TSTP Solution File: COM111_5 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM111_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 : Fri May 19 10:14:06 EDT 2023
% Result : Theorem 81.33s 64.54s
% Output : Refutation 82.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 202
% Syntax : Number of formulae : 347 ( 100 unt; 59 typ; 0 def)
% Number of atoms : 15224 ( 270 equ; 0 cnn)
% Maximal formula atoms : 1108 ( 52 avg)
% Number of connectives : 36738 ( 63 ~; 30 |; 46 &;36362 @)
% ( 23 <=>; 214 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 61 ( 59 usr; 15 con; 0-4 aty)
% Number of variables : 749 ( 0 ^; 687 !; 11 ?; 749 :)
% ( 51 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(ring_type,type,
ring:
!>[TA: $tType] : $o ).
thf(cl_Groups_Oplus_type,type,
cl_Groups_Oplus:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(cl_Groups_Ominus_type,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(ring_div_type,type,
ring_div:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(semiring_div_type,type,
semiring_div:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(linord2061991079up_add_type,type,
linord2061991079up_add:
!>[TA: $tType] : $o ).
thf(big_linorder_Max_type,type,
big_linorder_Max:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ TB ) @ ( fun @ ( fun @ TA @ TC ) @ ( fun @ TA @ TB ) ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ TB @ ( fun @ TC @ TA ) ) ) ).
thf(combi_type,type,
combi:
!>[TA: $tType] : ( fun @ TA @ TA ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( fun @ ( fun @ TC @ ( fun @ TB @ TA ) ) @ ( fun @ ( fun @ TC @ TB ) @ ( fun @ TC @ TA ) ) ) ).
thf(div_mod_type,type,
div_mod:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(finite_finite1_type,type,
finite_finite1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > $o ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ TA ) ) ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > ( fun @ TA @ TA ) ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(iprod_type,type,
iprod:
!>[TA: $tType] : ( fun @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) ) ).
thf(filter_type,type,
filter:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(map_type,type,
map:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( list @ TB ) > ( list @ TA ) ) ).
thf(set_type,type,
set:
!>[TA: $tType] : ( ( list @ TA ) > ( fun @ TA @ bool ) ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(i_Z_type,type,
i_Z: atom > ( list @ int ) > $o ).
thf(atom_case_type,type,
atom_case:
!>[TA: $tType] : ( ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ) ) > ( fun @ atom @ TA ) ) ).
thf(divisor_type,type,
divisor: fun @ atom @ int ).
thf(lbounds_type,type,
lbounds: ( list @ atom ) > ( list @ ( product_prod @ int @ ( list @ int ) ) ) ).
thf(zlcms_type,type,
zlcms: ( list @ int ) > int ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( fun @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fEx_type,type,
fEx:
!>[TA: $tType] : ( fun @ ( fun @ TA @ bool ) @ bool ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(a_type,type,
a: atom ).
thf(as_type,type,
as: list @ atom ).
thf(li_type,type,
li: int ).
thf(lks_type,type,
lks: list @ int ).
thf(x_type,type,
x: int ).
thf(xs_type,type,
xs: list @ int ).
thf(103,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_add__0__right) ).
thf(445,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(115,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( filter @ TA @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_filter_Osimps_I1_J) ).
thf(479,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( filter @ TA @ A @ ( nil @ TA ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(65,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(333,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(32,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Ominus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_list__diff__Cons__Cons) ).
thf(234,plain,
! [TA: $tType] :
( ( ( cl_Groups_Ominus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(140,axiom,
! [A: int] :
( ( div_mod @ int @ A @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_zmod__self) ).
thf(555,plain,
! [A: int] :
( ( div_mod @ int @ A @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(70,axiom,
monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(352,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(8,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_list_Osimps_I2_J) ).
thf(170,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_mod__add__right__eq) ).
thf(217,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(47,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: list @ TA] :
( ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ B ) ) )
=> ~ ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( ( filter @ TA @ A @ B )
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_filter__False) ).
thf(276,plain,
! [TA: $tType,A: fun @ TA @ bool,B: list @ TA] :
( ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ B ) ) )
=> ~ ( pp @ ( aa @ TA @ bool @ A @ C ) ) )
=> ( ( filter @ TA @ A @ B )
= ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(99,axiom,
ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(440,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(127,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(511,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(122,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(500,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
=> ( ( finite_finite1 @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) ) @ A ) ) ) )
<=> ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( finite_finite1 @ TB @ ( collect @ TB @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( combc @ TB @ TA @ bool ) @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_finite__Collect__bounded__ex) ).
