TSTP Solution File: COM069_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM069_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 10:14:01 EDT 2023
% Result : Theorem 47.56s 34.44s
% Output : Refutation 48.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 192
% Syntax : Number of formulae : 328 ( 78 unt; 58 typ; 0 def)
% Number of atoms : 5115 ( 264 equ; 0 cnn)
% Maximal formula atoms : 11 ( 18 avg)
% Number of connectives : 15501 ( 34 ~; 18 |; 21 &;15150 @)
% ( 16 <=>; 262 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 57 usr; 12 con; 0-4 aty)
% Number of variables : 758 ( 0 ^; 704 !; 0 ?; 758 :)
% ( 54 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(ring_type,type,
ring:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(ring_div_type,type,
ring_div:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(monoid_mult_type,type,
monoid_mult:
!>[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(comm_monoid_mult_type,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_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(ordere216010020id_add_type,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(big_linorder_Min_type,type,
big_linorder_Min:
!>[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(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( fun @ 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_div_type,type,
div_div:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(div_mod_type,type,
div_mod:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ TA ) ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_type,type,
times_times:
!>[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(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( fun @ ( list @ TA ) @ TB ) ) ).
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(tl_type,type,
tl:
!>[TA: $tType] : ( fun @ ( list @ TA ) @ ( list @ TA ) ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(c_PresArith_Oatom_OLe_type,type,
c_PresArith_Oatom_OLe: fun @ int @ ( fun @ ( list @ int ) @ atom ) ).
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(zlcms_type,type,
zlcms: ( list @ int ) > int ).
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(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(n_type,type,
n: int ).
thf(xs_type,type,
xs: list @ int ).
thf(18,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( div_mod @ TA @ B @ A ) ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zmod__simps_I2_J) ).
thf(181,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( div_mod @ TA @ B @ A ) ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(138,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(121,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(479,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(135,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(518,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ A @ A ) ) @ ( zero_zero @ TA ) ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ A ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_double__add__less__zero__iff__single__add__less__zero) ).
thf(468,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ A @ A ) ) @ ( zero_zero @ TA ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ A ) @ ( zero_zero @ TA ) ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ A ) @ ( zero_zero @ TA ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ A @ A ) ) @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( aa @ TA @ ( fun @ TB @ TA ) @ ( combk @ TA @ TB ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(333,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( aa @ TA @ ( fun @ TB @ TA ) @ ( combk @ TA @ TB ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(39,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/sandbox2/benchmark/theBenchmark.p',fact_81_zdiff__zmod__left) ).
thf(249,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)],[39]) ).
thf(122,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_mod__by__1) ).
thf(481,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(75,axiom,
comm_monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(352,plain,
comm_monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',fact_74_mem__def) ).
thf(408,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)],[95]) ).
thf(110,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ A )
= ( div_mod @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_mod__mult__self1) ).
thf(449,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ A )
= ( div_mod @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(84,axiom,
ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(379,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(46,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/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(269,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)],[46]) ).
thf(27,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(217,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(49,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(276,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',fact_0_norm) ).
thf(440,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)],[106]) ).
thf(131,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ B @ A ) @ B )
= ( div_mod @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_mod__add__self1) ).
thf(511,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ B @ A ) @ B )
= ( div_mod @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(5,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mod__add__right__eq) ).
thf(142,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(72,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_mod__mult__self2__is__0) ).
thf(340,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(66,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zero__reorient) ).
thf(320,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)],[66]) ).
thf(42,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_mult_Ocomm__neutral) ).
thf(257,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(88,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ B )
= ( div_mod @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_mod__mult__self2) ).
thf(389,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) @ B )
= ( div_mod @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(184,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_mod__by__0) ).
thf(157,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(98,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mod__mult__left__eq) ).
thf(416,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(33,axiom,
ordere223160158up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(228,plain,
ordere223160158up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(54,axiom,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( aa @ atom @ TA @ ( atom_case @ TA @ E @ D @ C ) @ ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ B ) @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_atom_Osimps_I10_J) ).
thf(289,plain,
! [TA: $tType,A: list @ int,B: int,C: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),D: fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ TA ) ),E: fun @ int @ ( fun @ ( list @ int ) @ TA )] :
( ( aa @ atom @ TA @ ( atom_case @ TA @ E @ D @ C ) @ ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ B ) @ A ) )
= ( aa @ ( list @ int ) @ TA @ ( aa @ int @ ( fun @ ( list @ int ) @ TA ) @ E @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(109,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(448,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(107,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_div @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_div__0) ).
