
cnf(i_0_1456,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_813]),
[final] ).
cnf(i_0_1457,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1458,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_815]),
[final] ).
cnf(i_0_1459,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_1460,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_1461,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatMost(X4,X1,X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_779]),
[final] ).
cnf(i_0_1462,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OlessThan(X4,X1,X3)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_780]),
[final] ).
cnf(i_0_1463,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeast(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_781]),
[final] ).
cnf(i_0_1464,plain,
( hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThan(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_782]),
[final] ).
cnf(i_0_1465,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_816]),
[final] ).
cnf(i_0_1466,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_817]),
[final] ).
cnf(i_0_1467,plain,
c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[i_0_818]),
[final] ).
cnf(i_0_1468,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_819]),
[final] ).
cnf(i_0_1469,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_819]),
[final] ).
cnf(i_0_1470,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Wellfounded_Omax__extp(X2,X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1471,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_820]),
[final] ).
cnf(i_0_1472,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_821]),
[final] ).
cnf(i_0_1473,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_822]),
[final] ).
cnf(i_0_1474,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_823]),
[final] ).
cnf(i_0_1475,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_824]),
[final] ).
cnf(i_0_1476,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk44_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_825]),
[final] ).
cnf(i_0_1477,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_808]),
[final] ).
cnf(i_0_1478,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_826]),
[final] ).
cnf(i_0_1479,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_827]),
[final] ).
cnf(i_0_1480,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_828]),
[final] ).
cnf(i_0_1481,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_819]),
[final] ).
cnf(i_0_1482,plain,
( c_Sum__Type_OPlus(X2,X4,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X4),tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_792]),
[final] ).
cnf(i_0_1483,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_829]),
[final] ).
cnf(i_0_1484,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_830]),
[final] ).
cnf(i_0_1485,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_831]),
[final] ).
cnf(i_0_1486,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_832]),
[final] ).
cnf(i_0_1487,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_833]),
[final] ).
cnf(i_0_1488,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_834]),
[final] ).
cnf(i_0_1489,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_835]),
[final] ).
cnf(i_0_1490,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1491,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1492,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_836]),
[final] ).
cnf(i_0_1493,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_837]),
[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(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_838]),
[final] ).
cnf(i_0_1495,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)),
inference(split_conjunct,[status(thm)],[i_0_839]),
[final] ).
cnf(i_0_1496,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_814]),
[final] ).
cnf(i_0_1497,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_840]),
[final] ).
cnf(i_0_1498,plain,
c_FuncSet_OPi(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X3) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1499,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_842]),
[final] ).
cnf(i_0_1500,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_843]),
[final] ).
cnf(i_0_1501,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_844]),
[final] ).
cnf(i_0_1502,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_845]),
[final] ).
cnf(i_0_1503,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_834]),
[final] ).
cnf(i_0_1504,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_834]),
[final] ).
cnf(i_0_1505,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_846]),
[final] ).
cnf(i_0_1506,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_847]),
[final] ).
cnf(i_0_1507,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord__class_OgreaterThan(X1,X3)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_848]),
[final] ).
cnf(i_0_1508,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_849]),
[final] ).
cnf(i_0_1509,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_850]),
[final] ).
cnf(i_0_1510,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_851]),
[final] ).
cnf(i_0_1511,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_852]),
[final] ).
cnf(i_0_1512,plain,
( hAPP(hAPP(X2,X5),hAPP(X3,X4)) = hAPP(X3,X4)
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X1,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_853]),
[final] ).
cnf(i_0_1513,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_854]),
[final] ).
cnf(i_0_1514,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_855]),
[final] ).
cnf(i_0_1515,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_856]),
[final] ).
cnf(i_0_1516,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_857]),
[final] ).
cnf(i_0_1517,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_858]),
[final] ).
cnf(i_0_1518,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_859]),
[final] ).
cnf(i_0_1519,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_860]),
[final] ).
cnf(i_0_1520,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_861]),
[final] ).
cnf(i_0_1521,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_862]),
[final] ).
cnf(i_0_1522,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_863]),
[final] ).
cnf(i_0_1523,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_864]),
[final] ).
cnf(i_0_1524,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_865]),
[final] ).
cnf(i_0_1525,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_866]),
[final] ).
cnf(i_0_1526,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_SetInterval_Oord__class_OgreaterThan(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_848]),
[final] ).
cnf(i_0_1527,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_829]),
[final] ).
cnf(i_0_1528,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_867]),
[final] ).
cnf(i_0_1529,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_868]),
[final] ).
cnf(i_0_1530,plain,
c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_869]),
[final] ).
cnf(i_0_1531,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1532,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk38_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_871]),
[final] ).
cnf(i_0_1533,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1534,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = c_Set_Oimage(X2,X3,X4,X1)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_810]),
[final] ).
cnf(i_0_1535,plain,
( c_Set_Oimage(X2,X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_811]),
[final] ).
cnf(i_0_1536,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1537,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_873]),
[final] ).
cnf(i_0_1538,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_874]),
[final] ).
cnf(i_0_1539,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1540,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_850]),
[final] ).
cnf(i_0_1541,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_851]),
[final] ).
cnf(i_0_1542,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_876]),
[final] ).
cnf(i_0_1543,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_877]),
[final] ).
cnf(i_0_1544,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_878]),
[final] ).
cnf(i_0_1545,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_825]),
[final] ).
cnf(i_0_1546,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_879]),
[final] ).
cnf(i_0_1547,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_880]),
[final] ).
cnf(i_0_1548,plain,
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,esk8_2(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_754]),
[final] ).
cnf(i_0_1549,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_881]),
[final] ).
cnf(i_0_1550,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1551,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_882]),
[final] ).
cnf(i_0_1552,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_883]),
[final] ).
cnf(i_0_1553,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_884]),
[final] ).
cnf(i_0_1554,plain,
c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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))),
inference(split_conjunct,[status(thm)],[fact_greaterThan__0]),
[final] ).
cnf(i_0_1555,plain,
( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk49_2(X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_885]),
[final] ).
cnf(i_0_1556,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastLessThan(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_886]),
[final] ).
cnf(i_0_1557,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_1558,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_888]),
[final] ).
cnf(i_0_1559,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1560,plain,
( c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk41_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1561,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,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(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1562,plain,
c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,esk2_0,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_812]),
[final] ).
cnf(i_0_1563,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_1564,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_892]),
[final] ).
cnf(i_0_1565,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1566,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_893]),
[final] ).
cnf(i_0_1567,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_894]),
[final] ).
cnf(i_0_1568,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 = hAPP(c_Nat_OSuc,X2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_895]),
[final] ).
cnf(i_0_1569,plain,
( hBOOL(hAPP(X1,esk5_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_748]),
[final] ).
cnf(i_0_1570,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_896]),
[final] ).
cnf(i_0_1571,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk37_1(X1)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_871]),
[final] ).
cnf(i_0_1572,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_897]),
[final] ).
cnf(i_0_1573,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_898]),
[final] ).
cnf(i_0_1574,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_899]),
[final] ).
cnf(i_0_1575,plain,
( X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1576,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_901]),
[final] ).
cnf(i_0_1577,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_902]),
[final] ).
cnf(i_0_1578,plain,
( X1 = hAPP(c_Nat_OSuc,esk44_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_825]),
[final] ).
cnf(i_0_1579,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_865]),
[final] ).
cnf(i_0_1580,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_891]),
[final] ).
cnf(i_0_1581,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_903]),
[final] ).
cnf(i_0_1582,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_904]),
[final] ).
cnf(i_0_1583,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_889]),
[final] ).
cnf(i_0_1584,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_905]),
[final] ).
cnf(i_0_1585,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_906]),
[final] ).
cnf(i_0_1586,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_885]),
[final] ).
cnf(i_0_1587,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),esk40_1(X1)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1588,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_907]),
[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),X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[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),X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_870]),
[final] ).
cnf(i_0_1591,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_909]),
[final] ).
cnf(i_0_1592,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_910]),
[final] ).
cnf(i_0_1593,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_911]),
[final] ).
cnf(i_0_1594,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_912]),
[final] ).
cnf(i_0_1595,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1596,plain,
c_Nat_Onat_Onat__case(X1,X2,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1597,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_907]),
[final] ).
cnf(i_0_1598,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1599,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_915]),
[final] ).
cnf(i_0_1600,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_916]),
[final] ).
cnf(i_0_1601,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_917]),
[final] ).
cnf(i_0_1602,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_918]),
[final] ).
cnf(i_0_1603,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_919]),
[final] ).
cnf(i_0_1604,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_881]),
[final] ).
cnf(i_0_1605,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_920]),
[final] ).
cnf(i_0_1606,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_838]),
[final] ).
cnf(i_0_1607,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_921]),
[final] ).
cnf(i_0_1608,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_922]),
[final] ).
cnf(i_0_1609,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_923]),
[final] ).
cnf(i_0_1610,plain,
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_924]),
[final] ).
cnf(i_0_1611,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_894]),
[final] ).
cnf(i_0_1612,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_925]),
[final] ).
cnf(i_0_1613,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X2),esk48_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1614,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk47_2(X2,X1)),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_927]),
[final] ).
cnf(i_0_1615,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_874]),
[final] ).
cnf(i_0_1616,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_847]),
[final] ).
cnf(i_0_1617,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_928]),
[final] ).
cnf(i_0_1618,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_929]),
[final] ).
cnf(i_0_1619,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1620,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_931]),
[final] ).
cnf(i_0_1621,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_932]),
[final] ).
cnf(i_0_1622,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_933]),
[final] ).
cnf(i_0_1623,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_934]),
[final] ).
cnf(i_0_1624,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_864]),
[final] ).
cnf(i_0_1625,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_935]),
[final] ).
cnf(i_0_1626,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_936]),
[final] ).
cnf(i_0_1627,plain,
( X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_937]),
[final] ).
cnf(i_0_1628,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_938]),
[final] ).
cnf(i_0_1629,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_939]),
[final] ).
cnf(i_0_1630,plain,
( c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_940]),
[final] ).
cnf(i_0_1631,plain,
( X1 = X2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_941]),
[final] ).
cnf(i_0_1632,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 = X2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1633,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_931]),
[final] ).
cnf(i_0_1634,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_942]),
[final] ).
cnf(i_0_1635,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_927]),
[final] ).
cnf(i_0_1636,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_926]),
[final] ).
cnf(i_0_1637,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk41_2(X1,X2)),X1))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_890]),
[final] ).
cnf(i_0_1638,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk38_2(X1,X2)),X1))
| c_Finite__Set_Ofinite(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_871]),
[final] ).
cnf(i_0_1639,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_943]),
[final] ).
cnf(i_0_1640,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[i_0_944]),
[final] ).
cnf(i_0_1641,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,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(X2,X1)))
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1642,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_939]),
[final] ).
cnf(i_0_1643,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_919]),
[final] ).
cnf(i_0_1644,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1645,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_884]),
[final] ).
cnf(i_0_1646,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_946]),
[final] ).
cnf(i_0_1647,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1648,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_882]),
[final] ).
cnf(i_0_1649,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_948]),
[final] ).
cnf(i_0_1650,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_886]),
[final] ).
cnf(i_0_1651,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_887]),
[final] ).
cnf(i_0_1652,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_949]),
[final] ).
cnf(i_0_1653,plain,
( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk45_2(X2,X1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_950]),
[final] ).
cnf(i_0_1654,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_951]),
[final] ).
cnf(i_0_1655,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_952]),
[final] ).
cnf(i_0_1656,plain,
( X1 = hAPP(c_Nat_OSuc,esk43_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_953]),
[final] ).
cnf(i_0_1657,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_907]),
[final] ).
cnf(i_0_1658,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_864]),
[final] ).
cnf(i_0_1659,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_954]),
[final] ).
cnf(i_0_1660,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_955]),
[final] ).
cnf(i_0_1661,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_956]),
[final] ).
cnf(i_0_1662,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_933]),
[final] ).
cnf(i_0_1663,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_933]),
[final] ).
cnf(i_0_1664,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_785]),
[final] ).
cnf(i_0_1665,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_785]),
[final] ).
cnf(i_0_1666,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_957]),
[final] ).
cnf(i_0_1667,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_957]),
[final] ).
cnf(i_0_1668,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_771]),
[final] ).
cnf(i_0_1669,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_958]),
[final] ).
cnf(i_0_1670,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_959]),
[final] ).
cnf(i_0_1671,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_960]),
[final] ).
cnf(i_0_1672,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(split_conjunct,[status(thm)],[i_0_961]),
[final] ).
cnf(i_0_1673,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_962]),
[final] ).
cnf(i_0_1674,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_963]),
[final] ).
cnf(i_0_1675,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_964]),
[final] ).
cnf(i_0_1676,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_965]),
[final] ).
cnf(i_0_1677,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_966]),
[final] ).
cnf(i_0_1678,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_967]),
[final] ).
cnf(i_0_1679,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_968]),
[final] ).
cnf(i_0_1680,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_969]),
[final] ).
cnf(i_0_1681,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_970]),
[final] ).
cnf(i_0_1682,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_971]),
[final] ).
cnf(i_0_1683,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_921]),
[final] ).
cnf(i_0_1684,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_972]),
[final] ).
cnf(i_0_1685,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_973]),
[final] ).
cnf(i_0_1686,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_974]),
[final] ).