thf(472,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ TA @ bool ),B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
=> ( ( ( finite_finite1 @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) ) @ A ) ) ) )
=> ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( finite_finite1 @ TB @ ( collect @ TB @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( combc @ TB @ TA @ bool ) @ A ) @ C ) ) ) ) )
& ( ! [C: TA] :
( ( pp @ ( aa @ TA @ bool @ B @ C ) )
=> ( finite_finite1 @ TB @ ( collect @ TB @ ( aa @ TA @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TB @ bool ) ) @ ( combc @ TB @ TA @ bool ) @ A ) @ C ) ) ) )
=> ( finite_finite1 @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(87,axiom,
pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ a ) @ ( set @ atom @ as ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096a_A_058_Aset_Aas_096) ).
thf(404,plain,
pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ a ) @ ( set @ atom @ as ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ( finite_finite @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(417,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ( finite_finite @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(51,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ ( aa @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(288,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ ( aa @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(55,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_finite__Diff) ).
thf(301,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_mod__0) ).
thf(257,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(80,axiom,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( plus_plus @ ( list @ TA ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( plus_plus @ ( list @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_list__add__Cons) ).
thf(389,plain,
! [TA: $tType] :
( ( ( cl_Groups_Oplus @ TA )
& ( zero @ TA ) )
=> ! [A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( plus_plus @ ( list @ TA ) @ ( cons @ TA @ D @ C ) ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ D ) @ B ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( plus_plus @ ( list @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(14,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_diff__add__cancel) ).
thf(184,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(124,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(504,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(49,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(284,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(104,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_diff__0__right) ).
thf(448,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ A ) @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(60,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(316,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(43,axiom,
! [A: int] :
( ( div_mod @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_zmod__zero) ).
thf(261,plain,
! [A: int] :
( ( div_mod @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(119,axiom,
( ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) )
= ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ li ) @ ( aa @ ( list @ int ) @ int @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( iprod @ int ) @ lks ) @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_lm) ).
thf(492,plain,
( ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) )
= ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ li ) @ ( aa @ ( list @ int ) @ int @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( iprod @ int ) @ lks ) @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_split__paired__All) ).
thf(376,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(117,axiom,
! [TA: $tType,A: list @ TA] : ( finite_finite1 @ TA @ ( set @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__set) ).
thf(485,plain,
! [TA: $tType,A: list @ TA] : ( finite_finite1 @ TA @ ( set @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA] :
( ( map @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_map_Osimps_I1_J) ).
thf(238,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ TA] :
( ( map @ TB @ TA @ A @ ( nil @ TB ) )
= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(71,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ D ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_diff__eq__diff__eq) ).
thf(353,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ D ) @ C )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) )
=> ( ( ( D = C )
=> ( B = A ) )
& ( ( B = A )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_not__Cons__self) ).
thf(147,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(106,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_diff__self) ).
thf(453,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ A ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(83,axiom,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_mod__diff__right__eq) ).
thf(396,plain,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(90,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_add__left__cancel) ).
thf(411,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(36,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( big_linorder_Max @ TA @ A ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Max__in) ).
thf(243,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( big_linorder_Max @ TA @ A ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(95,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_mod__add__left__eq) ).
thf(428,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(58,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(312,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(21,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(206,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(78,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_add__0__left) ).
thf(380,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(138,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_eq__iff__diff__eq__0) ).
thf(546,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) ) )
& ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(26,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_add__diff__cancel) ).
thf(220,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(135,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(534,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(81,axiom,
finite_finite @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(392,plain,
finite_finite @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(6,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_not__Cons__self2) ).
thf(165,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(260,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(349,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TA @ ( fun @ TB @ TC ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combs @ TA @ TB @ TC ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(111,axiom,
! [A: atom] :
( ( pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ A ) @ ( set @ atom @ as ) ) )
=> ( i_Z @ A @ ( cons @ int @ x @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_x) ).
thf(467,plain,
! [A: atom] :
( ( pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ A ) @ ( set @ atom @ as ) ) )
=> ( i_Z @ A @ ( cons @ int @ x @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(142,axiom,
pp @ ( aa @ atom @ bool @ ( atom_case @ bool @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fFalse ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) ) @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096is__dvd_Aa_096) ).
thf(566,plain,
pp @ ( aa @ atom @ bool @ ( atom_case @ bool @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fFalse ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) ) @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(38,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mod__self) ).
thf(252,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(109,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(461,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(107,axiom,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ C ) @ ( div_mod @ int @ B @ A ) ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zdiff__zmod__right) ).
thf(456,plain,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ C ) @ ( div_mod @ int @ B @ A ) ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(63,axiom,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Oplus @ TA ) )
=> ( cl_Groups_Oplus @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
thf(324,plain,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Oplus @ TA ) )
=> ( cl_Groups_Oplus @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_mod__diff__left__eq) ).
thf(224,plain,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fEx @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
thf(519,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ~ ( pp @ ( aa @ TA @ bool @ B @ A ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( fEx @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(61,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_right__minus__eq) ).