thf(443,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_div @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(376,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)],[83]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add__less__imp__less__left) ).
thf(238,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(132,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ A @ C ) ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__strict__left__mono) ).
thf(514,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ A @ C ) ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(76,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C
= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( zero_zero @ TA ) ) )
& ( ( C
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( div_div @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_div__mult__mult1__if) ).
thf(353,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C
= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( zero_zero @ TA ) ) )
& ( ( C
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( div_div @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(51,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_mult__1) ).
thf(280,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(96,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(411,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)],[96]) ).
thf(37,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add__right__imp__eq) ).
thf(243,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(102,axiom,
ordere216010020id_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
thf(428,plain,
ordere216010020id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(62,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_mult__1__right) ).
thf(312,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',fact_48_eq__iff__diff__eq__0) ).
thf(206,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)],[24]) ).
thf(55,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mod__mult__eq) ).
thf(292,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(111,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_add__right__cancel) ).
thf(452,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(85,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add_Ocomm__neutral) ).
thf(380,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',fact_77_mod__diff__right__eq) ).
thf(160,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)],[11]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_add__less__cancel__left) ).
thf(392,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(103,axiom,
! [A: int,B: int] :
( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( zero_zero @ int ) ) @ B ) )
=> ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( div_mod @ int @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_pos__mod__bound) ).
thf(429,plain,
! [A: int,B: int] :
( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( zero_zero @ int ) ) @ B ) )
=> ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( div_mod @ int @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(48,axiom,
ordere236663937imp_le @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(275,plain,
ordere236663937imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(43,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( div_div @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_div__mult__mult1) ).
thf(260,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( div_div @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(74,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( plus_plus @ ( list @ TA ) @ C @ B ) ) @ A )
= ( plus_plus @ TA @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ C ) @ A ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_iprod__left__add__distrib) ).
thf(349,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( plus_plus @ ( list @ TA ) @ C @ B ) ) @ A )
= ( plus_plus @ TA @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ C ) @ A ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(115,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(467,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(40,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(252,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)],[40]) ).
thf(78,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(361,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(113,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 @ ( plus_plus @ TA @ E @ B ) @ D )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mod__add__cong) ).
thf(461,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 @ ( plus_plus @ TA @ E @ B ) @ D )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(31,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ B ) ) @ A ) @ B )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_zmod__simps_I4_J) ).
thf(224,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ B ) ) @ A ) @ B )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(34,axiom,
! [A: list @ int,B: int,C: list @ int,D: int] :
( ( ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ D ) @ C )
= ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_atom_Osimps_I1_J) ).
thf(229,plain,
! [A: list @ int,B: int,C: list @ int,D: int] :
( ( ( ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ D ) @ C )
= ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ D ) @ C )
= ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(123,axiom,
! [A: int,B: int] :
( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ B ) @ ( zero_zero @ int ) ) )
=> ( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( zero_zero @ int ) ) @ A ) )
=> ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( div_div @ int @ B @ A ) ) @ ( zero_zero @ int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_div__neg__pos__less0) ).
thf(484,plain,
! [A: int,B: int] :
( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ B ) @ ( zero_zero @ int ) ) )
=> ( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( zero_zero @ int ) ) @ A ) )
=> ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( div_div @ int @ B @ A ) ) @ ( zero_zero @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(93,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_mult__1__left) ).
thf(403,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(14,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_mod__mult__mult1) ).
thf(169,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',fact_76_mod__diff__left__eq) ).
thf(499,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)],[127]) ).
thf(117,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/sandbox2/benchmark/theBenchmark.p',help_fEx_1_1_U) ).
thf(471,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)],[117]) ).
thf(71,axiom,
semiring_div @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(339,plain,
semiring_div @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(120,axiom,
! [A: int] :
( ( div_mod @ int @ A @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_zmod__self) ).
thf(476,plain,
! [A: int] :
( ( div_mod @ int @ A @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(125,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_one__reorient) ).
thf(489,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(25,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add__less__imp__less__right) ).
thf(212,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(73,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_double__zero__sym) ).
thf(343,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(45,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( map @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_iprod__assoc) ).
thf(266,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( map @ TA @ TA @ ( times_times @ TA @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(130,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_mod__self) ).