cnf(i_0_1687,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_975]),
[final] ).
cnf(i_0_1688,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_924]),
[final] ).
cnf(i_0_1689,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1690,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_976]),
[final] ).
cnf(i_0_1691,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_977]),
[final] ).
cnf(i_0_1692,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_978]),
[final] ).
cnf(i_0_1693,plain,
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_931]),
[final] ).
cnf(i_0_1694,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_979]),
[final] ).
cnf(i_0_1695,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_980]),
[final] ).
cnf(i_0_1696,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_952]),
[final] ).
cnf(i_0_1697,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_952]),
[final] ).
cnf(i_0_1698,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_950]),
[final] ).
cnf(i_0_1699,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1700,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1701,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_983]),
[final] ).
cnf(i_0_1702,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_984]),
[final] ).
cnf(i_0_1703,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_825]),
[final] ).
cnf(i_0_1704,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1705,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_894]),
[final] ).
cnf(i_0_1706,plain,
( c_Arrow__Order__Mirabelle_Odictator(X1,X2)
| hAPP(X1,esk22_2(X2,X1)) != hAPP(esk22_2(X2,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_655]),
[final] ).
cnf(i_0_1707,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(split_conjunct,[status(thm)],[i_0_985]),
[final] ).
cnf(i_0_1708,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1709,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_987]),
[final] ).
cnf(i_0_1710,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1711,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1712,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_953]),
[final] ).
cnf(i_0_1713,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_1714,plain,
( hAPP(hAPP(X2,X4),X4) = X4
| ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_1715,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1716,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1717,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1718,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1719,plain,
( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1720,plain,
c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1721,plain,
c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1722,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Orderings_Obot__class_Obot(X1)),X2))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_995]),
[final] ).
cnf(i_0_1723,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_996]),
[final] ).
cnf(i_0_1724,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_962]),
[final] ).
cnf(i_0_1725,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_997]),
[final] ).
cnf(i_0_1726,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1727,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1728,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_998]),
[final] ).
cnf(i_0_1729,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_999]),
[final] ).
cnf(i_0_1730,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_1000]),
[final] ).
cnf(i_0_1731,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_1001]),
[final] ).
cnf(i_0_1732,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1733,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_988]),
[final] ).
cnf(i_0_1734,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1735,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)
| X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1736,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_899]),
[final] ).
cnf(i_0_1737,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_899]),
[final] ).
cnf(i_0_1738,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_1002]),
[final] ).
cnf(i_0_1739,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X3,X1),X2))
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1740,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1741,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_1742,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_1005]),
[final] ).
cnf(i_0_1743,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1006]),
[final] ).
cnf(i_0_1744,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_1007]),
[final] ).
cnf(i_0_1745,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_1008]),
[final] ).
cnf(i_0_1746,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_987]),
[final] ).
cnf(i_0_1747,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1009]),
[final] ).
cnf(i_0_1748,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1010]),
[final] ).
cnf(i_0_1749,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1)
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1011]),
[final] ).
cnf(i_0_1750,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_1012]),
[final] ).
cnf(i_0_1751,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_1013]),
[final] ).
cnf(i_0_1752,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_1013]),
[final] ).
cnf(i_0_1753,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1754,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_928]),
[final] ).
cnf(i_0_1755,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_930]),
[final] ).
cnf(i_0_1756,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1015]),
[final] ).
cnf(i_0_1757,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1758,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1759,plain,
( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Finite__Set_Ocard(X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1760,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1019]),
[final] ).
cnf(i_0_1761,plain,
( c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1020]),
[final] ).
cnf(i_0_1762,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1763,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1022]),
[final] ).
cnf(i_0_1764,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1023]),
[final] ).
cnf(i_0_1765,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_999]),
[final] ).
cnf(i_0_1766,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_1000]),
[final] ).
cnf(i_0_1767,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_1001]),
[final] ).
cnf(i_0_1768,plain,
c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1769,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_1025]),
[final] ).
cnf(i_0_1770,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_1026]),
[final] ).
cnf(i_0_1771,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_1027]),
[final] ).
cnf(i_0_1772,plain,
c_Finite__Set_Ofinite(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[final] ).
cnf(i_0_1773,plain,
c_Finite__Set_Ofinite(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1774,plain,
( c_Finite__Set_Ocard(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1775,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_1013]),
[final] ).
cnf(i_0_1776,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_1777,plain,
( X2 = X3
| c_SetInterval_Oord__class_OgreaterThan(X1,X2) != c_SetInterval_Oord__class_OgreaterThan(X1,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1778,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_1031]),
[final] ).
cnf(i_0_1779,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_1032]),
[final] ).
cnf(i_0_1780,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_1033]),
[final] ).
cnf(i_0_1781,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_1034]),
[final] ).
cnf(i_0_1782,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_1035]),
[final] ).
cnf(i_0_1783,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_1036]),
[final] ).
cnf(i_0_1784,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1785,plain,
( X1 = X2
| hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1786,plain,
( class_Orderings_Obot(tc_fun(X2,X1))
| ~ class_Orderings_Obot(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1787,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1788,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1789,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1790,plain,
( class_Orderings_Otop(tc_fun(X2,X1))
| ~ class_Orderings_Otop(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1791,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_1018]),
[final] ).
cnf(i_0_1792,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_1044]),
[final] ).
cnf(i_0_1793,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1794,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1795,plain,
hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1796,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1797,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1798,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1799,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1800,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1052]),
[final] ).
cnf(i_0_1801,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1053]),
[final] ).
cnf(i_0_1802,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[i_0_1054]),
[final] ).
cnf(i_0_1803,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_1055]),
[final] ).
cnf(i_0_1804,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_1805,plain,
( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1806,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1057]),
[final] ).
cnf(i_0_1807,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_1808,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_bot__nat__def]),
[final] ).
cnf(i_0_1809,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_bool_Osize_I1_J]),
[final] ).
cnf(i_0_1810,plain,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_bool_Osize_I2_J]),
[final] ).
cnf(i_0_1811,plain,
~ hBOOL(c_fFalse),
inference(split_conjunct,[status(thm)],[i_0_1058]),
[final] ).
cnf(i_0_1812,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_1813,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_1814,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_1815,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_1816,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_1817,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_1818,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_1819,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_1820,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_1821,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_1822,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_1823,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_1824,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_1825,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
[final] ).
cnf(i_0_1826,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]),
[final] ).
cnf(i_0_1827,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
[final] ).
cnf(i_0_1828,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_1829,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_1830,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_1831,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_1832,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_1833,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_1834,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_1835,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(split_conjunct,[status(thm)],[fact_assms_I3_J]),
[final] ).
cnf(i_0_1836,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(split_conjunct,[status(thm)],[fact_u]),
[final] ).
cnf(i_0_1837,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
[final] ).
cnf(i_0_1838,plain,
hBOOL(c_fTrue),
inference(split_conjunct,[status(thm)],[help_c__fTrue__1]),
[final] ).
cnf(i_0_1839,plain,
v_a____ != v_b____,
inference(split_conjunct,[status(thm)],[fact__096a_A_126_061_Ab_096]),
[final] ).
cnf(i_0_1840,negated_conjecture,
v_Lba____ != v_Lab____,
inference(split_conjunct,[status(thm)],[i_0_769]),
[final] ).
cnf(i_0_1841,axiom,
X1 = X1 ).
cnf(i_0_1842,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1843,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1844,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1845,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1846,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1847,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1848,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1849,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1850,axiom,
( X1 != X2
| c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).
cnf(i_0_1851,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1852,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1853,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1854,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1855,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1856,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1857,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1858,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1859,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1860,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1861,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1862,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3,X4,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_1863,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1,X4,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_1864,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X1,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_1865,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X5,X1) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_1866,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1867,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1868,axiom,
( X1 != X2
| esk21_2(X1,X3) = esk21_2(X2,X3) ) ).
cnf(i_0_1869,axiom,
( X1 != X2
| esk21_2(X3,X1) = esk21_2(X3,X2) ) ).
cnf(i_0_1870,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1871,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1872,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1873,axiom,
( X1 != X2
| esk4_5(X1,X3,X4,X5,X6) = esk4_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1874,axiom,
( X1 != X2
| esk4_5(X3,X1,X4,X5,X6) = esk4_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1875,axiom,
( X1 != X2
| esk4_5(X3,X4,X1,X5,X6) = esk4_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1876,axiom,
( X1 != X2
| esk4_5(X3,X4,X5,X1,X6) = esk4_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1877,axiom,
( X1 != X2
| esk4_5(X3,X4,X5,X6,X1) = esk4_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1878,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1879,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1880,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1881,axiom,
( X1 != X2
| esk3_4(X1,X3,X4,X5) = esk3_4(X2,X3,X4,X5) ) ).
cnf(i_0_1882,axiom,
( X1 != X2
| esk3_4(X3,X1,X4,X5) = esk3_4(X3,X2,X4,X5) ) ).
cnf(i_0_1883,axiom,
( X1 != X2
| esk3_4(X3,X4,X1,X5) = esk3_4(X3,X4,X2,X5) ) ).
cnf(i_0_1884,axiom,
( X1 != X2
| esk3_4(X3,X4,X5,X1) = esk3_4(X3,X4,X5,X2) ) ).
cnf(i_0_1885,axiom,
( X1 != X2
| esk10_4(X1,X3,X4,X5) = esk10_4(X2,X3,X4,X5) ) ).
cnf(i_0_1886,axiom,
( X1 != X2
| esk10_4(X3,X1,X4,X5) = esk10_4(X3,X2,X4,X5) ) ).
cnf(i_0_1887,axiom,
( X1 != X2
| esk10_4(X3,X4,X1,X5) = esk10_4(X3,X4,X2,X5) ) ).
cnf(i_0_1888,axiom,
( X1 != X2
| esk10_4(X3,X4,X5,X1) = esk10_4(X3,X4,X5,X2) ) ).
cnf(i_0_1889,axiom,
( X1 != X2
| esk9_4(X1,X3,X4,X5) = esk9_4(X2,X3,X4,X5) ) ).
cnf(i_0_1890,axiom,
( X1 != X2
| esk9_4(X3,X1,X4,X5) = esk9_4(X3,X2,X4,X5) ) ).
cnf(i_0_1891,axiom,
( X1 != X2
| esk9_4(X3,X4,X1,X5) = esk9_4(X3,X4,X2,X5) ) ).
cnf(i_0_1892,axiom,
( X1 != X2
| esk9_4(X3,X4,X5,X1) = esk9_4(X3,X4,X5,X2) ) ).
cnf(i_0_1893,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_1894,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_1895,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_1896,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_1897,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1898,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1899,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1900,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1901,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThan(X1,X3) = c_SetInterval_Oord__class_OgreaterThan(X2,X3) ) ).
cnf(i_0_1902,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThan(X3,X1) = c_SetInterval_Oord__class_OgreaterThan(X3,X2) ) ).
cnf(i_0_1903,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1904,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1905,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1906,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1907,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1908,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1909,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1910,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1911,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1912,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1913,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1914,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1915,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1916,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1917,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1918,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1919,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1920,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1921,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
| c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).
cnf(i_0_1922,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
| c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).
cnf(i_0_1923,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
| c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).
cnf(i_0_1924,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
| c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).
cnf(i_0_1925,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1926,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1927,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1928,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1929,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1930,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1931,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1932,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_1933,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1934,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1935,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
| c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).
cnf(i_0_1936,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
| c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).
cnf(i_0_1937,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
| c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).
cnf(i_0_1938,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1939,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1940,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1941,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1942,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1943,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1944,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1945,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1946,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1947,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1948,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_1949,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_1950,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_1951,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_1952,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_1953,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_1841_001,axiom,
X1 = X1 ).
cnf(i_0_1842_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1843_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1844_004,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1845_005,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1846_006,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1847_007,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X1,X3) = c_Nat_Osize__class_Osize(X2,X3) ) ).
cnf(i_0_1848_008,axiom,
( X1 != X2
| c_Nat_Osize__class_Osize(X3,X1) = c_Nat_Osize__class_Osize(X3,X2) ) ).
cnf(i_0_1849_009,axiom,
( X1 != X2
| c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).
cnf(i_0_1850_010,axiom,
( X1 != X2
| c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).
cnf(i_0_1851_011,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X1,X3) = c_Orderings_Oord__class_Oless__eq(X2,X3) ) ).
cnf(i_0_1852_012,axiom,
( X1 != X2
| c_Orderings_Oord__class_Oless__eq(X3,X1) = c_Orderings_Oord__class_Oless__eq(X3,X2) ) ).
cnf(i_0_1853_013,axiom,
( X1 != X2
| c_FuncSet_OPi(X1,X3,X4,X5) = c_FuncSet_OPi(X2,X3,X4,X5) ) ).
cnf(i_0_1854_014,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X1,X4,X5) = c_FuncSet_OPi(X3,X2,X4,X5) ) ).
cnf(i_0_1855_015,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X1,X5) = c_FuncSet_OPi(X3,X4,X2,X5) ) ).
cnf(i_0_1856_016,axiom,
( X1 != X2
| c_FuncSet_OPi(X3,X4,X5,X1) = c_FuncSet_OPi(X3,X4,X5,X2) ) ).
cnf(i_0_1857_017,axiom,
( X1 != X2
| c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).