thf(317,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(16,axiom,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Ominus @ TA ) )
=> ( cl_Groups_Ominus @ ( list @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
thf(188,plain,
! [TA: $tType] :
( ( ( zero @ TA )
& ( cl_Groups_Ominus @ TA ) )
=> ( cl_Groups_Ominus @ ( list @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(40,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(256,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(67,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( filter @ TA @ B @ A )
= A )
<=> ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_filter__id__conv) ).
thf(339,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( ( filter @ TA @ B @ A )
= A )
=> ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ B @ C ) ) ) )
& ( ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ B @ C ) ) )
=> ( ( filter @ TA @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: list @ TA,C: fun @ TA @ TB] :
( ( ( map @ TA @ TB @ C @ B )
= ( map @ TA @ TB @ A @ B ) )
<=> ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( set @ TA @ B ) ) )
=> ( ( aa @ TA @ TB @ C @ D )
= ( aa @ TA @ TB @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_map__eq__conv) ).
thf(193,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: list @ TA,C: fun @ TA @ TB] :
( ( ( ( map @ TA @ TB @ C @ B )
= ( map @ TA @ TB @ A @ B ) )
=> ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( set @ TA @ B ) ) )
=> ( ( aa @ TA @ TB @ C @ D )
= ( aa @ TA @ TB @ A @ D ) ) ) )
& ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( set @ TA @ B ) ) )
=> ( ( aa @ TA @ TB @ C @ D )
= ( aa @ TA @ TB @ A @ D ) ) )
=> ( ( map @ TA @ TB @ C @ B )
= ( map @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(114,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( nil @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_iprod__Nil) ).
thf(476,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( nil @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(23,axiom,
! [TA: $tType] : ( finite_finite1 @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite_OemptyI) ).
thf(212,plain,
! [TA: $tType] : ( finite_finite1 @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(82,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ ( cons @ TA @ B @ A ) ) ) )
=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_set__ConsD) ).
thf(393,plain,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ ( cons @ TA @ B @ A ) ) ) )
=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(9,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_finite__code) ).
thf(173,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(371,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(33,axiom,
cl_Groups_Oplus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
thf(237,plain,
cl_Groups_Oplus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(72,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_add_Ocomm__neutral) ).
thf(360,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(126,axiom,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_mod__diff__cong) ).
thf(508,plain,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_Pair__eq) ).
thf(558,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(54,axiom,
( ( lbounds @ as )
!= ( nil @ ( product_prod @ int @ ( list @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096lbounds_Aas_A_126_061_A_091_093_096) ).
thf(298,plain,
( ( lbounds @ as )
!= ( nil @ ( product_prod @ int @ ( list @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(94,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mod__by__0) ).
thf(425,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(128,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_mod__add__cong) ).
thf(513,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( div_mod @ TA @ E @ D )
= ( div_mod @ TA @ C @ D ) )
=> ( ( ( div_mod @ TA @ B @ D )
= ( div_mod @ TA @ A @ D ) )
=> ( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(44,axiom,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ ( div_mod @ int @ C @ B ) ) @ A ) @ B )
= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_zdiff__zmod__left) ).
thf(264,plain,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ ( div_mod @ int @ C @ B ) ) @ A ) @ B )
= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(144,axiom,
ring_div @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Oring__div) ).
thf(573,plain,
ring_div @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(102,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(444,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(50,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(286,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(52,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fdisj ) @ B ) ) @ A ) ) )
<=> ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
& ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_finite__Collect__disjI) ).
thf(291,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fdisj ) @ B ) ) @ A ) ) )
=> ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
& ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) ) )
& ( ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
& ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fdisj ) @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(48,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_mod__add__self2) ).
thf(281,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(15,axiom,
cl_Groups_Ominus @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
thf(187,plain,
cl_Groups_Ominus @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(92,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(419,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(30,axiom,
i_Z @ a @ ( cons @ int @ x @ xs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71__096I_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
thf(230,plain,
i_Z @ a @ ( cons @ int @ x @ xs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(97,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_add__imp__eq) ).
thf(434,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(56,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( set @ TA @ A ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_set__empty2) ).
thf(303,plain,
! [TA: $tType,A: list @ TA] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( set @ TA @ A ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( set @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(105,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(451,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(143,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_double__zero__sym) ).
thf(567,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(120,axiom,
linorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(494,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(62,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(323,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(367,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(139,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ A ) @ B ) )
<=> ( finite_finite1 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite__Diff2) ).