thf(508,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(57,axiom,
monoid_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(298,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(101,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(425,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)],[101]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ C ) @ A ) ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_iprod__left__diff__distrib) ).
thf(166,plain,
! [TA: $tType] :
( ( ring @ TA )
=> ! [A: list @ TA,B: list @ TA,C: list @ TA] :
( ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ ( aa @ ( list @ TA ) @ ( list @ TA ) @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ ( list @ TA ) ) @ ( minus_minus @ ( list @ TA ) ) @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ C ) @ A ) ) @ ( aa @ ( list @ TA ) @ TA @ ( aa @ ( list @ TA ) @ ( fun @ ( list @ TA ) @ TA ) @ ( iprod @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(148,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,axiom,
one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(279,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(92,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(402,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(53,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_div__mult__self1__is__id) ).
thf(286,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(97,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_div @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_div__by__1) ).
thf(413,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_div @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',fact_37_diff__eq__diff__eq) ).
thf(187,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)],[20]) ).
thf(94,axiom,
! [A: int,B: int] :
( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ B ) @ ( zero_zero @ int ) ) )
=> ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ B ) @ ( div_mod @ int @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_neg__mod__bound) ).
thf(406,plain,
! [A: int,B: int] :
( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ B ) @ ( zero_zero @ int ) ) )
=> ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ B ) @ ( div_mod @ int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(15,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_div__mult__self2__is__id) ).
thf(172,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( B
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_mod__mult__mult2) ).
thf(219,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ B ) )
= ( aa @ TA @ TA @ ( times_times @ TA @ ( div_mod @ TA @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(99,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add__0__left) ).
thf(419,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(64,axiom,
ab_semigroup_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(318,plain,
ab_semigroup_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',fact_71_mod__diff__cong) ).
thf(303,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)],[59]) ).
thf(80,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_div @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_div__by__0) ).
thf(367,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_div @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(36,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_diff__add__cancel) ).
thf(240,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: 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)],[36]) ).
thf(68,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mod__mult__right__eq) ).
thf(330,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ B ) @ A )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(60,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( div_mod @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_mod__0) ).
thf(306,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)],[60]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(299,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)],[58]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',fact_73_ext) ).
thf(505,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)],[129]) ).
thf(104,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_add__left__cancel) ).
thf(431,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(118,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(473,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(133,axiom,
ordered_ab_group_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add) ).
thf(516,plain,
ordered_ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',fact_82_zdiff__zmod__right) ).
thf(458,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)],[112]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',fact_47_right__minus__eq) ).
thf(194,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)],[21]) ).
thf(6,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mod__add__eq) ).
thf(145,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) @ ( div_mod @ TA @ B @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(56,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_less__iff__diff__less__0) ).
thf(295,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) ) @ ( zero_zero @ TA ) ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ B ) @ A ) ) @ ( zero_zero @ TA ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(67,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mod__add__left__eq) ).
thf(327,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ A ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(44,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_mod__add__self2) ).
thf(263,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ B @ A ) @ A )
= ( div_mod @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(81,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) @ B )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_mod__mult__self1__is__0) ).
thf(370,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ A ) @ B )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(128,axiom,
! [A: int] :
( ( div_div @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zdiv__zero) ).
thf(502,plain,
! [A: int] :
( ( div_div @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(77,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__pos__pos) ).
thf(359,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ B ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(70,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__0) ).
thf(336,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(9,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: list @ TA] :
( ( map @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_scale1) ).
thf(154,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: list @ TA] :
( ( map @ TA @ TA @ ( times_times @ TA @ ( one_one @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(108,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ D ) @ C ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ D @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__strict__mono) ).
thf(446,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ D ) @ C ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ D @ B ) ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(16,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ B ) @ A ) @ B )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zmod__simps_I1_J) ).
thf(175,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( div_mod @ TA @ ( plus_plus @ TA @ ( div_mod @ TA @ C @ B ) @ A ) @ B )
= ( div_mod @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(87,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 @ ( times_times @ TA @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_mod__mult__cong) ).
thf(386,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 @ ( times_times @ TA @ E ) @ B ) @ D )
= ( div_mod @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(23,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ A @ A )
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_div__self) ).
thf(203,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ A @ A )
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(218,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(134,axiom,
ring_div @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Oring__div) ).
thf(517,plain,
ring_div @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(65,axiom,
group_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(319,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',fact_72_mod__diff__eq) ).
thf(139,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)],[4]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_add__less__cancel__right) ).