cnf(i_0_1858_018,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1859_019,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1860_020,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1861_021,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1862_022,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X1,X3,X4,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_1863_023,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X1,X4,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_1864_024,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X1,X5) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_1865_025,axiom,
( X1 != X2
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X5,X1) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_1866_026,axiom,
( X1 != X2
| esk20_2(X1,X3) = esk20_2(X2,X3) ) ).
cnf(i_0_1867_027,axiom,
( X1 != X2
| esk20_2(X3,X1) = esk20_2(X3,X2) ) ).
cnf(i_0_1868_028,axiom,
( X1 != X2
| esk21_2(X1,X3) = esk21_2(X2,X3) ) ).
cnf(i_0_1869_029,axiom,
( X1 != X2
| esk21_2(X3,X1) = esk21_2(X3,X2) ) ).
cnf(i_0_1870_030,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X1,X3) = c_Finite__Set_Ocard(X2,X3) ) ).
cnf(i_0_1871_031,axiom,
( X1 != X2
| c_Finite__Set_Ocard(X3,X1) = c_Finite__Set_Ocard(X3,X2) ) ).
cnf(i_0_1872_032,axiom,
( X1 != X2
| c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).
cnf(i_0_1873_033,axiom,
( X1 != X2
| esk4_5(X1,X3,X4,X5,X6) = esk4_5(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1874_034,axiom,
( X1 != X2
| esk4_5(X3,X1,X4,X5,X6) = esk4_5(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1875_035,axiom,
( X1 != X2
| esk4_5(X3,X4,X1,X5,X6) = esk4_5(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1876_036,axiom,
( X1 != X2
| esk4_5(X3,X4,X5,X1,X6) = esk4_5(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1877_037,axiom,
( X1 != X2
| esk4_5(X3,X4,X5,X6,X1) = esk4_5(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1878_038,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,X4) ) ).
cnf(i_0_1879_039,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X2,X4) ) ).
cnf(i_0_1880_040,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastLessThan(X3,X4,X2) ) ).
cnf(i_0_1881_041,axiom,
( X1 != X2
| esk3_4(X1,X3,X4,X5) = esk3_4(X2,X3,X4,X5) ) ).
cnf(i_0_1882_042,axiom,
( X1 != X2
| esk3_4(X3,X1,X4,X5) = esk3_4(X3,X2,X4,X5) ) ).
cnf(i_0_1883_043,axiom,
( X1 != X2
| esk3_4(X3,X4,X1,X5) = esk3_4(X3,X4,X2,X5) ) ).
cnf(i_0_1884_044,axiom,
( X1 != X2
| esk3_4(X3,X4,X5,X1) = esk3_4(X3,X4,X5,X2) ) ).
cnf(i_0_1885_045,axiom,
( X1 != X2
| esk10_4(X1,X3,X4,X5) = esk10_4(X2,X3,X4,X5) ) ).
cnf(i_0_1886_046,axiom,
( X1 != X2
| esk10_4(X3,X1,X4,X5) = esk10_4(X3,X2,X4,X5) ) ).
cnf(i_0_1887_047,axiom,
( X1 != X2
| esk10_4(X3,X4,X1,X5) = esk10_4(X3,X4,X2,X5) ) ).
cnf(i_0_1888_048,axiom,
( X1 != X2
| esk10_4(X3,X4,X5,X1) = esk10_4(X3,X4,X5,X2) ) ).
cnf(i_0_1889_049,axiom,
( X1 != X2
| esk9_4(X1,X3,X4,X5) = esk9_4(X2,X3,X4,X5) ) ).
cnf(i_0_1890_050,axiom,
( X1 != X2
| esk9_4(X3,X1,X4,X5) = esk9_4(X3,X2,X4,X5) ) ).
cnf(i_0_1891_051,axiom,
( X1 != X2
| esk9_4(X3,X4,X1,X5) = esk9_4(X3,X4,X2,X5) ) ).
cnf(i_0_1892_052,axiom,
( X1 != X2
| esk9_4(X3,X4,X5,X1) = esk9_4(X3,X4,X5,X2) ) ).
cnf(i_0_1893_053,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).
cnf(i_0_1894_054,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).
cnf(i_0_1895_055,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).
cnf(i_0_1896_056,axiom,
( X1 != X2
| c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).
cnf(i_0_1897_057,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).
cnf(i_0_1898_058,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).
cnf(i_0_1899_059,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).
cnf(i_0_1900_060,axiom,
( X1 != X2
| c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).
cnf(i_0_1901_061,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThan(X1,X3) = c_SetInterval_Oord__class_OgreaterThan(X2,X3) ) ).
cnf(i_0_1902_062,axiom,
( X1 != X2
| c_SetInterval_Oord__class_OgreaterThan(X3,X1) = c_SetInterval_Oord__class_OgreaterThan(X3,X2) ) ).
cnf(i_0_1903_063,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1904_064,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X1,X3,X4,X5)
| c_Fun_Oinj__on(X2,X3,X4,X5) ) ).
cnf(i_0_1905_065,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5)
| c_Fun_Oinj__on(X3,X2,X4,X5) ) ).
cnf(i_0_1906_066,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X1,X5)
| c_Fun_Oinj__on(X3,X4,X2,X5) ) ).
cnf(i_0_1907_067,axiom,
( X1 != X2
| ~ c_Fun_Oinj__on(X3,X4,X5,X1)
| c_Fun_Oinj__on(X3,X4,X5,X2) ) ).
cnf(i_0_1908_068,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Ounanimity(X1)
| c_Arrow__Order__Mirabelle_Ounanimity(X2) ) ).
cnf(i_0_1909_069,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X1,X3,X4,X5,X6)
| c_FunDef_Oin__rel(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1910_070,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X1,X4,X5,X6)
| c_FunDef_Oin__rel(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1911_071,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X1,X5,X6)
| c_FunDef_Oin__rel(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1912_072,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X1,X6)
| c_FunDef_Oin__rel(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1913_073,axiom,
( X1 != X2
| ~ c_FunDef_Oin__rel(X3,X4,X5,X6,X1)
| c_FunDef_Oin__rel(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1914_074,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1915_075,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1916_076,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1917_077,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1918_078,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_1919_079,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_1920_080,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_1921_081,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
| c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).
cnf(i_0_1922_082,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
| c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).
cnf(i_0_1923_083,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
| c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).
cnf(i_0_1924_084,axiom,
( X1 != X2
| ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
| c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).
cnf(i_0_1925_085,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1926_086,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_1927_087,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1928_088,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1929_089,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_1930_090,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1931_091,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1932_092,axiom,
( X1 != X2
| ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(X2) ) ).
cnf(i_0_1933_093,axiom,
( X1 != X2
| ~ class_Orderings_Otop(X1)
| class_Orderings_Otop(X2) ) ).
cnf(i_0_1934_094,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_1935_095,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
| c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).
cnf(i_0_1936_096,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
| c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).
cnf(i_0_1937_097,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
| c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).
cnf(i_0_1938_098,axiom,
( X1 != X2
| ~ class_Finite__Set_Ofinite(X1)
| class_Finite__Set_Ofinite(X2) ) ).
cnf(i_0_1939_099,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_1940_100,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_1941_101,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X1,X3)
| c_Finite__Set_Ofinite(X2,X3) ) ).
cnf(i_0_1942_102,axiom,
( X1 != X2
| ~ c_Finite__Set_Ofinite(X3,X1)
| c_Finite__Set_Ofinite(X3,X2) ) ).
cnf(i_0_1943_103,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_OIIA(X1)
| c_Arrow__Order__Mirabelle_OIIA(X2) ) ).
cnf(i_0_1944_104,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1945_105,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X3)
| c_Arrow__Order__Mirabelle_Odictator(X2,X3) ) ).
cnf(i_0_1946_106,axiom,
( X1 != X2
| ~ c_Arrow__Order__Mirabelle_Odictator(X3,X1)
| c_Arrow__Order__Mirabelle_Odictator(X3,X2) ) ).
cnf(i_0_1947_107,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_1948_108,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_1949_109,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_1950_110,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_1951_111,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_1952_112,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_1953_113,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_1954,plain,
X1 = X1,
inference(equality_inference,[],[1070]) ).
cnf(i_0_1955,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X5))),c_Wellfounded_Olex__prod(X1,X2,X6,X7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X5)),X7)) ),
inference(equality_inference,[],[1113]) ).
cnf(i_0_1956,plain,
( c_Set_Oimage(X1,X2,X3,X4) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,esk51_4(X4,X1,X2,c_Set_Oimage(X1,X2,X3,X4)),c_Set_Oimage(X1,X2,X3,X4))),X4)) ),
inference(equality_inference,[],[1130]) ).
cnf(i_0_1957,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),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Wellfounded_Omax__ext(X1,X3))),
inference(equality_inference,[],[1140]) ).
cnf(i_0_1958,plain,
( X1 = X2
| X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1146]) ).
cnf(i_0_1959,plain,
( X1 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1147]) ).
cnf(i_0_1960,plain,
( X1 = X2
| X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1148]) ).
cnf(i_0_1961,plain,
( X1 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1149]) ).
cnf(i_0_1962,plain,
( X1 = X2
| X3 = X1
| X3 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1172]) ).
cnf(i_0_1963,plain,
( X1 = X2
| X3 = X2
| X3 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1173]) ).
cnf(i_0_1964,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1177]) ).
cnf(i_0_1965,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1178]) ).
cnf(i_0_1966,plain,
( X1 = X2
| X3 = X2
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1184]) ).
cnf(i_0_1967,plain,
( X1 = X2
| X3 = X1
| X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1185]) ).
cnf(i_0_1968,plain,
( X1 = X2
| X1 = X2
| X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1186]) ).
cnf(i_0_1969,plain,
( X1 = X2
| X2 = X1
| X3 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1187]) ).
cnf(i_0_1970,plain,
( X1 = X2
| X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1190]) ).
cnf(i_0_1971,plain,
( X1 = X2
| X3 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1191]) ).
cnf(i_0_1972,plain,
( X1 = esk3_4(hAPP(X2,X1),X2,X3,X4)
| ~ c_Fun_Oinj__on(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X2,X1)),c_Set_Oimage(X4,X3,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))) ),
inference(equality_inference,[],[1203]) ).
cnf(i_0_1973,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X3)),c_Arrow__Order__Mirabelle_Oabove(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1206]) ).
cnf(i_0_1974,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_inference,[],[1207]) ).
cnf(i_0_1975,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),c_Set_Oimage(X2,X1,X3,X5)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X4),X5)) ),
inference(equality_inference,[],[1239]) ).
cnf(i_0_1976,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_Omktop(X3,X1))),
inference(equality_inference,[],[1254]) ).
cnf(i_0_1977,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_Omkbot(X3,X2))),
inference(equality_inference,[],[1255]) ).
cnf(i_0_1978,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(equality_inference,[],[1267]) ).
cnf(i_0_1979,plain,
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
inference(equality_inference,[],[1273]) ).
cnf(i_0_1980,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1275]) ).
cnf(i_0_1981,plain,
( c_Fun_Oinj__on(X1,X2,esk51_4(X3,X2,X1,c_Set_Oimage(X2,X1,X4,X3)),c_Set_Oimage(X2,X1,X4,X3))
| c_Set_Oimage(X2,X1,X4,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(equality_inference,[],[1286]) ).
cnf(i_0_1982,plain,
X1 = X1,
inference(equality_inference,[],[1290]) ).
cnf(i_0_1983,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
| hAPP(c_Fun_Othe__inv__into(X1,X2,X4,X3),hAPP(X3,X5)) = X5
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4)) ),
inference(equality_inference,[],[1293]) ).
cnf(i_0_1984,plain,
( X1 = X2
| X2 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X1))) ),
inference(equality_inference,[],[1313]) ).
cnf(i_0_1985,plain,
( X1 = X2
| X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omktop(X3,X2))) ),
inference(equality_inference,[],[1314]) ).
cnf(i_0_1986,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,X5)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X5)) ),
inference(equality_inference,[],[1356]) ).
cnf(i_0_1987,plain,
( X1 = X1
| ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
inference(equality_inference,[],[1437]) ).
cnf(i_0_1988,plain,
( X1 = X1
| ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X3)) ),
inference(equality_inference,[],[1440]) ).
cnf(i_0_1989,plain,
( X1 = X1
| ~ class_Orderings_Olinorder(X2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X1)) ),
inference(equality_inference,[],[1441]) ).
cnf(i_0_1990,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),X2)),
inference(equality_inference,[],[1442]) ).
cnf(i_0_1991,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
inference(equality_inference,[],[1455]) ).
cnf(i_0_1992,plain,
~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(equality_inference,[],[1470]) ).
cnf(i_0_1993,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(equality_inference,[],[1534]) ).
cnf(i_0_1994,plain,
c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(equality_inference,[],[1535]) ).
cnf(i_0_1995,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(equality_inference,[],[1545]) ).
cnf(i_0_1996,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_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(equality_inference,[],[1561]) ).
cnf(i_0_1997,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(equality_inference,[],[1585]) ).
cnf(i_0_1998,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
inference(equality_inference,[],[1586]) ).
cnf(i_0_1999,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(equality_inference,[],[1636]) ).
cnf(i_0_2000,plain,
( ~ class_Orderings_Olinorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1643]) ).
cnf(i_0_2001,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1660]) ).
cnf(i_0_2002,plain,
( ~ class_Orderings_Oorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1661]) ).