thf(552,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ A ) @ B ) )
=> ( finite_finite1 @ TA @ A ) )
& ( ( finite_finite1 @ TA @ A )
=> ( finite_finite1 @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( minus_minus @ ( fun @ TA @ bool ) ) @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(521,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(84,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(399,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(27,axiom,
cl_Groups_Ominus @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(223,plain,
cl_Groups_Ominus @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(45,axiom,
! [TA: $tType,A: list @ TA] :
( ( ( set @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_set__empty) ).
thf(267,plain,
! [TA: $tType,A: list @ TA] :
( ( ( ( set @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( set @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(125,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ A ) @ ( nil @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_iprod__Nil2) ).
thf(505,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ A ) @ ( nil @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(96,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ B ) ) @ A ) @ B )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_zmod__simps_I1_J) ).
thf(431,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ B ) ) @ A ) @ B )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).
thf(241,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(134,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_add__0) ).
thf(531,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(39,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(255,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(129,axiom,
( ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) )
!= ( bot_bot @ ( fun @ int @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__096_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_A_126_061_A_123_125_096) ).
thf(516,plain,
( ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) )
!= ( bot_bot @ ( fun @ int @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1,conjecture,
( ( div_mod @ int @ ( aa @ int @ int @ ( plus_plus @ int @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ x ) @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fFalse ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) ) @ as ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) )
= ( div_mod @ int @ ( aa @ int @ int @ ( plus_plus @ int @ ( div_mod @ int @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( div_mod @ int @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ x ) @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fFalse ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( div_mod @ int @ ( aa @ int @ int @ ( plus_plus @ int @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ x ) @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fFalse ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) ) @ as ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) )
!= ( div_mod @ int @ ( aa @ int @ int @ ( plus_plus @ int @ ( div_mod @ int @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( div_mod @ int @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ x ) @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fFalse ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(145,plain,
( ( div_mod @ int @ ( aa @ int @ int @ ( plus_plus @ int @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ x ) @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fFalse ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) ) @ as ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) )
!= ( div_mod @ int @ ( aa @ int @ int @ ( plus_plus @ int @ ( div_mod @ int @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( div_mod @ int @ ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ x ) @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fFalse ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int @ ( combk @ bool @ ( list @ int ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_mod__add__eq) ).
thf(209,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Pair__inject) ).
thf(487,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ D ) @ C )
= ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB] :
( ( ( map @ TA @ TB @ B @ A )
= ( nil @ TB ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_map__is__Nil__conv) ).
thf(525,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB] :
( ( ( ( map @ TA @ TB @ B @ A )
= ( nil @ TB ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( map @ TA @ TB @ B @ A )
= ( nil @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(295,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) @ ( aa @ ( fun @ TB @ TC ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ TC ) ) @ ( combb @ TB @ TC @ TA ) @ C ) @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(4,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_list_Oinject) ).
thf(150,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
pp @ ( aa @ ( fun @ int @ bool ) @ bool @ ( aa @ int @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( member @ int ) @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096Max_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_058_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
thf(182,plain,
pp @ ( aa @ ( fun @ int @ bool ) @ bool @ ( aa @ int @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( member @ int ) @ ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ) ) @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(100,axiom,
pp @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool @ ( aa @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) @ ( aa @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) @ ( aa @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) @ li ) @ lks ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_Ili_M_Alks_J_A_058_Aset_A_Ilbounds_Aas_J_096) ).
thf(441,plain,
pp @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool @ ( aa @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) @ ( aa @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) @ ( aa @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) @ li ) @ lks ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(123,axiom,
? [A: int] :
! [B: atom] :
( ( pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ B ) @ ( set @ atom @ as ) ) )
=> ( i_Z @ B @ ( cons @ int @ A @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
thf(502,plain,
? [A: int] :
! [B: atom] :
( ( pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ B ) @ ( set @ atom @ as ) ) )
=> ( i_Z @ B @ ( cons @ int @ A @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(66,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
| ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_finite__Collect__conjI) ).
thf(336,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
| ( finite_finite1 @ TA @ ( collect @ TA @ A ) ) )
=> ( finite_finite1 @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(10,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_list_Osimps_I3_J) ).
thf(175,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(231,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_split__paired__Ex) ).
thf(363,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( aa @ TA @ ( product_prod @ TB @ TA ) @ ( aa @ TB @ ( fun @ TA @ ( product_prod @ TB @ TA ) ) @ ( product_Pair @ TB @ TA ) @ B ) @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(137,axiom,
! [A: list @ int] :
( ( ( zlcms @ A )
= ( zero_zero @ int ) )
<=> ( pp @ ( aa @ ( fun @ int @ bool ) @ bool @ ( aa @ int @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( member @ int ) @ ( zero_zero @ int ) ) @ ( set @ int @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_zlcms0__iff) ).