thf(246,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ B ) ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(47,axiom,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ ( div_mod @ int @ B @ A ) ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_zmod__simps_I3_J) ).
thf(272,plain,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ ( div_mod @ int @ B @ A ) ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',fact_20_diff__self) ).
thf(383,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)],[86]) ).
thf(26,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ ( plus_plus @ TA @ A @ A ) ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_zero__less__double__add__iff__zero__less__single__add) ).
thf(214,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ ( plus_plus @ TA @ A @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ A ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( zero_zero @ TA ) ) @ ( plus_plus @ TA @ A @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_div @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_mod__div__trivial) ).
thf(151,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA] :
( ( div_div @ TA @ ( div_mod @ TA @ B @ A ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(63,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add__imp__eq) ).
thf(315,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(100,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Collect__def) ).
thf(422,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(82,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( plus_plus @ TA @ B @ A ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_add__diff__cancel) ).
thf(373,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ ( minus_minus @ TA ) @ ( plus_plus @ TA @ B @ A ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1,conjecture,
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( aa @ int @ int @ ( times_times @ int @ ( plus_plus @ int @ ( div_div @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( big_linorder_Min @ 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 ) ) @ ( 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 ) @ ( aa @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combb @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( list @ int ) ) @ ( iprod @ int ) ) @ ( tl @ int ) ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ atom @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( combb @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ int ) @ ( member @ atom ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( combc @ int @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe ) ) ) ) @ ( collect @ atom @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combs @ atom @ bool @ bool ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ atom ) @ fconj ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combc @ atom @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) ) @ ( set @ atom @ as ) ) ) ) @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( list_case @ bool @ int @ fFalse @ ( aa @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ bool @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( combk @ bool @ ( list @ int ) ) ) @ ( aa @ int @ ( fun @ int @ bool ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( combc @ int @ int @ bool ) @ ( ord_less @ int ) ) @ ( zero_zero @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( one_one @ int ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) )
= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ ( div_mod @ int @ n @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ ( plus_plus @ int @ ( div_div @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( big_linorder_Min @ 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 ) ) @ ( 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 ) @ ( aa @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combb @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( list @ int ) ) @ ( iprod @ int ) ) @ ( tl @ int ) ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ atom @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( combb @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ int ) @ ( member @ atom ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( combc @ int @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe ) ) ) ) @ ( collect @ atom @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combs @ atom @ bool @ bool ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ atom ) @ fconj ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combc @ atom @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) ) @ ( set @ atom @ as ) ) ) ) @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( list_case @ bool @ int @ fFalse @ ( aa @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ bool @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( combk @ bool @ ( list @ int ) ) ) @ ( aa @ int @ ( fun @ int @ bool ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( combc @ int @ int @ bool ) @ ( ord_less @ int ) ) @ ( zero_zero @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( one_one @ int ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( aa @ int @ int @ ( times_times @ int @ ( plus_plus @ int @ ( div_div @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( big_linorder_Min @ 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 ) ) @ ( 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 ) @ ( aa @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combb @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( list @ int ) ) @ ( iprod @ int ) ) @ ( tl @ int ) ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ atom @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( combb @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ int ) @ ( member @ atom ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( combc @ int @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe ) ) ) ) @ ( collect @ atom @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combs @ atom @ bool @ bool ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ atom ) @ fconj ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combc @ atom @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) ) @ ( set @ atom @ as ) ) ) ) @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( list_case @ bool @ int @ fFalse @ ( aa @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ bool @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( combk @ bool @ ( list @ int ) ) ) @ ( aa @ int @ ( fun @ int @ bool ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( combc @ int @ int @ bool ) @ ( ord_less @ int ) ) @ ( zero_zero @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( one_one @ int ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) )
!= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ ( div_mod @ int @ n @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ ( plus_plus @ int @ ( div_div @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( big_linorder_Min @ 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 ) ) @ ( 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 ) @ ( aa @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combb @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( list @ int ) ) @ ( iprod @ int ) ) @ ( tl @ int ) ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ atom @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( combb @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ int ) @ ( member @ atom ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( combc @ int @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe ) ) ) ) @ ( collect @ atom @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combs @ atom @ bool @ bool ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ atom ) @ fconj ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combc @ atom @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) ) @ ( set @ atom @ as ) ) ) ) @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( list_case @ bool @ int @ fFalse @ ( aa @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ bool @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( combk @ bool @ ( list @ int ) ) ) @ ( aa @ int @ ( fun @ int @ bool ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( combc @ int @ int @ bool ) @ ( ord_less @ int ) ) @ ( zero_zero @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( one_one @ int ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( aa @ atom @ int @ divisor @ a ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(136,plain,
( ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( aa @ int @ int @ ( times_times @ int @ ( plus_plus @ int @ ( div_div @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( big_linorder_Min @ 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 ) ) @ ( 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 ) @ ( aa @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combb @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( list @ int ) ) @ ( iprod @ int ) ) @ ( tl @ int ) ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ atom @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( combb @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ int ) @ ( member @ atom ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( combc @ int @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe ) ) ) ) @ ( collect @ atom @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combs @ atom @ bool @ bool ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ atom ) @ fconj ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combc @ atom @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) ) @ ( set @ atom @ as ) ) ) ) @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( list_case @ bool @ int @ fFalse @ ( aa @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ bool @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( combk @ bool @ ( list @ int ) ) ) @ ( aa @ int @ ( fun @ int @ bool ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( combc @ int @ int @ bool ) @ ( ord_less @ int ) ) @ ( zero_zero @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( one_one @ int ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) ) @ ( aa @ atom @ int @ divisor @ a ) )
!= ( div_mod @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ ( div_mod @ int @ n @ ( aa @ atom @ int @ divisor @ a ) ) ) @ ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ ( plus_plus @ int @ ( div_div @ int @ ( aa @ int @ int @ ( aa @ int @ ( fun @ int @ int ) @ ( minus_minus @ int ) @ n ) @ ( big_linorder_Min @ 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 ) ) @ ( 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 ) @ ( aa @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( list @ int ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) ) ) @ ( combb @ ( list @ int ) @ ( fun @ ( list @ int ) @ int ) @ ( list @ int ) ) @ ( iprod @ int ) ) @ ( tl @ int ) ) ) @ xs ) ) ) ) ) ) ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ ( list @ int ) @ ( fun @ int @ bool ) ) ) @ ( combc @ ( list @ int ) @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( list @ int ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) ) ) @ ( combb @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ int @ bool ) ) @ ( list @ int ) ) @ ( combc @ int @ ( fun @ atom @ bool ) @ bool ) ) @ ( aa @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( aa @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( fun @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) ) @ ( combb @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( list @ int ) ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ int @ atom ) @ ( fun @ int @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) ) @ ( combb @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) @ int ) @ ( member @ atom ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ atom ) ) @ ( fun @ ( list @ int ) @ ( fun @ int @ atom ) ) @ ( combc @ int @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe ) ) ) ) @ ( collect @ atom @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combs @ atom @ bool @ bool ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ atom ) @ fconj ) @ ( aa @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) @ ( aa @ ( fun @ atom @ ( fun @ ( fun @ atom @ bool ) @ bool ) ) @ ( fun @ ( fun @ atom @ bool ) @ ( fun @ atom @ bool ) ) @ ( combc @ atom @ ( fun @ atom @ bool ) @ bool ) @ ( member @ atom ) ) @ ( set @ atom @ as ) ) ) ) @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( list_case @ bool @ int @ fFalse @ ( aa @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( aa @ ( fun @ bool @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ ( fun @ int @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combb @ bool @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( combk @ bool @ ( list @ int ) ) ) @ ( aa @ int @ ( fun @ int @ bool ) @ ( aa @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( fun @ int @ ( fun @ int @ bool ) ) @ ( combc @ int @ int @ bool ) @ ( ord_less @ int ) ) @ ( zero_zero @ int ) ) ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) ) @ as ) ) ) ) @ ( one_one @ int ) ) ) @ ( zlcms @ ( map @ atom @ int @ divisor @ ( filter @ atom @ ( atom_case @ bool @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fFalse ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( combk @ bool @ ( list @ int ) ) @ fTrue ) ) ) @ ( aa @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( fun @ int @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) ) @ ( combk @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ int ) @ ( aa @ ( fun @ ( list @ int ) @ bool ) @ ( fun @ int @ ( fun @ ( list @ int ) @ bool ) ) @ ( combk @ ( fun @ ( list @ int ) @ bool ) @ int ) @ ( aa @ bool @ ( fun @ ( list @ int ) @ bool ) @ ( 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(105,axiom,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ B ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ ( div_mod @ int @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zmod__zmult1__eq) ).