cnf(i_0_2003,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1662]) ).
cnf(i_0_2004,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
inference(equality_inference,[],[1663]) ).
cnf(i_0_2005,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1669]) ).
cnf(i_0_2006,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(equality_inference,[],[1670]) ).
cnf(i_0_2007,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[1675]) ).
cnf(i_0_2008,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[1676]) ).
cnf(i_0_2009,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[1678]) ).
cnf(i_0_2010,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(equality_inference,[],[1688]) ).
cnf(i_0_2011,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[1690]) ).
cnf(i_0_2012,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1696]) ).
cnf(i_0_2013,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(equality_inference,[],[1697]) ).
cnf(i_0_2014,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(equality_inference,[],[1698]) ).
cnf(i_0_2015,plain,
X1 = X1,
inference(equality_inference,[],[1701]) ).
cnf(i_0_2016,plain,
X1 = X1,
inference(equality_inference,[],[1702]) ).
cnf(i_0_2017,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[1703]) ).
cnf(i_0_2018,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[1704]) ).
cnf(i_0_2019,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
inference(equality_inference,[],[1712]) ).
cnf(i_0_2020,plain,
X1 = X1,
inference(equality_inference,[],[1713]) ).
cnf(i_0_2021,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1737]) ).
cnf(i_0_2022,plain,
( ~ class_Orderings_Opreorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1738]) ).
cnf(i_0_2023,plain,
( ~ class_Orderings_Oorder(X1)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X2)) ),
inference(equality_inference,[],[1739]) ).
cnf(i_0_2024,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(equality_inference,[],[1756]) ).
cnf(i_0_2025,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_inference,[],[1757]) ).
cnf(i_0_2026,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[1765]) ).
cnf(i_0_2027,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[1766]) ).
cnf(i_0_2028,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[1767]) ).
cnf(i_0_2029,plain,
c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[1774]) ).
cnf(i_0_2030,plain,
( ~ class_Orderings_Olinorder(X1)
| X2 = X2 ),
inference(equality_inference,[],[1777]) ).
cnf(i_0_2031,plain,
X1 = X1,
inference(equality_inference,[],[1785]) ).
cnf(i_0_2032,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))))),
inference(scs_inference,[],[i_0_1444,i_0_1343]) ).
cnf(i_0_2033,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
inference(rename_variables,[],[i_0_1444]) ).
cnf(i_0_2034,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
inference(rename_variables,[],[i_0_1343]) ).
cnf(i_0_2035,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(v_h____,v_Sledgehammer_058p__2))),hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_1390,i_0_1444,i_0_1343,i_0_1457]) ).
cnf(i_0_2036,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(rename_variables,[],[i_0_1457]) ).
cnf(i_0_2037,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1707,i_0_1444,i_0_1343,i_0_1457,i_0_1493]) ).
cnf(i_0_2038,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1707]) ).
cnf(i_0_2039,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rename_variables,[],[i_0_1493]) ).
cnf(i_0_2040,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
inference(scs_inference,[],[i_0_1390,i_0_1707,i_0_1592,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511]) ).
cnf(i_0_2041,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(rename_variables,[],[i_0_1592]) ).
cnf(i_0_2042,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rename_variables,[],[i_0_1511]) ).
cnf(i_0_2043,plain,
c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1707,i_0_1592,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586]) ).
cnf(i_0_2044,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)) ),
inference(rename_variables,[],[i_0_1586]) ).
cnf(i_0_2045,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,hAPP(v_h____,v_Sledgehammer_058p__2)))),
inference(scs_inference,[],[i_0_1390,i_0_1707,i_0_1592,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616]) ).
cnf(i_0_2046,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
inference(rename_variables,[],[i_0_1616]) ).
cnf(i_0_2047,plain,
hBOOL(hAPP(c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(X3,X4))),
inference(scs_inference,[],[i_0_1390,i_0_1707,i_0_1260,i_0_1592,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644]) ).
cnf(i_0_2048,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1644]) ).
cnf(i_0_2049,plain,
X1 = c_Nat_Osize__class_Osize(tc_Nat_Onat,X1),
inference(scs_inference,[],[i_0_1390,i_0_1806,i_0_1707,i_0_1260,i_0_1592,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842]) ).
cnf(i_0_2050,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),c_FuncSet_OPi(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X3)),c_FuncSet_OPi(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4))),
inference(scs_inference,[],[i_0_1390,i_0_1806,i_0_1707,i_0_1529,i_0_1260,i_0_1592,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105]) ).
cnf(i_0_2051,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1529]) ).
cnf(i_0_2052,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk42_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(rename_variables,[],[i_0_1105]) ).
cnf(i_0_2053,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4))),
inference(scs_inference,[],[i_0_1390,i_0_1806,i_0_1707,i_0_1529,i_0_2051,i_0_1260,i_0_1592,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110]) ).
cnf(i_0_2054,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1529]) ).
cnf(i_0_2055,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk32_5(X2,X3,X4,X5,X1)),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X5,X2))) ),
inference(rename_variables,[],[i_0_1110]) ).
cnf(i_0_2056,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X2)),c_Wellfounded_Ofinite__psubset(X1))),
inference(scs_inference,[],[i_0_1390,i_0_1991,i_0_1806,i_0_1707,i_0_1529,i_0_2051,i_0_1260,i_0_1592,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138]) ).
cnf(i_0_2057,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2),X3)),c_Wellfounded_Ofinite__psubset(X1))) ),
inference(rename_variables,[],[i_0_1138]) ).
cnf(i_0_2058,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X1,X1,c_COMBI(X1),X2)),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1991,i_0_1806,i_0_1707,i_0_1529,i_0_2051,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139]) ).
cnf(i_0_2059,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),c_Set_Oimage(X1,X2,X3,X4)),X5)) ),
inference(rename_variables,[],[i_0_1139]) ).
cnf(i_0_2060,plain,
c_Set_Oimage(X1,X2,X3,X4) = c_Set_Oimage(X1,X2,X3,esk36_5(X4,X3,X1,c_Set_Oimage(X1,X2,X3,X4),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1991,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156]) ).
cnf(i_0_2061,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1672]) ).
cnf(i_0_2062,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
| X2 = c_Set_Oimage(X3,X1,X4,esk36_5(X5,X4,X3,X2,X1)) ),
inference(rename_variables,[],[i_0_1156]) ).
cnf(i_0_2063,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1991,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_2054,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164]) ).
cnf(i_0_2064,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1529]) ).
cnf(i_0_2065,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk11_4(X2,X3,X1,X4)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X4),c_Set_Oimage(X1,X5,X3,X2))) ),
inference(rename_variables,[],[i_0_1164]) ).
cnf(i_0_2066,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),c_FuncSet_OPi(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),c_FuncSet_OPi(X1,X2,X4,X3))),
inference(scs_inference,[],[i_0_1390,i_0_1991,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_2054,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171]) ).
cnf(i_0_2067,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X1,X4),tc_HOL_Obool),c_FuncSet_OPi(X1,X4,X3,X5)),c_FuncSet_OPi(X1,X4,X2,X5))) ),
inference(rename_variables,[],[i_0_1171]) ).
cnf(i_0_2068,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),c_Set_Oimage(X2,X1,X3,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1991,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_2054,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192]) ).
cnf(i_0_2069,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),c_Set_Oimage(X1,X4,X5,X2)),c_Set_Oimage(X1,X4,X5,X3))) ),
inference(rename_variables,[],[i_0_1192]) ).
cnf(i_0_2070,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,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____)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_Lab____)),v_Lba____)),v_a____,v_b____),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_2054,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198]) ).
cnf(i_0_2071,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
| ~ c_FunDef_Oin__rel(X1,X2,X5,X3,X4) ),
inference(rename_variables,[],[i_0_1198]) ).
cnf(i_0_2072,plain,
c_FunDef_Oin__rel(X1,X2,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X3,X4),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_2054,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201]) ).
cnf(i_0_2073,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2010]) ).
cnf(i_0_2074,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),X5))
| c_FunDef_Oin__rel(X1,X2,X5,X3,X4) ),
inference(rename_variables,[],[i_0_1201]) ).
cnf(i_0_2075,plain,
c_FuncSet_OPi(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X3) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208]) ).
cnf(i_0_2076,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1529]) ).
cnf(i_0_2077,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk46_4(X2,X3,X4,X1)),X3))
| c_FuncSet_OPi(X1,X4,X3,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X4),tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1208]) ).
cnf(i_0_2078,plain,
c_Fun_Oinj__on(X1,X2,X3,c_Set_Oimage(X4,X1,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221]) ).
cnf(i_0_2079,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk10_4(X2,X3,X4,X1)),X2))
| c_Fun_Oinj__on(X1,X4,X3,X2) ),
inference(rename_variables,[],[i_0_1221]) ).
cnf(i_0_2080,plain,
hAPP(X1,X2) = hAPP(X1,esk11_4(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),X1,X3,hAPP(X1,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_1672,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224]) ).
cnf(i_0_2081,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
| X2 = hAPP(X4,esk11_4(X5,X4,X3,X2)) ),
inference(rename_variables,[],[i_0_1224]) ).
cnf(i_0_2082,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Wellfounded_Omeasure(X1,X3))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236]) ).
cnf(i_0_2083,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1700]) ).
cnf(i_0_2084,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omeasure(X4,X1))) ),
inference(rename_variables,[],[i_0_1236]) ).
cnf(i_0_2085,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(esk13_0,X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246]) ).
cnf(i_0_2086,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omkbot(X1,X2)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(rename_variables,[],[i_0_1246]) ).
cnf(i_0_2087,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(esk13_0,X1)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247]) ).
cnf(i_0_2088,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Omktop(X1,X2)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(rename_variables,[],[i_0_1247]) ).
cnf(i_0_2089,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),hAPP(c_Nat_OSuc,X2))),c_Wellfounded_Omlex__prod(X1,c_Nat_OSuc,X3))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_2038,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1592,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248]) ).
cnf(i_0_2090,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1707]) ).
cnf(i_0_2091,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omlex__prod(X4,X1,X5))) ),
inference(rename_variables,[],[i_0_1248]) ).
cnf(i_0_2092,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Finite__Set_Ocard(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_2038,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1495,i_0_1592,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250]) ).
cnf(i_0_2093,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)),
inference(rename_variables,[],[i_0_1495]) ).
cnf(i_0_2094,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),X1),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Finite__Set_Ocard(tc_Nat_Onat,X1)))))
| X1 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Finite__Set_Ocard(tc_Nat_Onat,X1))) ),
inference(rename_variables,[],[i_0_1250]) ).
cnf(i_0_2095,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),hAPP(c_Nat_OSuc,X2))),c_Wellfounded_Omeasure(X1,c_Nat_OSuc))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_1806,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1495,i_0_1592,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256]) ).
cnf(i_0_2096,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1707]) ).
cnf(i_0_2097,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X1,X2)),hAPP(X1,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X3)),c_Wellfounded_Omeasure(X4,X1))) ),
inference(rename_variables,[],[i_0_1256]) ).
cnf(i_0_2098,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,hAPP(c_fequal,X3)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_2073,i_0_1806,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1260,i_0_1495,i_0_1592,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262]) ).
cnf(i_0_2099,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3))) ),
inference(rename_variables,[],[i_0_1262]) ).
cnf(i_0_2100,plain,
~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_2073,i_0_1806,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308]) ).
cnf(i_0_2101,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1308]) ).
cnf(i_0_2102,plain,
hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346]) ).
cnf(i_0_2103,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2104,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1346]) ).
cnf(i_0_2105,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359]) ).
cnf(i_0_2106,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(rename_variables,[],[i_0_1592]) ).
cnf(i_0_2107,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(rename_variables,[],[i_0_1359]) ).
cnf(i_0_2108,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),X3))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360]) ).
cnf(i_0_2109,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(rename_variables,[],[i_0_1592]) ).
cnf(i_0_2110,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(rename_variables,[],[i_0_1360]) ).
cnf(i_0_2111,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatMost(X1,c_fequal,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461]) ).
cnf(i_0_2112,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OatMost(X4,X1,X3))) ),
inference(rename_variables,[],[i_0_1461]) ).
cnf(i_0_2113,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OlessThan(X1,c_fequal,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462]) ).
cnf(i_0_2114,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_member(X4),X2),c_SetInterval_Oord_OlessThan(X4,X1,X3))) ),
inference(rename_variables,[],[i_0_1462]) ).
cnf(i_0_2115,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeast(X1,c_fequal,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463]) ).
cnf(i_0_2116,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OatLeast(X4,X1,X2))) ),
inference(rename_variables,[],[i_0_1463]) ).
cnf(i_0_2117,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThan(X1,c_fequal,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464]) ).
cnf(i_0_2118,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| hBOOL(hAPP(hAPP(c_member(X4),X3),c_SetInterval_Oord_OgreaterThan(X4,X1,X2))) ),
inference(rename_variables,[],[i_0_1464]) ).
cnf(i_0_2119,plain,
~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_1231,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470]) ).
cnf(i_0_2120,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2121,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ c_Wellfounded_Omax__extp(X2,X3,X4,X1) ),
inference(rename_variables,[],[i_0_1470]) ).
cnf(i_0_2122,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_1231,i_0_1376,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473]) ).
cnf(i_0_2123,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(rename_variables,[],[i_0_1376]) ).
cnf(i_0_2124,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rename_variables,[],[i_0_1473]) ).