thf(539,plain,
! [A: list @ int] :
( ( ( ( zlcms @ A )
= ( zero_zero @ int ) )
=> ( pp @ ( aa @ ( fun @ int @ bool ) @ bool @ ( aa @ int @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( member @ int ) @ ( zero_zero @ int ) ) @ ( set @ int @ A ) ) ) )
& ( ( pp @ ( aa @ ( fun @ int @ bool ) @ bool @ ( aa @ int @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( member @ int ) @ ( zero_zero @ int ) ) @ ( set @ int @ A ) ) )
=> ( ( zlcms @ A )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(132,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(524,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(121,axiom,
~ ! [A: int,B: list @ int] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool @ ( aa @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) @ ( aa @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) @ ( aa @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) @ A ) @ B ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) )
=> ( ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) )
!= ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ A ) @ ( aa @ ( list @ int ) @ int @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( iprod @ int ) @ B ) @ xs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096_B_Bthesis_O_A_I_B_Bli_Alks_O_A_091_124_A_Ili_M_Alks_J_A_058_Aset_A_Ilbounds_Aas_J_059_AMax_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_A_061_Ali_A_N_A_092_060langle_062lks_Mxs_092_060rangle_062_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(495,plain,
~ ! [A: int,B: list @ int] :
( ( pp @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool @ ( aa @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) @ ( aa @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) @ ( aa @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) @ A ) @ B ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) )
=> ( ( big_linorder_Max @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ) )
!= ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ A ) @ ( aa @ ( list @ int ) @ int @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( iprod @ int ) @ B ) @ xs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( map @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( map @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_map_Osimps_I2_J) ).
thf(482,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ TB] :
( ( map @ TA @ TB @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TB @ ( aa @ TA @ TB @ C @ B ) @ ( map @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(20,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__right__imp__eq) ).
thf(203,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_zero__reorient) ).
thf(158,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(86,axiom,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mod__diff__eq) ).
thf(401,plain,
! [TA: $tType] :
( ( ring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB] :
( ( ( nil @ TB )
= ( map @ TA @ TB @ B @ A ) )
<=> ( A
= ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Nil__is__map__conv) ).
thf(246,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: fun @ TA @ TB] :
( ( ( ( nil @ TB )
= ( map @ TA @ TB @ B @ A ) )
=> ( A
= ( nil @ TA ) ) )
& ( ( A
= ( nil @ TA ) )
=> ( ( nil @ TB )
= ( map @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(79,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_add__right__cancel) ).
thf(383,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(68,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( set @ TA @ ( filter @ TA @ B @ A ) )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ ( set @ TA @ A ) ) ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_set__filter) ).
thf(346,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( set @ TA @ ( filter @ TA @ B @ A ) )
= ( collect @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ ( set @ TA @ A ) ) ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(136,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_zmod__simps_I2_J) ).
thf(536,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(24,axiom,
! [TA: $tType] :
( ( set @ TA @ ( nil @ TA ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_List_Oset_Osimps_I1_J) ).
thf(214,plain,
! [TA: $tType] :
( ( set @ TA @ ( nil @ TA ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(59,axiom,
finite_finite1 @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096finite_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096) ).
thf(315,plain,
finite_finite1 @ int @ ( collect @ int @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ bool ) @ bool ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ bool ) ) @ ( combb @ ( fun @ ( list @ int ) @ bool ) @ bool @ int ) @ ( fEx @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ bool ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ bool ) ) @ ( combb @ ( fun @ int @ bool ) @ bool @ ( list @ int ) ) @ ( fEx @ int ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combs @ ( list @ int ) @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combs @ int @ bool @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ int ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ int ) @ fconj ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combc @ int @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( aa @ ( fun @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( fun @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) ) ) @ ( combb @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ int ) @ ( combb @ ( fun @ int @ int ) @ ( fun @ int @ bool ) @ ( list @ int ) ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ bool ) @ ( fun @ ( fun @ int @ int ) @ ( fun @ int @ bool ) ) @ int ) @ ( combb @ int @ bool @ int ) ) @ ( fequal @ int ) ) ) ) @ ( aa @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ int ) @ ( fun @ ( list @ int ) @ ( fun @ int @ int ) ) ) @ ( combb @ int @ ( fun @ int @ int ) @ ( list @ int ) ) @ ( aa @ ( fun @ int @ ( fun @ int @ int ) ) @ ( fun @ int @ ( fun @ int @ int ) ) @ ( combc @ int @ int @ int ) @ ( minus_minus @ int ) ) ) @ ( aa @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( combc @ ( list @ int ) @ ( list @ int ) @ int ) @ ( iprod @ int ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) @ ( fun @ int @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) ) ) @ ( combb @ ( product_prod @ int @ ( list @ int ) ) @ ( fun @ ( fun @ ( product_prod @ int @ ( list @ int ) ) @ bool ) @ bool ) @ int ) @ ( member @ ( product_prod @ int @ ( list @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( product_prod @ int @ ( list @ int ) ) ) ) @ ( combc @ int @ ( list @ int ) @ ( product_prod @ int @ ( list @ int ) ) ) @ ( product_Pair @ int @ ( list @ int ) ) ) ) ) ) @ ( set @ ( product_prod @ int @ ( list @ int ) ) @ ( lbounds @ as ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(89,axiom,
semiring_div @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(410,plain,
semiring_div @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(7,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_finite) ).