thf(437,plain,
! [A: int,B: int,C: int] :
( ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ B ) @ A )
= ( div_mod @ int @ ( aa @ int @ int @ ( times_times @ int @ C ) @ ( div_mod @ int @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(119,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ A ) ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__strict__right__mono) ).
thf(474,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ C @ A ) ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(91,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(400,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(283,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)],[52]) ).
thf(90,axiom,
! [TA: $tType] :
( ( ordered_ab_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 ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ D ) @ C ) )
<=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_diff__eq__diff__less) ).
thf(395,plain,
! [TA: $tType] :
( ( ordered_ab_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 ) )
=> ( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) ) )
& ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ D ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(114,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add__left__imp__eq) ).
thf(464,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(178,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)],[17]) ).
thf(12,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add__0__right) ).
thf(163,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,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/sandbox2/benchmark/theBenchmark.p',fact_15_mod__mod__trivial) ).
thf(200,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)],[22]) ).
thf(124,axiom,
! [A: list @ int,B: int] :
( ( aa @ atom @ int @ divisor @ ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ B ) @ A ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_divisor_Osimps_I1_J) ).
thf(486,plain,
! [A: list @ int,B: int] :
( ( aa @ atom @ int @ divisor @ ( aa @ ( list @ int ) @ atom @ ( aa @ int @ ( fun @ ( list @ int ) @ atom ) @ c_PresArith_Oatom_OLe @ B ) @ A ) )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(61,axiom,
! [A: int] :
( ( div_mod @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zmod__zero) ).
thf(309,plain,
! [A: int] :
( ( div_mod @ int @ ( zero_zero @ int ) @ A )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(30,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ ( zero_zero @ TA ) ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ A ) @ ( zero_zero @ TA ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ B @ A ) ) @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__neg__neg) ).
thf(222,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ B ) @ ( zero_zero @ TA ) ) )
=> ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ A ) @ ( zero_zero @ TA ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( ord_less @ TA ) @ ( plus_plus @ TA @ B @ A ) ) @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(126,axiom,
! [A: int,B: int,C: int] :
( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( zero_zero @ int ) ) @ C ) )
=> ( ( div_mod @ int @ B @ ( aa @ int @ int @ ( times_times @ int @ A ) @ C ) )
= ( plus_plus @ int @ ( aa @ int @ int @ ( times_times @ int @ A ) @ ( div_mod @ int @ ( div_div @ int @ B @ A ) @ C ) ) @ ( div_mod @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_zmod__zmult2__eq) ).
thf(496,plain,
! [A: int,B: int,C: int] :
( ( pp @ ( aa @ int @ bool @ ( aa @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( zero_zero @ int ) ) @ C ) )
=> ( ( div_mod @ int @ B @ ( aa @ int @ int @ ( times_times @ int @ A ) @ C ) )
= ( plus_plus @ int @ ( aa @ int @ int @ ( times_times @ int @ A ) @ ( div_mod @ int @ ( div_div @ int @ B @ A ) @ C ) ) @ ( div_mod @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(79,axiom,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ C ) )
= ( div_div @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_div__mult__mult2) ).
thf(364,plain,
! [TA: $tType] :
( ( semiring_div @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( C
!= ( zero_zero @ TA ) )
=> ( ( div_div @ TA @ ( aa @ TA @ TA @ ( times_times @ TA @ B ) @ C ) @ ( aa @ TA @ TA @ ( times_times @ TA @ A ) @ C ) )
= ( div_div @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(41,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/sandbox2/benchmark/theBenchmark.p',fact_49_diff__0__right) ).
thf(254,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)],[41]) ).
thf(32,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(227,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(519,plain,
$false,
inference(e,[status(thm)],[181,138,479,518,468,333,249,481,352,408,449,379,269,217,276,440,511,142,340,320,257,389,184,157,416,228,289,448,443,376,238,514,353,280,411,243,428,312,206,292,452,380,160,392,429,275,260,349,467,252,361,461,224,229,484,403,169,499,471,339,476,489,212,343,266,508,298,425,166,148,279,402,286,413,187,406,172,219,419,318,303,367,240,330,306,299,505,431,473,516,458,194,145,295,327,263,370,502,359,336,154,446,175,386,203,218,517,319,139,246,272,383,214,151,315,422,373,136,437,474,400,283,395,464,178,163,200,486,309,222,496,364,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM069_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n005.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 03:15:09 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.87/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.06 % [INFO] Parsing done (210ms).