cnf(i_0_2125,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X3)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475]) ).
cnf(i_0_2126,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(rename_variables,[],[i_0_1376]) ).
cnf(i_0_2127,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X3)) ),
inference(rename_variables,[],[i_0_1475]) ).
cnf(i_0_2128,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494]) ).
cnf(i_0_2129,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(rename_variables,[],[i_0_1592]) ).
cnf(i_0_2130,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(rename_variables,[],[i_0_1494]) ).
cnf(i_0_2131,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497]) ).
cnf(i_0_2132,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2))) ),
inference(rename_variables,[],[i_0_1497]) ).
cnf(i_0_2133,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500]) ).
cnf(i_0_2134,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2135,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1500]) ).
cnf(i_0_2136,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502]) ).
cnf(i_0_2137,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2138,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(rename_variables,[],[i_0_1502]) ).
cnf(i_0_2139,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506]) ).
cnf(i_0_2140,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1))) ),
inference(rename_variables,[],[i_0_1506]) ).
cnf(i_0_2141,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525]) ).
cnf(i_0_2142,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2143,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1525]) ).
cnf(i_0_2144,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527]) ).
cnf(i_0_2145,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1527]) ).
cnf(i_0_2146,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_Set_Oimage(X2,X1,X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534]) ).
cnf(i_0_2147,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2148,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = c_Set_Oimage(X2,X3,X4,X1) ),
inference(rename_variables,[],[i_0_1534]) ).
cnf(i_0_2149,plain,
c_Set_Oimage(X1,X2,X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535]) ).
cnf(i_0_2150,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2151,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X2,X3,X4,X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1535]) ).
cnf(i_0_2152,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk49_2(hAPP(c_Nat_OSuc,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555]) ).
cnf(i_0_2153,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk49_2(X2,X1))) ),
inference(rename_variables,[],[i_0_1555]) ).
cnf(i_0_2154,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559]) ).
cnf(i_0_2155,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1559]) ).
cnf(i_0_2156,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565]) ).
cnf(i_0_2157,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) ),
inference(rename_variables,[],[i_0_1565]) ).
cnf(i_0_2158,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(v_h____,v_Sledgehammer_058p__2))),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584]) ).
cnf(i_0_2159,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1584]) ).
cnf(i_0_2160,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),hAPP(v_h____,v_Sledgehammer_058p__2))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606]) ).
cnf(i_0_2161,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(rename_variables,[],[i_0_1606]) ).
cnf(i_0_2162,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612]) ).
cnf(i_0_2163,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2164,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1612]) ).
cnf(i_0_2165,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621]) ).
cnf(i_0_2166,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1621]) ).
cnf(i_0_2167,plain,
hAPP(c_fequal,X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636]) ).
cnf(i_0_2168,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| X3 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1636]) ).
cnf(i_0_2169,plain,
X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk45_2(X1,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653]) ).
cnf(i_0_2170,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk45_2(X2,X1)) ),
inference(rename_variables,[],[i_0_1653]) ).
cnf(i_0_2171,plain,
hAPP(c_Nat_OSuc,X1) = hAPP(c_Nat_OSuc,esk43_1(hAPP(c_Nat_OSuc,X1))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656]) ).
cnf(i_0_2172,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,esk43_1(X1)) ),
inference(rename_variables,[],[i_0_1656]) ).
cnf(i_0_2173,plain,
~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_Omktop(X1,X2),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689]) ).
cnf(i_0_2174,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(rename_variables,[],[i_0_1689]) ).
cnf(i_0_2175,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690]) ).
cnf(i_0_2176,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1690]) ).
cnf(i_0_2177,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691]) ).
cnf(i_0_2178,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X1)) ),
inference(rename_variables,[],[i_0_1691]) ).
cnf(i_0_2179,plain,
X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696]) ).
cnf(i_0_2180,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1696]) ).
cnf(i_0_2181,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697]) ).
cnf(i_0_2182,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_1697]) ).
cnf(i_0_2183,plain,
X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698]) ).
cnf(i_0_2184,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3) ),
inference(rename_variables,[],[i_0_1698]) ).
cnf(i_0_2185,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703]) ).
cnf(i_0_2186,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(rename_variables,[],[i_0_1376]) ).
cnf(i_0_2187,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1703]) ).
cnf(i_0_2188,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) != X1,
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704]) ).
cnf(i_0_2189,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1375]) ).
cnf(i_0_2190,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1704]) ).
cnf(i_0_2191,plain,
c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,X2),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712]) ).
cnf(i_0_2192,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| X1 != hAPP(c_Nat_OSuc,X2) ),
inference(rename_variables,[],[i_0_1712]) ).
cnf(i_0_2193,plain,
~ class_Orderings_Otop(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728]) ).
cnf(i_0_2194,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2195,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
inference(rename_variables,[],[i_0_1728]) ).
cnf(i_0_2196,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))) != hAPP(c_Nat_OSuc,X2),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756]) ).
cnf(i_0_2197,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1756]) ).
cnf(i_0_2198,plain,
c_Finite__Set_Ocard(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774]) ).
cnf(i_0_2199,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2200,plain,
( X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1774]) ).
cnf(i_0_2201,plain,
hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(X1,X2))) != X1,
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844]) ).
cnf(i_0_2202,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) != X2,
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845]) ).
cnf(i_0_2203,plain,
~ c_Wellfounded_Omax__extp(tc_Nat_Onat,X1,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X2),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490]) ).
cnf(i_0_2204,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
inference(rename_variables,[],[i_0_1490]) ).
cnf(i_0_2205,plain,
~ c_Wellfounded_Omax__extp(tc_Nat_Onat,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491]) ).
cnf(i_0_2206,plain,
( c_Finite__Set_Ofinite(X1,X2)
| ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
inference(rename_variables,[],[i_0_1491]) ).
cnf(i_0_2207,plain,
c_Finite__Set_Ofinite(tc_HOL_Obool,X1),
inference(scs_inference,[],[i_0_1390,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800]) ).
cnf(i_0_2208,plain,
( ~ class_Finite__Set_Ofinite(X1)
| c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1800]) ).
cnf(i_0_2209,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____),X1)),c_Arrow__Order__Mirabelle_Omkbot(c_Arrow__Order__Mirabelle_Omktop(X2,v_Lba____),v_Lab____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215]) ).
cnf(i_0_2210,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_Omktop(X3,X1))),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_2211,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X4)))
| X1 = X4 ),
inference(rename_variables,[],[i_0_1215]) ).
cnf(i_0_2212,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),v_Lba____)),c_Arrow__Order__Mirabelle_Omktop(c_Arrow__Order__Mirabelle_Omktop(X2,X1),v_Lab____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216]) ).
cnf(i_0_2213,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_Omktop(X3,X1))),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_2214,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omktop(X3,X4)))
| X2 = X4 ),
inference(rename_variables,[],[i_0_1216]) ).
cnf(i_0_2215,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(esk13_0,v_Lba____,v_Lab____)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233]) ).
cnf(i_0_2216,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Oabove(X1,X2,X3)),c_Arrow__Order__Mirabelle_OLin))
| X2 = X3 ),
inference(rename_variables,[],[i_0_1233]) ).
cnf(i_0_2217,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(esk13_0,v_Lba____,v_Lab____)),c_Arrow__Order__Mirabelle_OLin)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234]) ).
cnf(i_0_2218,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X1,X2,X3)),c_Arrow__Order__Mirabelle_OLin))
| X2 = X3 ),
inference(rename_variables,[],[i_0_1234]) ).
cnf(i_0_2219,plain,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))),hAPP(X1,X2)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1817,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235]) ).
cnf(i_0_2220,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X1))),hAPP(X4,X1))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(rename_variables,[],[i_0_1235]) ).
cnf(i_0_2221,plain,
X1 = esk36_5(X1,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_1817,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275]) ).
cnf(i_0_2222,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1608]) ).
cnf(i_0_2223,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| c_Set_Oimage(X1,X2,X3,X4) != c_Set_Oimage(X1,X2,X3,X5)
| X4 = X5 ),
inference(rename_variables,[],[i_0_1275]) ).
cnf(i_0_2224,plain,
X1 = esk11_4(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Nat_OSuc,X2,hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437]) ).
cnf(i_0_2225,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1608]) ).
cnf(i_0_2226,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| hAPP(X3,X4) != hAPP(X3,X5)
| X4 = X5 ),
inference(rename_variables,[],[i_0_1437]) ).
cnf(i_0_2227,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),hAPP(c_Nat_OSuc,X1)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(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(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492]) ).
cnf(i_0_2228,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X4) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2) ),
inference(rename_variables,[],[i_0_1492]) ).
cnf(i_0_2229,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,hAPP(v_h____,v_Sledgehammer_058p__2)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507]) ).
cnf(i_0_2230,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_SetInterval_Oord__class_OgreaterThan(X1,X2)))
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_1507]) ).
cnf(i_0_2231,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514]) ).
cnf(i_0_2232,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X2)),
inference(rename_variables,[],[i_0_1495]) ).
cnf(i_0_2233,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X2,X4)) ),
inference(rename_variables,[],[i_0_1514]) ).
cnf(i_0_2234,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539]) ).
cnf(i_0_2235,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1692]) ).
cnf(i_0_2236,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 = X2 ),
inference(rename_variables,[],[i_0_1539]) ).
cnf(i_0_2237,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633]) ).
cnf(i_0_2238,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1375]) ).
cnf(i_0_2239,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| X1 = X2 ),
inference(rename_variables,[],[i_0_1633]) ).
cnf(i_0_2240,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649]) ).
cnf(i_0_2241,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1649]) ).
cnf(i_0_2242,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(v_h____,v_Sledgehammer_058p__2),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650]) ).
cnf(i_0_2243,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1650]) ).
cnf(i_0_2244,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(v_h____,v_Sledgehammer_058p__2),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651]) ).
cnf(i_0_2245,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1651]) ).
cnf(i_0_2246,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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655]) ).
cnf(i_0_2247,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1375]) ).
cnf(i_0_2248,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| X1 = X2 ),
inference(rename_variables,[],[i_0_1655]) ).
cnf(i_0_2249,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)),c_Arrow__Order__Mirabelle_Oabove(esk13_0,v_Lba____,v_Lab____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973]) ).
cnf(i_0_2250,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X2)),c_Arrow__Order__Mirabelle_Oabove(X1,X3,X4)))
| X3 = X4 ),
inference(rename_variables,[],[i_0_1973]) ).
cnf(i_0_2251,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)),c_Arrow__Order__Mirabelle_Obelow(esk13_0,v_Lba____,v_Lab____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974]) ).
cnf(i_0_2252,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X2)),c_Arrow__Order__Mirabelle_Obelow(X1,X3,X4)))
| X3 = X4 ),
inference(rename_variables,[],[i_0_1974]) ).
cnf(i_0_2253,plain,
hAPP(c_Nat_OSuc,c_Set_Oimage(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843]) ).
cnf(i_0_2254,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2255,plain,
hAPP(hAPP(c_fequal,X1),X1) != hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903]) ).
cnf(i_0_2256,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(c_fequal,X1)),X2)),c_Wellfounded_Omax__ext(tc_Arrow__Order__Mirabelle_Oalt,c_Arrow__Order__Mirabelle_Omktop(X3,X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091]) ).
cnf(i_0_2257,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_Omktop(X3,X1))),
inference(rename_variables,[],[i_0_1976]) ).
cnf(i_0_2258,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2010]) ).
cnf(i_0_2259,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk57_5(X3,X4,X5,X1,X2))),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X5))
| ~ 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)),X5),X4)),c_Wellfounded_Omax__ext(X1,X3))) ),
inference(rename_variables,[],[i_0_1091]) ).
cnf(i_0_2260,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Nat_Onat),X2),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116]) ).
cnf(i_0_2261,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2262,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk35_4(X3,X2,X4,X1))),hAPP(X3,esk35_4(X3,X2,X4,X1))))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2),X3))
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_1116]) ).
cnf(i_0_2263,plain,
~ c_Wellfounded_Omax__extp(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_fun(X3,tc_HOL_Obool))),hAPP(c_fequal,X4),X5),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135]) ).
cnf(i_0_2264,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2010]) ).
cnf(i_0_2265,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),X3),X4)),
inference(rename_variables,[],[i_0_1296]) ).
cnf(i_0_2266,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(X4,X2),esk52_5(X5,X3,X4,X1,X2)))
| ~ c_Wellfounded_Omax__extp(X1,X4,X3,X5) ),
inference(rename_variables,[],[i_0_1135]) ).
cnf(i_0_2267,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeastLessThan(X1,c_fequal,c_fequal,X2,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143]) ).
cnf(i_0_2268,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5))
| hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OatLeastLessThan(X6,X1,X4,X2,X5))) ),
inference(rename_variables,[],[i_0_1143]) ).
cnf(i_0_2269,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThanAtMost(X1,c_fequal,c_fequal,X2,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144]) ).
cnf(i_0_2270,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X4,X3),X5))
| hBOOL(hAPP(hAPP(c_member(X6),X3),c_SetInterval_Oord_OgreaterThanAtMost(X6,X4,X1,X2,X5))) ),
inference(rename_variables,[],[i_0_1144]) ).
cnf(i_0_2271,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__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____)),esk13_0)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166]) ).
cnf(i_0_2272,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),X1)) ),
inference(rename_variables,[],[i_0_1166]) ).