thf(168,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(88,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( filter @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( filter @ TA @ C @ A ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( filter @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( filter @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_filter_Osimps_I2_J) ).
thf(405,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( filter @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ B @ ( filter @ TA @ C @ A ) ) ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( ( filter @ TA @ C @ ( cons @ TA @ B @ A ) )
= ( filter @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(17,axiom,
! [TA: $tType] :
( ( linord2061991079up_add @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( big_linorder_Max @ TA @ B ) )
= ( big_linorder_Max @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TA ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TA ) @ ( combs @ TA @ bool @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) ) @ ( aa @ ( fun @ TA @ TA ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) ) @ ( combc @ TA @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) @ TA ) @ ( combb @ TA @ bool @ TA ) ) @ ( fequal @ TA ) ) ) @ ( plus_plus @ TA @ A ) ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__Max__commute) ).
thf(190,plain,
! [TA: $tType] :
( ( linord2061991079up_add @ TA )
=> ! [A: TA,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( big_linorder_Max @ TA @ B ) )
= ( big_linorder_Max @ TA @ ( collect @ TA @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TA ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TA ) @ ( combs @ TA @ bool @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ TA ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) ) @ ( aa @ ( fun @ TA @ TA ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ ( fun @ TA @ bool ) ) ) @ ( combc @ TA @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ ( fun @ TA @ bool ) ) @ ( fun @ TA @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ ( fun @ TA @ TA ) @ ( fun @ TA @ bool ) ) @ TA ) @ ( combb @ TA @ bool @ TA ) ) @ ( fequal @ TA ) ) ) @ ( plus_plus @ TA @ A ) ) ) ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) ) @ B ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(183,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(93,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_mod__mod__trivial) ).
thf(422,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(46,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( filter @ TA @ C @ ( filter @ TA @ B @ A ) )
= ( filter @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_filter__filter) ).
thf(273,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( filter @ TA @ C @ ( filter @ TA @ B @ A ) )
= ( filter @ TA @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) @ ( aa @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( combs @ TA @ bool @ bool ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) @ B ) ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(76,axiom,
! [A: atom] :
( ( pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ A ) @ ( set @ atom @ as ) ) )
=> ( ( aa @ atom @ int @ divisor @ A )
!= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_norm) ).
thf(373,plain,
! [A: atom] :
( ( pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ A ) @ ( set @ atom @ as ) ) )
=> ( ( aa @ atom @ int @ divisor @ A )
!= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(64,axiom,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( filter @ TA @ B @ A )
= ( nil @ TA ) )
<=> ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
=> ~ ( pp @ ( aa @ TA @ bool @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_filter__empty__conv) ).
thf(326,plain,
! [TA: $tType,A: list @ TA,B: fun @ TA @ bool] :
( ( ( ( filter @ TA @ B @ A )
= ( nil @ TA ) )
=> ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
=> ~ ( pp @ ( aa @ TA @ bool @ B @ C ) ) ) )
& ( ! [C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( set @ TA @ A ) ) )
=> ~ ( pp @ ( aa @ TA @ bool @ B @ C ) ) )
=> ( ( filter @ TA @ B @ A )
= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(437,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( aa @ TA @ ( fun @ TC @ TB ) @ ( aa @ ( fun @ TC @ ( fun @ TA @ TB ) ) @ ( fun @ TA @ ( fun @ TC @ TB ) ) @ ( combc @ TC @ TA @ TB ) @ C ) @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(85,axiom,
linord2061991079up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__semigroup__add) ).
thf(400,plain,
linord2061991079up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(110,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) @ B )
= ( div_mod @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_mod__add__self1) ).
thf(464,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( plus_plus @ TA @ B ) @ A ) @ B )
= ( div_mod @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
=> ( finite_finite1 @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combs @ TA @ bool @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ TB ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combb @ TB @ bool @ TA ) ) @ ( fequal @ TB ) ) ) @ A ) ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__image__set) ).