cnf(i_0_2273,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_COMBI(X1),X2)),hAPP(c_fequal,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181]) ).
cnf(i_0_2274,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X2,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))),
inference(rename_variables,[],[i_0_1231]) ).
cnf(i_0_2275,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X3),c_FuncSet_OPi(X1,X2,X4,hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X5))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
| hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X6)),X5)) ),
inference(rename_variables,[],[i_0_1181]) ).
cnf(i_0_2276,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Wellfounded_Omlex__prod(X1,X3,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193]) ).
cnf(i_0_2277,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2010]) ).
cnf(i_0_2278,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2279,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X5,X2)),hAPP(X5,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Wellfounded_Omlex__prod(X1,X5,X4))) ),
inference(rename_variables,[],[i_0_1193]) ).
cnf(i_0_2280,plain,
hAPP(c_Nat_OSuc,hAPP(c_Fun_Othe__inv__into(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc),hAPP(c_Nat_OSuc,X1))) = hAPP(c_Nat_OSuc,X1),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195]) ).
cnf(i_0_2281,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_1260]) ).
cnf(i_0_2282,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1608]) ).
cnf(i_0_2283,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,X5)))
| hAPP(X4,hAPP(c_Fun_Othe__inv__into(X3,X1,X5,X4),X2)) = X2
| ~ c_Fun_Oinj__on(X3,X1,X4,X5) ),
inference(rename_variables,[],[i_0_1195]) ).
cnf(i_0_2284,plain,
hAPP(c_COMBI(X1),X2) = hAPP(c_COMBI(X1),esk3_4(hAPP(c_COMBI(X1),X2),c_COMBI(X1),X1,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197]) ).
cnf(i_0_2285,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_1260]) ).
cnf(i_0_2286,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1595]) ).
cnf(i_0_2287,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))
| X2 = hAPP(X4,esk3_4(X2,X4,X1,X3))
| ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1197]) ).
cnf(i_0_2288,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_COMBI(X1),X2)),hAPP(hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),hAPP(c_fequal,X2)),X2))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211]) ).
cnf(i_0_2289,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2010]) ).
cnf(i_0_2290,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X2,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))),
inference(rename_variables,[],[i_0_1231]) ).
cnf(i_0_2291,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),hAPP(X6,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X5),c_FuncSet_OPi(X1,X4,X3,X6))) ),
inference(rename_variables,[],[i_0_1211]) ).
cnf(i_0_2292,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBI(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2))),c_Set_Oimage(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_COMBI(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(X3,X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212]) ).
cnf(i_0_2293,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1595]) ).
cnf(i_0_2294,plain,
( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X4),hAPP(X5,X2)),c_Set_Oimage(X1,X4,X5,X3)))
| ~ c_Fun_Oinj__on(X1,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
inference(rename_variables,[],[i_0_1212]) ).
cnf(i_0_2295,plain,
c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237]) ).
cnf(i_0_2296,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1672]) ).
cnf(i_0_2297,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Set_Oimage(X3,X1,X4,X5)))
| c_Finite__Set_Ofinite(X1,X2)
| ~ c_Finite__Set_Ofinite(X3,X5) ),
inference(rename_variables,[],[i_0_1237]) ).
cnf(i_0_2298,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Set_Oimage(tc_fun(X2,X3),X1,X4,c_FuncSet_OPi(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X5)))),c_Set_Oimage(tc_fun(X2,X3),X1,X4,c_FuncSet_OPi(X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X6)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239]) ).
cnf(i_0_2299,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2300,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X5),c_Set_Oimage(X1,X4,X6,X3)))
| X5 != c_Set_Oimage(X1,X4,X6,X2) ),
inference(rename_variables,[],[i_0_1239]) ).
cnf(i_0_2301,plain,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X2)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261]) ).
cnf(i_0_2302,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X3),hAPP(X4,X1)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X2)))
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(rename_variables,[],[i_0_1261]) ).
cnf(i_0_2303,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OatLeastAtMost(X1,c_fequal,X2,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263]) ).
cnf(i_0_2304,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4))
| hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OatLeastAtMost(X5,X1,X2,X4))) ),
inference(rename_variables,[],[i_0_1263]) ).
cnf(i_0_2305,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_SetInterval_Oord_OgreaterThanLessThan(X1,c_fequal,X2,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264]) ).
cnf(i_0_2306,plain,
( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
| ~ hBOOL(hAPP(hAPP(X1,X3),X4))
| hBOOL(hAPP(hAPP(c_member(X5),X3),c_SetInterval_Oord_OgreaterThanLessThan(X5,X1,X2,X4))) ),
inference(rename_variables,[],[i_0_1264]) ).
cnf(i_0_2307,plain,
hBOOL(hAPP(hAPP(c_member(X1),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(X2,X3))),c_Set_Oimage(X4,X1,X2,hAPP(c_fequal,X3)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_1801,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273]) ).
cnf(i_0_2308,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2309,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X4),X5),c_Set_Oimage(X1,X4,X6,X3)))
| X5 != hAPP(X6,X2) ),
inference(rename_variables,[],[i_0_1273]) ).
cnf(i_0_2310,plain,
c_Fun_Oinj__on(X1,X1,esk51_4(hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X1,X1,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286]) ).
cnf(i_0_2311,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2312,plain,
c_Set_Oimage(X1,X1,c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1594]) ).
cnf(i_0_2313,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X3,X2,X4,X5) != X1
| c_Fun_Oinj__on(X2,X3,esk51_4(X5,X3,X2,X1),X1) ),
inference(rename_variables,[],[i_0_1286]) ).
cnf(i_0_2314,plain,
hAPP(c_Fun_Othe__inv__into(X1,X1,hAPP(c_fequal,X2),c_COMBI(X1)),hAPP(c_COMBI(X1),X2)) = X2,
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292]) ).
cnf(i_0_2315,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2010]) ).
cnf(i_0_2316,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1595]) ).
cnf(i_0_2317,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Fun_Othe__inv__into(X1,X4,X3,X5),hAPP(X5,X2)) = X2
| ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
inference(rename_variables,[],[i_0_1292]) ).
cnf(i_0_2318,plain,
c_FuncSet_OPi(X1,X2,hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),c_COMBI(X3)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X2),tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416]) ).
cnf(i_0_2319,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
inference(rename_variables,[],[i_0_2010]) ).
cnf(i_0_2320,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1803]) ).
cnf(i_0_2321,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| c_FuncSet_OPi(X1,X4,X3,X5) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X4),tc_HOL_Obool))
| hAPP(X5,X2) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1416]) ).
cnf(i_0_2322,plain,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417]) ).
cnf(i_0_2323,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X3,X4,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,hAPP(c_Nat_OSuc,X1))) = c_Groups_Ozero__class_Ozero(X3)
| ~ class_Groups_Ocomm__monoid__add(X3) ),
inference(rename_variables,[],[i_0_1417]) ).
cnf(i_0_2324,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X2,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426]) ).
cnf(i_0_2325,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X2,hAPP(c_COMBK(tc_fun(X1,tc_HOL_Obool),X1),X2)))),
inference(rename_variables,[],[i_0_1231]) ).
cnf(i_0_2326,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
inference(rename_variables,[],[i_0_1426]) ).
cnf(i_0_2327,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X1,X2)),hAPP(X1,X2))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432]) ).
cnf(i_0_2328,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3),X4))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X2,hAPP(X3,X5)),hAPP(X4,X5)))
| ~ class_Orderings_Oord(X2) ),
inference(rename_variables,[],[i_0_1432]) ).
cnf(i_0_2329,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,X1)),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434]) ).
cnf(i_0_2330,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1570]) ).
cnf(i_0_2331,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,X2)),c_Finite__Set_Ocard(X1,X3)))
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(rename_variables,[],[i_0_1434]) ).
cnf(i_0_2332,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518]) ).
cnf(i_0_2333,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1518]) ).
cnf(i_0_2334,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522]) ).
cnf(i_0_2335,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1522]) ).
cnf(i_0_2336,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523]) ).
cnf(i_0_2337,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1523]) ).
cnf(i_0_2338,plain,
hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526]) ).
cnf(i_0_2339,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_SetInterval_Oord__class_OgreaterThan(X1,X2)))
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_1526]) ).
cnf(i_0_2340,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544]) ).
cnf(i_0_2341,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
inference(rename_variables,[],[i_0_1745]) ).
cnf(i_0_2342,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3),X1)) ),
inference(rename_variables,[],[i_0_1544]) ).
cnf(i_0_2343,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545]) ).
cnf(i_0_2344,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1700]) ).
cnf(i_0_2345,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_OSuc,X2)))
| X3 != hAPP(c_Nat_OSuc,X1) ),
inference(rename_variables,[],[i_0_1545]) ).
cnf(i_0_2346,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550]) ).
cnf(i_0_2347,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1550]) ).
cnf(i_0_2348,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553]) ).
cnf(i_0_2349,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1553]) ).
cnf(i_0_2350,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556]) ).
cnf(i_0_2351,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1556]) ).
cnf(i_0_2352,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557]) ).
cnf(i_0_2353,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1557]) ).
cnf(i_0_2354,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571]) ).
cnf(i_0_2355,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_1260]) ).
cnf(i_0_2356,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(rename_variables,[],[i_0_1376]) ).
cnf(i_0_2357,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),esk37_1(X2)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(rename_variables,[],[i_0_1571]) ).
cnf(i_0_2358,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_OSuc,esk44_2(hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578]) ).
cnf(i_0_2359,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2360,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)))
| X1 = hAPP(c_Nat_OSuc,esk44_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1578]) ).
cnf(i_0_2361,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Set_Oimage(X1,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587]) ).
cnf(i_0_2362,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_1260]) ).
cnf(i_0_2363,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2364,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),X2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),esk40_1(X2)))
| ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X2) ),
inference(rename_variables,[],[i_0_1587]) ).
cnf(i_0_2365,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589]) ).
cnf(i_0_2366,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1589]) ).
cnf(i_0_2367,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591]) ).
cnf(i_0_2368,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1591]) ).
cnf(i_0_2369,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630]) ).
cnf(i_0_2370,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X3,X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1630]) ).
cnf(i_0_2371,plain,
X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660]) ).
cnf(i_0_2372,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1660]) ).
cnf(i_0_2373,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X2,
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661]) ).
cnf(i_0_2374,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1661]) ).
cnf(i_0_2375,plain,
X1 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662]) ).
cnf(i_0_2376,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1662]) ).
cnf(i_0_2377,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))) != X2,
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663]) ).
cnf(i_0_2378,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1663]) ).
cnf(i_0_2379,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680]) ).
cnf(i_0_2380,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X2))
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1680]) ).
cnf(i_0_2381,plain,
esk45_2(hAPP(X1,esk35_4(X1,X1,X2,tc_Nat_Onat)),hAPP(X1,esk35_4(X1,X1,X2,tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731]) ).
cnf(i_0_2382,plain,
( X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(rename_variables,[],[i_0_1731]) ).
cnf(i_0_2383,plain,
X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737]) ).
cnf(i_0_2384,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1737]) ).
cnf(i_0_2385,plain,
hAPP(c_Nat_OSuc,hAPP(v_h____,v_Sledgehammer_058p__2)) != c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738]) ).
cnf(i_0_2386,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(rename_variables,[],[i_0_1738]) ).
cnf(i_0_2387,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739]) ).
cnf(i_0_2388,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1739]) ).
cnf(i_0_2389,plain,
c_Finite__Set_Ocard(tc_HOL_Obool,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759]) ).
cnf(i_0_2390,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2391,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Finite__Set_Ocard(X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Finite__Set_Ofinite(X2,X1) ),
inference(rename_variables,[],[i_0_1759]) ).
cnf(i_0_2392,plain,
X1 = esk3_4(hAPP(c_COMBI(X2),X1),c_COMBI(X2),X2,X2),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972]) ).
cnf(i_0_2393,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1595]) ).
cnf(i_0_2394,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_1260]) ).
cnf(i_0_2395,plain,
( ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X4)),c_Set_Oimage(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))
| X4 = esk3_4(hAPP(X3,X4),X3,X2,X1) ),
inference(rename_variables,[],[i_0_1972]) ).
cnf(i_0_2396,plain,
class_Finite__Set_Ofinite(esk36_5(tc_HOL_Obool,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_HOL_Obool),tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938]) ).
cnf(i_0_2397,plain,
class_Groups_Omonoid__add(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939]) ).
cnf(i_0_2398,plain,
class_Groups_Ozero(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940]) ).
cnf(i_0_2399,plain,
~ c_Finite__Set_Ofinite(c_Nat_Osize__class_Osize(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941]) ).
cnf(i_0_2400,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2401,plain,
~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942]) ).
cnf(i_0_2402,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2403,plain,
c_Arrow__Order__Mirabelle_OIIA(esk3_4(hAPP(c_COMBI(X1),v_F),c_COMBI(X1),X1,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943]) ).
cnf(i_0_2404,plain,
class_Groups_Ocomm__monoid__add(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944]) ).
cnf(i_0_2405,plain,
class_Orderings_Oord(esk36_5(tc_HOL_Obool,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_HOL_Obool),tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947]) ).
cnf(i_0_2406,plain,
c_Arrow__Order__Mirabelle_Ounanimity(esk3_4(hAPP(c_COMBI(X1),v_F),c_COMBI(X1),X1,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908]) ).
cnf(i_0_2407,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,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____)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_Lab____)),v_Lba____)),c_Nat_Osize__class_Osize(tc_Nat_Onat,v_a____),v_b____),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912]) ).
cnf(i_0_2408,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2409,plain,
~ c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,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____)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_Lab____)),v_Lba____)),v_a____,c_Nat_Osize__class_Osize(tc_Nat_Onat,v_b____)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913]) ).
cnf(i_0_2410,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2411,plain,
class_Orderings_Olinorder(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914]) ).
cnf(i_0_2412,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1816,i_0_1817,i_0_1819,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915]) ).
cnf(i_0_2413,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1815,i_0_1816,i_0_1817,i_0_1819,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916]) ).
cnf(i_0_2414,plain,
class_Groups_Oordered__ab__semigroup__add(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917]) ).
cnf(i_0_2415,plain,
class_Groups_Oordered__comm__monoid__add(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920]) ).
cnf(i_0_2416,plain,
~ c_Wellfounded_Omax__extp(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2,X3,c_Orderings_Obot__class_Obot(tc_fun(c_Set_Oimage(X4,X1,X5,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921]) ).
cnf(i_0_2417,plain,
~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_1992]) ).
cnf(i_0_2418,plain,
~ c_Wellfounded_Omax__extp(X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_fun(X3,tc_HOL_Obool)))),hAPP(c_fequal,X4),X5),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922]) ).
cnf(i_0_2419,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2420,plain,
~ c_Wellfounded_Omax__extp(tc_Nat_Onat,X1,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X2),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923]) ).
cnf(i_0_2421,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2422,plain,
~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1813,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924]) ).
cnf(i_0_2423,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2424,plain,
class_Rings_Ocomm__semiring__1(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925]) ).
cnf(i_0_2425,plain,
class_Rings_Olinordered__semidom(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926]) ).
cnf(i_0_2426,plain,
class_Orderings_Opreorder(esk36_5(tc_HOL_Obool,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_HOL_Obool),tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927]) ).
cnf(i_0_2427,plain,
class_Orderings_Oorder(esk36_5(tc_HOL_Obool,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_HOL_Obool),tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928]) ).
cnf(i_0_2428,plain,
class_Groups_Oab__semigroup__add(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1822,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929]) ).
cnf(i_0_2429,plain,
class_Groups_Ocancel__semigroup__add(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930]) ).
cnf(i_0_2430,plain,
class_Groups_Ocancel__ab__semigroup__add(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931]) ).
cnf(i_0_2431,plain,
class_Orderings_Obot(esk36_5(tc_HOL_Obool,c_Nat_OSuc,tc_Nat_Onat,c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,tc_HOL_Obool),tc_Nat_Onat)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932]) ).
cnf(i_0_2432,plain,
tc_HOL_Obool != tc_Nat_Onat,
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933]) ).
cnf(i_0_2433,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(esk11_4(c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Nat_OSuc,tc_Nat_Onat,hAPP(c_Nat_OSuc,tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934]) ).
cnf(i_0_2434,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),c_Arrow__Order__Mirabelle_Oabove(esk13_0,v_Lba____,v_Lab____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206]) ).
cnf(i_0_2435,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Oabove(X1,X4,X5)))
| X4 = X5
| X2 != X3 ),
inference(rename_variables,[],[i_0_1206]) ).
cnf(i_0_2436,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),c_Set_Oimage(X2,X1,X3,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),c_Arrow__Order__Mirabelle_Obelow(esk13_0,v_Lba____,v_Lab____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207]) ).
cnf(i_0_2437,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X4,X5)))
| X4 = X5
| X2 != X3 ),
inference(rename_variables,[],[i_0_1207]) ).
cnf(i_0_2438,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465]) ).
cnf(i_0_2439,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1700]) ).
cnf(i_0_2440,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1465]) ).
cnf(i_0_2441,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Finite__Set_Ocard(X2,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466]) ).
cnf(i_0_2442,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X4))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1466]) ).
cnf(i_0_2443,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484]) ).
cnf(i_0_2444,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
inference(rename_variables,[],[i_0_1700]) ).
cnf(i_0_2445,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1484]) ).
cnf(i_0_2446,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),c_Finite__Set_Ocard(X2,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485]) ).
cnf(i_0_2447,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1485]) ).
cnf(i_0_2448,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(v_h____,v_Sledgehammer_058p__2)),X1))),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486]) ).
cnf(i_0_2449,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))),
inference(rename_variables,[],[i_0_1443]) ).
cnf(i_0_2450,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1486]) ).
cnf(i_0_2451,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487]) ).
cnf(i_0_2452,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1375]) ).
cnf(i_0_2453,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1487]) ).
cnf(i_0_2454,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628]) ).
cnf(i_0_2455,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1375]) ).
cnf(i_0_2456,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1628]) ).
cnf(i_0_2457,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(c_Nat_OSuc,v_a____)),v_b____)),c_Arrow__Order__Mirabelle_Oabove(esk13_0,v_a____,hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_1802,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964]) ).
cnf(i_0_2458,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1802]) ).
cnf(i_0_2459,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),c_Arrow__Order__Mirabelle_Oabove(X1,X2,X4)))
| X2 = X4 ),
inference(rename_variables,[],[i_0_1964]) ).
cnf(i_0_2460,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),hAPP(c_Nat_OSuc,v_b____))),c_Arrow__Order__Mirabelle_Obelow(esk13_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_1802,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965]) ).
cnf(i_0_2461,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2462,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X3,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),X1))
| X3 = X4 ),
inference(rename_variables,[],[i_0_1965]) ).
cnf(i_0_2463,plain,
c_Set_Oimage(X1,X1,esk50_4(c_Set_Oimage(X1,X1,c_COMBI(X1),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X1,X1,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Set_Oimage(X1,X1,c_COMBI(X1),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155]) ).
cnf(i_0_2464,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1672]) ).
cnf(i_0_2465,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2466,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1595]) ).
cnf(i_0_2467,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),X5))
| X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Set_Oimage(X1,X2,esk50_4(X5,X1,X2,X4),X5) = X4
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_1155]) ).
cnf(i_0_2468,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Finite__Set_Ocard(X1,c_Set_Oimage(X1,X1,c_COMBI(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162]) ).
cnf(i_0_2469,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2),X2)),
inference(rename_variables,[],[i_0_1672]) ).
cnf(i_0_2470,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1595]) ).
cnf(i_0_2471,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oimage(X2,X1,X3,X4)),X5))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(X2,X4)),c_Finite__Set_Ocard(X1,X5)))
| ~ c_Finite__Set_Ofinite(X1,X5)
| ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_1162]) ).
cnf(i_0_2472,plain,
X1 = esk3_4(hAPP(c_COMBI(X2),hAPP(c_COMBI(X2),X1)),c_COMBI(X2),X2,X2),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203]) ).
cnf(i_0_2473,plain,
hBOOL(hAPP(hAPP(c_member(X1),hAPP(X2,X3)),c_Set_Oimage(X4,X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))))),
inference(rename_variables,[],[i_0_1260]) ).
cnf(i_0_2474,plain,
c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
inference(rename_variables,[],[i_0_1595]) ).
cnf(i_0_2475,plain,
hAPP(c_COMBI(X1),X2) = X2,
inference(rename_variables,[],[i_0_1803]) ).
cnf(i_0_2476,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oimage(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)))
| X2 != hAPP(X4,X5)
| X5 = esk3_4(X2,X4,X1,X3) ),
inference(rename_variables,[],[i_0_1203]) ).
cnf(i_0_2477,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X2))),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X2))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X2)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204]) ).
cnf(i_0_2478,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),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X2))),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2,X3))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X4,X5,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1,X3))
| ~ class_Groups_Ocomm__monoid__add(X4) ),
inference(rename_variables,[],[i_0_1204]) ).
cnf(i_0_2479,plain,
~ c_Fun_Oinj__on(X1,X2,hAPP(c_COMBK(X3,X4),X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293]) ).
cnf(i_0_2480,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1640]) ).
cnf(i_0_2481,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1802]) ).
cnf(i_0_2482,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(rename_variables,[],[i_0_1740]) ).
cnf(i_0_2483,plain,
( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
| hAPP(c_Fun_Othe__inv__into(X1,X4,X3,X5),X6) = X2
| hAPP(X5,X2) != X6
| ~ c_Fun_Oinj__on(X1,X4,X5,X3) ),
inference(rename_variables,[],[i_0_1293]) ).
cnf(i_0_2484,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303]) ).
cnf(i_0_2485,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1)),
inference(rename_variables,[],[i_0_1375]) ).
cnf(i_0_2486,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X5))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_1303]) ).
cnf(i_0_2487,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2)),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304]) ).
cnf(i_0_2488,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(rename_variables,[],[i_0_1376]) ).
cnf(i_0_2489,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X4),X5)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_1304]) ).
cnf(i_0_2490,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344]) ).
cnf(i_0_2491,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2492,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),c_Groups_Ozero__class_Ozero(X1)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1344]) ).
cnf(i_0_2493,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X2)),X3))),X3)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387]) ).
cnf(i_0_2494,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X2)),
inference(rename_variables,[],[i_0_1376]) ).
cnf(i_0_2495,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1387]) ).
cnf(i_0_2496,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405]) ).
cnf(i_0_2497,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2498,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1405]) ).
cnf(i_0_2499,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406]) ).
cnf(i_0_2500,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X1)),
inference(rename_variables,[],[i_0_1760]) ).
cnf(i_0_2501,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1406]) ).
cnf(i_0_2502,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2))),X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515]) ).
cnf(i_0_2503,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X1)),
inference(rename_variables,[],[i_0_1582]) ).
cnf(i_0_2504,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X3))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X4),X2))
| ~ class_Orderings_Opreorder(X1) ),
inference(rename_variables,[],[i_0_1515]) ).
cnf(i_0_2505,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2))),X3)),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516]) ).
cnf(i_0_2506,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X3))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X2),X4))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,X3),X4))
| ~ class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_1516]) ).
cnf(i_0_2507,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,v_a____))),v_b____)),c_Arrow__Order__Mirabelle_Oabove(esk13_0,v_a____,hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_1802,i_0_2458,i_0_2481,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177]) ).
cnf(i_0_2508,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1802]) ).
cnf(i_0_2509,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2510,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),c_Arrow__Order__Mirabelle_Oabove(X1,X2,X5)))
| X2 = X5
| X4 != X5 ),
inference(rename_variables,[],[i_0_1177]) ).
cnf(i_0_2511,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,v_b____)))),c_Arrow__Order__Mirabelle_Obelow(esk13_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_1802,i_0_2458,i_0_2481,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178]) ).
cnf(i_0_2512,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2513,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,X1) = X1,
inference(rename_variables,[],[i_0_1806]) ).
cnf(i_0_2514,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),c_Arrow__Order__Mirabelle_Obelow(X1,X5,X3)))
| X5 = X3
| X4 != X5 ),
inference(rename_variables,[],[i_0_1178]) ).
cnf(i_0_2515,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_1802,i_0_2458,i_0_2481,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440]) ).
cnf(i_0_2516,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1707]) ).
cnf(i_0_2517,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2518,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| X2 = X4
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1440]) ).
cnf(i_0_2519,plain,
c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) != c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_1802,i_0_2458,i_0_2481,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441]) ).
cnf(i_0_2520,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
inference(rename_variables,[],[i_0_1707]) ).
cnf(i_0_2521,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2522,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X4),X5))
| c_SetInterval_Oord__class_OatLeastLessThan(X1,X2,X3) != c_SetInterval_Oord__class_OatLeastLessThan(X1,X4,X5)
| X3 = X5
| ~ class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_1441]) ).
cnf(i_0_2523,plain,
c_Wellfounded_Omax__extp(tc_HOL_Obool,X1,c_Orderings_Obot__class_Obot(tc_fun(tc_HOL_Obool,tc_HOL_Obool)),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_fun(tc_HOL_Obool,tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_1802,i_0_2458,i_0_2481,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214]) ).
cnf(i_0_2524,plain,
~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1529]) ).
cnf(i_0_2525,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2526,plain,
c_Finite__Set_Ofinite(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_1773]) ).
cnf(i_0_2527,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk53_4(X2,X3,X4,X1)),X3))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| c_Wellfounded_Omax__extp(X1,X4,X3,X2)
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X1,X2) ),
inference(rename_variables,[],[i_0_1214]) ).
cnf(i_0_2528,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X1))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_1802,i_0_2458,i_0_2481,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468]) ).
cnf(i_0_2529,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),
inference(rename_variables,[],[i_0_1592]) ).
cnf(i_0_2530,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1468]) ).
cnf(i_0_2531,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_1802,i_0_2458,i_0_2481,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469]) ).
cnf(i_0_2532,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))),
inference(rename_variables,[],[i_0_1593]) ).
cnf(i_0_2533,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1)),X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X2) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_1469]) ).
cnf(i_0_2534,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____),v_Lba____)),c_Arrow__Order__Mirabelle_Obelow(c_Arrow__Order__Mirabelle_Omkbot(esk13_0,v_Lba____),v_Lab____,hAPP(c_Nat_OSuc,v_Lab____)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175]) ).
cnf(i_0_2535,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_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_Omkbot(X3,X2))),
inference(rename_variables,[],[i_0_1977]) ).