thf(459,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ ( collect @ TA @ B ) )
=> ( finite_finite1 @ TB @ ( collect @ TB @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ bool ) ) @ ( combb @ ( fun @ TA @ bool ) @ bool @ TB ) @ ( fEx @ TA ) ) @ ( aa @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combs @ TA @ bool @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( fun @ TB @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) ) @ ( combb @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) @ TB ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ TA @ bool ) @ ( fun @ TA @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA ) @ fconj ) ) @ ( aa @ ( fun @ TA @ TB ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TB @ ( fun @ TA @ bool ) ) ) @ ( combc @ TB @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) @ ( aa @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ TB @ bool ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) @ ( fun @ ( fun @ TB @ ( fun @ TB @ bool ) ) @ ( fun @ TB @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) ) ) @ ( combb @ ( fun @ TB @ bool ) @ ( fun @ ( fun @ TA @ TB ) @ ( fun @ TA @ bool ) ) @ TB ) @ ( combb @ TB @ bool @ TA ) ) @ ( fequal @ TB ) ) ) @ A ) ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(19,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(200,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
~ ! [A: int] :
~ ! [B: atom] :
( ( pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ B ) @ ( set @ atom @ as ) ) )
=> ( i_Z @ B @ ( cons @ int @ A @ xs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72__096_B_Bthesis_O_A_I_B_Bx_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(178,plain,
~ ! [A: int] :
~ ! [B: atom] :
( ( pp @ ( aa @ ( fun @ atom @ bool ) @ bool @ ( aa @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) @ B ) @ ( set @ atom @ as ) ) )
=> ( i_Z @ B @ ( cons @ int @ A @ xs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(101,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(442,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(29,axiom,
! [TA: $tType,A: list @ TA] :
( ( map @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_map__ident) ).
thf(227,plain,
! [TA: $tType,A: list @ TA] :
( ( map @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(469,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(57,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_add__left__imp__eq) ).
thf(309,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ B )
= ( aa @ TA @ TA @ ( plus_plus @ TA @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(574,plain,
$false,
inference(e,[status(thm)],[445,479,333,234,555,352,170,217,276,440,511,500,472,404,417,288,301,257,389,184,504,284,448,316,261,492,376,485,238,353,147,453,396,411,243,428,312,206,380,546,220,534,392,165,260,349,467,566,252,461,456,324,224,519,317,188,256,339,193,476,212,393,173,371,237,360,508,558,298,425,513,264,573,444,286,291,281,187,419,230,434,303,451,567,494,323,367,552,521,399,223,267,505,431,241,531,255,516,145,209,487,525,295,150,182,441,502,336,175,231,363,539,524,495,482,203,158,401,246,383,346,536,214,315,410,168,405,190,183,422,273,373,326,437,400,464,459,200,178,442,227,469,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM111_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri May 19 03:34:53 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.87/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.85/1.11 % [INFO] Parsing done (245ms).
% 1.85/1.11 % [INFO] Running in sequential loop mode.
% 2.60/1.32 % [INFO] eprover registered as external prover.
% 2.60/1.33 % [INFO] cvc4 registered as external prover.
% 2.60/1.33 % [INFO] Scanning for conjecture ...
% 3.43/1.58 % [INFO] Found a conjecture and 142 axioms. Running axiom selection ...
% 4.00/1.72 % [INFO] Axiom selection finished. Selected 142 axioms (removed 0 axioms).
% 4.55/1.85 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.55/1.88 % [INFO] Type checking passed.
% 4.55/1.88 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.01/2.59 % [INFO] [Domain constraints] Detected constraint on bool
% 7.01/2.59 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 7.01/2.66 % [INFO] [Domain constraints] Detected constraint on bool
% 7.01/2.66 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 81.33/64.54 % External prover 'e' found a proof!
% 81.33/64.54 % [INFO] Killing All external provers ...