cnf(i_0_2536,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1802]) ).
cnf(i_0_2537,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X4,X5)))
| X3 = X4
| X2 = X4
| X4 = X5 ),
inference(rename_variables,[],[i_0_1175]) ).
cnf(i_0_2538,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_Lba____),v_Lba____)),c_Arrow__Order__Mirabelle_Oabove(c_Arrow__Order__Mirabelle_Omkbot(esk13_0,v_Lba____),v_Lba____,v_Lab____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1331,i_0_1400,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176]) ).
cnf(i_0_2539,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))),
inference(rename_variables,[],[i_0_1977]) ).
cnf(i_0_2540,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Oabove(X1,X4,X5)))
| X2 = X5
| X3 = X5
| X4 = X5 ),
inference(rename_variables,[],[i_0_1176]) ).
cnf(i_0_2541,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),c_Arrow__Order__Mirabelle_Oabove(esk12_0,v_a____,hAPP(c_Nat_OSuc,v_a____)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960]) ).
cnf(i_0_2542,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(rename_variables,[],[i_0_1802]) ).
cnf(i_0_2543,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Oabove(X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| X2 = X4
| X2 = X3 ),
inference(rename_variables,[],[i_0_1960]) ).
cnf(i_0_2544,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),c_Arrow__Order__Mirabelle_Obelow(esk12_0,hAPP(c_Nat_OSuc,v_b____),v_b____))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961]) ).
cnf(i_0_2545,plain,
hAPP(c_Nat_OSuc,X1) != X1,
inference(rename_variables,[],[i_0_1801]) ).
cnf(i_0_2546,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X1,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),X1))
| X4 = X3
| X2 = X3 ),
inference(rename_variables,[],[i_0_1961]) ).
cnf(i_0_2547,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),c_Wellfounded_Omax__ext(tc_Arrow__Order__Mirabelle_Oindi,c_Wellfounded_Omlex__prod(tc_Arrow__Order__Mirabelle_Oindi,c_Nat_OSuc,X1)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_1747,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097]) ).
cnf(i_0_2548,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1640]) ).
cnf(i_0_2549,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1747]) ).
cnf(i_0_2550,plain,
c_Finite__Set_Ofinite(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_1773]) ).
cnf(i_0_2551,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk58_4(X2,X3,X4,X1)),X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),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)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1,X4)
| ~ c_Finite__Set_Ofinite(X1,X3) ),
inference(rename_variables,[],[i_0_1097]) ).
cnf(i_0_2552,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))),c_Wellfounded_Omax__ext(tc_Arrow__Order__Mirabelle_Oindi,c_Wellfounded_Omeasure(tc_Arrow__Order__Mirabelle_Oindi,c_Nat_OSuc)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_1747,i_0_2549,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098]) ).
cnf(i_0_2553,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1640]) ).
cnf(i_0_2554,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1747]) ).
cnf(i_0_2555,plain,
c_Finite__Set_Ofinite(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_1773]) ).
cnf(i_0_2556,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk54_4(X2,X3,X4,X1)),X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),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)),X4),X3)),c_Wellfounded_Omax__ext(X1,X2)))
| X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X1,X3)
| ~ c_Finite__Set_Ofinite(X1,X4) ),
inference(rename_variables,[],[i_0_1098]) ).
cnf(i_0_2557,plain,
c_Wellfounded_Omax__extp(tc_Arrow__Order__Mirabelle_Oindi,c_fequal,c_Orderings_Obot__class_Obot(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169]) ).
cnf(i_0_2558,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(rename_variables,[],[i_0_2025]) ).
cnf(i_0_2559,plain,
hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_1640]) ).
cnf(i_0_2560,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rename_variables,[],[i_0_1747]) ).
cnf(i_0_2561,plain,
c_Finite__Set_Ofinite(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rename_variables,[],[i_0_1773]) ).
cnf(i_0_2562,plain,
( ~ hBOOL(hAPP(hAPP(X1,esk53_4(X2,X3,X1,X4)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))
| ~ c_Finite__Set_Ofinite(X4,X3)
| ~ c_Finite__Set_Ofinite(X4,X2)
| c_Wellfounded_Omax__extp(X4,X1,X3,X2) ),
inference(rename_variables,[],[i_0_1169]) ).
cnf(i_0_2563,plain,
c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk49_2(hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169,i_0_1785]) ).
cnf(i_0_2564,plain,
( hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1785]) ).
cnf(i_0_2565,plain,
hAPP(c_COMBI(X1),esk46_4(c_COMBI(X1),hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169,i_0_1785,i_0_1300]) ).
cnf(i_0_2566,plain,
( c_FuncSet_OPi(X1,X2,X3,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,X2),tc_HOL_Obool))
| hAPP(X4,esk46_4(X4,X3,X2,X1)) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rename_variables,[],[i_0_1300]) ).
cnf(i_0_2567,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)))),X2)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169,i_0_1785,i_0_1300,i_0_1363]) ).
cnf(i_0_2568,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),X2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X3)) ),
inference(rename_variables,[],[i_0_1363]) ).
cnf(i_0_2569,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3))),X3)),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169,i_0_1785,i_0_1300,i_0_1363,i_0_1364]) ).
cnf(i_0_2570,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X3)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2),X3)) ),
inference(rename_variables,[],[i_0_1364]) ).
cnf(i_0_2571,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X3)))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169,i_0_1785,i_0_1300,i_0_1363,i_0_1364,i_0_1483]) ).
cnf(i_0_2572,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1),X2)) ),
inference(rename_variables,[],[i_0_1483]) ).
cnf(i_0_2573,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Finite__Set_Ocard(X2,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169,i_0_1785,i_0_1300,i_0_1363,i_0_1364,i_0_1483,i_0_1542]) ).
cnf(i_0_2574,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
inference(rename_variables,[],[i_0_1542]) ).
cnf(i_0_2575,plain,
c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,X1,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169,i_0_1785,i_0_1300,i_0_1363,i_0_1364,i_0_1483,i_0_1542,i_0_1758]) ).
cnf(i_0_2576,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_1758]) ).
cnf(i_0_2577,plain,
$false,
inference(scs_inference,[],[i_0_1390,i_0_1840,i_0_1060,i_0_1976,i_0_2210,i_0_2213,i_0_2257,i_0_1977,i_0_2535,i_0_1991,i_0_1996,i_0_1992,i_0_2025,i_0_2010,i_0_2073,i_0_2258,i_0_2264,i_0_2277,i_0_2289,i_0_2315,i_0_1993,i_0_1806,i_0_2120,i_0_2147,i_0_2150,i_0_2199,i_0_2299,i_0_2308,i_0_2400,i_0_2402,i_0_2408,i_0_2410,i_0_2419,i_0_2421,i_0_2423,i_0_2509,i_0_1594,i_0_1803,i_0_2320,i_0_1740,i_0_1760,i_0_2103,i_0_2142,i_0_2261,i_0_2278,i_0_2491,i_0_2497,i_0_1692,i_0_2235,i_0_1707,i_0_2038,i_0_2090,i_0_2096,i_0_2516,i_0_1686,i_0_1672,i_0_2061,i_0_2296,i_0_2464,i_0_1700,i_0_2083,i_0_2344,i_0_2439,i_0_1529,i_0_2051,i_0_2054,i_0_2064,i_0_2076,i_0_1570,i_0_1640,i_0_2480,i_0_2548,i_0_2553,i_0_1745,i_0_1582,i_0_2134,i_0_2137,i_0_2163,i_0_2194,i_0_2363,i_0_2503,i_0_1260,i_0_2281,i_0_2285,i_0_2355,i_0_2362,i_0_2394,i_0_1495,i_0_2093,i_0_1592,i_0_2041,i_0_2106,i_0_2109,i_0_2129,i_0_1593,i_0_1231,i_0_2274,i_0_2290,i_0_1296,i_0_1375,i_0_2189,i_0_2238,i_0_2247,i_0_2452,i_0_2455,i_0_1376,i_0_2123,i_0_2126,i_0_2186,i_0_2356,i_0_2488,i_0_1443,i_0_1444,i_0_2033,i_0_1333,i_0_1331,i_0_1400,i_0_1401,i_0_1595,i_0_2286,i_0_2293,i_0_2316,i_0_2393,i_0_2466,i_0_2470,i_0_1801,i_0_2254,i_0_2311,i_0_2359,i_0_2390,i_0_2461,i_0_2465,i_0_2512,i_0_2517,i_0_2521,i_0_2525,i_0_1802,i_0_2458,i_0_2481,i_0_2508,i_0_2536,i_0_1608,i_0_2222,i_0_2225,i_0_1812,i_0_1813,i_0_1814,i_0_1815,i_0_1816,i_0_1817,i_0_1818,i_0_1819,i_0_1820,i_0_1821,i_0_1822,i_0_1823,i_0_1824,i_0_1825,i_0_1827,i_0_1828,i_0_1829,i_0_1830,i_0_1831,i_0_1832,i_0_1833,i_0_1834,i_0_1835,i_0_1836,i_0_1837,i_0_1839,i_0_1773,i_0_2526,i_0_2550,i_0_2555,i_0_1747,i_0_2549,i_0_2554,i_0_1741,i_0_1776,i_0_1343,i_0_1457,i_0_1493,i_0_1511,i_0_1586,i_0_1616,i_0_1644,i_0_1842,i_0_1105,i_0_1110,i_0_1138,i_0_1139,i_0_1156,i_0_1164,i_0_1171,i_0_1192,i_0_1198,i_0_1201,i_0_1208,i_0_1221,i_0_1224,i_0_1236,i_0_1246,i_0_1247,i_0_1248,i_0_1250,i_0_1256,i_0_1262,i_0_1308,i_0_1346,i_0_1359,i_0_1360,i_0_1461,i_0_1462,i_0_1463,i_0_1464,i_0_1470,i_0_1473,i_0_1475,i_0_1494,i_0_1497,i_0_1500,i_0_1502,i_0_1506,i_0_1525,i_0_1527,i_0_1534,i_0_1535,i_0_1555,i_0_1559,i_0_1565,i_0_1584,i_0_1606,i_0_1612,i_0_1621,i_0_1636,i_0_1653,i_0_1656,i_0_1689,i_0_1690,i_0_1691,i_0_1696,i_0_1697,i_0_1698,i_0_1703,i_0_1704,i_0_1712,i_0_1728,i_0_1756,i_0_1774,i_0_1844,i_0_1845,i_0_1490,i_0_1491,i_0_1800,i_0_1215,i_0_1216,i_0_1233,i_0_1234,i_0_1235,i_0_1275,i_0_1437,i_0_1492,i_0_1507,i_0_1514,i_0_1539,i_0_1633,i_0_1649,i_0_1650,i_0_1651,i_0_1655,i_0_1973,i_0_1974,i_0_1843,i_0_1903,i_0_1091,i_0_1116,i_0_1135,i_0_1143,i_0_1144,i_0_1166,i_0_1181,i_0_1193,i_0_1195,i_0_1197,i_0_1211,i_0_1212,i_0_1237,i_0_1239,i_0_1261,i_0_1263,i_0_1264,i_0_1273,i_0_1286,i_0_1292,i_0_1416,i_0_1417,i_0_1426,i_0_1432,i_0_1434,i_0_1518,i_0_1522,i_0_1523,i_0_1526,i_0_1544,i_0_1545,i_0_1550,i_0_1553,i_0_1556,i_0_1557,i_0_1571,i_0_1578,i_0_1587,i_0_1589,i_0_1591,i_0_1630,i_0_1660,i_0_1661,i_0_1662,i_0_1663,i_0_1680,i_0_1731,i_0_1737,i_0_1738,i_0_1739,i_0_1759,i_0_1972,i_0_1938,i_0_1939,i_0_1940,i_0_1941,i_0_1942,i_0_1943,i_0_1944,i_0_1947,i_0_1908,i_0_1912,i_0_1913,i_0_1914,i_0_1915,i_0_1916,i_0_1917,i_0_1920,i_0_1921,i_0_1922,i_0_1923,i_0_1924,i_0_1925,i_0_1926,i_0_1927,i_0_1928,i_0_1929,i_0_1930,i_0_1931,i_0_1932,i_0_1933,i_0_1934,i_0_1206,i_0_1207,i_0_1465,i_0_1466,i_0_1484,i_0_1485,i_0_1486,i_0_1487,i_0_1628,i_0_1964,i_0_1965,i_0_1155,i_0_1162,i_0_1203,i_0_1204,i_0_1293,i_0_1303,i_0_1304,i_0_1344,i_0_1387,i_0_1405,i_0_1406,i_0_1515,i_0_1516,i_0_1177,i_0_1178,i_0_1440,i_0_1441,i_0_1214,i_0_1468,i_0_1469,i_0_1175,i_0_1176,i_0_1960,i_0_1961,i_0_1097,i_0_1098,i_0_1169,i_0_1785,i_0_1300,i_0_1363,i_0_1364,i_0_1483,i_0_1542,i_0_1758,i_0_1433]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT161+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:59:20 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.79/5.74 % Version : CSE_E---1.7
% 2.79/5.74 % Problem : theBenchmark.p
% 2.79/5.74 % SZS status Theorem for theBenchmark.p
% 2.79/5.74 % SZS output start CNFRefutation
% See solution above
% 10.98/14.01 % Total time : 5.395s
%------------------------------------------------------------------------------