% 81.33/64.54 % Time passed: 64013ms (effective reasoning time: 63421ms)
% 81.33/64.54 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 81.33/64.54 % Axioms used in derivation (142): arity_fun___Finite__Set_Ofinite, fact_82_list_Osimps_I2_J, fact_21_map__is__Nil__conv, fact_14_map__ident, fact_86_add_Ocomm__neutral, fact_68_zmod__zero, fact_87_diff__0__right, fact_25_List_Oset_Osimps_I1_J, arity_HOL_Obool___Finite__Set_Ofinite, fact_19_Pair__eq, help_COMBS_1_1_U, fact_40_zmod__simps_I2_J, fact_27_set__empty, fact_70_filter_Osimps_I2_J, fact_81_list_Osimps_I3_J, help_fconj_3_1_U, fact_31_add__right__imp__eq, fact_5__096a_A_058_Aset_Aas_096, arity_Int_Oint___Groups_Ominus, fact_94_iprod__Nil, fact_96_zlcms0__iff, fact_1__096_Ili_M_Alks_J_A_058_Aset_A_Ilbounds_Aas_J_096, fact_57_Max__in, arity_Int_Oint___Groups_Ocomm__monoid__add, help_COMBI_1_1_U, fact_80_set__ConsD, fact_69_zmod__self, fact_71__096I_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096, fact_17_add__right__cancel, arity_HOL_Obool___Groups_Ominus, fact_92_finite__image__set, fact_32_add__imp__eq, help_fTrue_1_1_T, fact_75_mem__def, arity_Int_Oint___Rings_Oring, fact_51_add__Max__commute, fact_64_diff__self, fact_83_add__0__left, fact_36_add__diff__cancel, fact_34_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, help_fTrue_1_1_U, fact_15_mod__mod__trivial, arity_HOL_Obool___Orderings_Olinorder, fact_85_add__0__right, fact_43_mod__add__right__eq, arity_Int_Oint___Groups_Oplus, fact_38_mod__add__cong, help_fFalse_1_1_T, fact_7__096finite_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096, fact_39_zmod__simps_I1_J, fact_3__096Max_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_058_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_096, fact_74_ext, arity_List_Olist___Groups_Ominus, arity_Int_Oint___Groups_Olinordered__ab__semigroup__add, fact_24_filter_Osimps_I1_J, help_COMBB_1_1_U, fact_10_map__eq__conv, fact_66_mod__self, fact_2__096lbounds_Aas_A_126_061_A_091_093_096, help_fdisj_1_1_U, fact_63_double__zero__sym, fact_60_finite__code, fact_93_finite__Collect__bounded__ex, fact_76_Collect__def, fact_35_diff__eq__diff__eq, arity_List_Olist___Groups_Oplus, arity_Int_Oint___Divides_Oring__div, fact_95_iprod__Nil2, fact_53_filter__False, help_fconj_2_1_U, fact_54_finite__Collect__disjI, fact_49_zdiff__zmod__left, fact_16_add__left__cancel, fact_62__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096, fact_42_mod__add__left__eq, arity_Int_Oint___Orderings_Olinorder, fact_56_split__paired__Ex, fact_48_filter__id__conv, fact_65_mod__0, fact_59_finite__Diff, help_fequal_1_1_T, arity_Int_Oint___Groups_Omonoid__add, fact_46_mod__diff__left__eq, fact_11_mod__add__self2, fact_0__096is__dvd_Aa_096, fact_6__096_B_Bthesis_O_A_I_B_Bli_Alks_O_A_091_124_A_Ili_M_Alks_J_A_058_Aset_A_Ilbounds_Aas_J_059_AMax_A_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_A_061_Ali_A_N_A_092_060langle_062lks_Mxs_092_060rangle_062_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_33_add__left__imp__eq, fact_8__096_123i_A_N_A_092_060langle_062ks_Mxs_092_060rangle_062_A_124ks_Ai_O_A_Ii_M_Aks_J_A_058_Aset_A_Ilbounds_Aas_J_125_A_126_061_A_123_125_096, fact_41_mod__add__eq, fact_4_lm, fact_20_finite__set, arity_Int_Oint___Groups_Ogroup__add, arity_Int_Oint___Groups_Ocancel__semigroup__add, help_COMBC_1_1_U, fact_88_eq__iff__diff__eq__0, help_fequal_2_1_T, fact_58_x, fact_97_list__add__Cons, fact_28_norm, fact_73_not__Cons__self, fact_67_map_Osimps_I2_J, fact_29_filter__empty__conv, arity_prod___Finite__Set_Ofinite, help_fconj_1_1_U, fact_22_map_Osimps_I1_J, fact_52_finite_OemptyI, help_fdisj_3_1_U, fact_23_Nil__is__map__conv, fact_98_list__diff__Cons__Cons, help_fFalse_1_1_U, arity_Int_Oint___Groups_Oab__semigroup__add, fact_44_mod__diff__cong, fact_91_finite, fact_47_mod__diff__right__eq, fact_30_Pair__inject, fact_77_not__Cons__self2, fact_50_zdiff__zmod__right, help_pp_1_1_U, fact_12_mod__add__self1, arity_Int_Oint___Divides_Osemiring__div, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_78_zero__reorient, fact_61_list_Oinject, fact_79_finite__Diff2, fact_72__096_B_Bthesis_O_A_I_B_Bx_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, arity_Int_Oint___Groups_Ozero, fact_18_split__paired__All, fact_13_filter__filter, fact_84_add__0, help_pp_2_1_U, fact_37_diff__add__cancel, fact_26_set__empty2, help_fEx_1_1_U, arity_fun___Groups_Ominus, fact_90_mod__by__0, fact_45_mod__diff__eq, fact_89_right__minus__eq, fact_55_finite__Collect__conjI, fact_9_set__filter
% 81.33/64.54 % No. of inferences in proof: 288
% 81.33/64.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 64013 ms resp. 63421 ms w/o parsing
% 82.12/64.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 82.12/64.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------