% 1.56/1.06 % [INFO] Running in sequential loop mode.
% 2.25/1.26 % [INFO] eprover registered as external prover.
% 2.25/1.26 % [INFO] cvc4 registered as external prover.
% 2.25/1.26 % [INFO] Scanning for conjecture ...
% 3.05/1.47 % [INFO] Found a conjecture and 133 axioms. Running axiom selection ...
% 3.30/1.56 % [INFO] Axiom selection finished. Selected 133 axioms (removed 0 axioms).
% 3.60/1.64 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.60/1.66 % [INFO] Type checking passed.
% 3.60/1.66 % [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 ...
% 5.67/2.23 % [INFO] [Domain constraints] Detected constraint on bool
% 5.67/2.23 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 5.67/2.30 % [INFO] [Domain constraints] Detected constraint on bool
% 5.67/2.30 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 47.56/34.43 % External prover 'e' found a proof!
% 47.56/34.44 % [INFO] Killing All external provers ...
% 47.56/34.44 % Time passed: 33914ms (effective reasoning time: 33368ms)
% 47.56/34.44 % 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)>
% 47.56/34.44 % Axioms used in derivation (133): fact_84_iprod__left__diff__distrib, arity_Int_Oint___Groups_Omonoid__add, fact_55_add__diff__cancel, fact_3_mod__div__trivial, fact_64_mod__mult__right__eq, arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add, fact_4_mod__mult__self2, help_COMBS_1_1_U, fact_89_div__mult__mult1, arity_Int_Oint___Groups_Oone, fact_51_mult_Ocomm__neutral, fact_20_diff__self, fact_97_div__neg__pos__less0, arity_Int_Oint___Groups_Oordered__comm__monoid__add, fact_70_mod__add__right__eq, fact_36_one__reorient, fact_87_add__pos__pos, help_fconj_3_1_U, fact_28_zmod__zero, fact_81_zdiff__zmod__left, fact_16_atom_Osimps_I1_J, fact_35_ab__semigroup__add__class_Oadd__ac_I1_J, fact_67_zmod__simps_I2_J, fact_18_add__less__cancel__left, arity_Int_Oint___Groups_Ocomm__monoid__add, fact_58_mod__mult__cong, fact_60_mod__mult__mult2, fact_10_zero__less__double__add__iff__zero__less__single__add, fact_62_mod__mult__eq, fact_29_zdiv__zero, fact_74_mem__def, help_fTrue_1_1_T, fact_76_mod__diff__left__eq, arity_Int_Oint___Rings_Oring, fact_66_zmod__simps_I1_J, fact_93_div__self, fact_1_divisor_Osimps_I1_J, fact_69_mod__add__left__eq, fact_78_div__by__1, fact_46_add__strict__right__mono, fact_47_right__minus__eq, fact_25_mod__add__self1, fact_79_zmod__simps_I3_J, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_96_pos__mod__bound, help_fTrue_1_1_U, fact_15_mod__mod__trivial, fact_30_zero__reorient, fact_52_mult__1__right, fact_71_mod__diff__cong, fact_63_mod__mult__left__eq, help_fFalse_1_1_T, fact_83_iprod__left__add__distrib, fact_94_scale1, fact_37_diff__eq__diff__eq, fact_27_zmod__self, help_COMBB_1_1_U, fact_21_mod__self, fact_91_div__mult__self1__is__id, fact_13_add__right__cancel, fact_50_diff__eq__diff__less, fact_9_mod__mult__self1__is__0, fact_73_ext, help_fconj_2_1_U, fact_38_add_Ocomm__neutral, fact_17_double__zero__sym, arity_Int_Oint___Divides_Oring__div, fact_57_mod__by__0, fact_45_add__strict__left__mono, fact_34_add__left__imp__eq, arity_Int_Oint___Groups_Omonoid__mult, fact_6_mod__by__1, fact_53_mult__1, fact_49_diff__0__right, fact_68_mod__add__eq, fact_80_zmod__zmult1__eq, fact_88_less__iff__diff__less__0, fact_40_add__0, help_fequal_1_1_T, fact_54_mult__1__left, fact_85_atom_Osimps_I10_J, fact_48_eq__iff__diff__eq__0, fact_12_zmod__zmult2__eq, help_COMBK_1_1_U, fact_26_mod__add__self2, arity_Int_Oint___Groups_Ogroup__add, fact_11_double__add__less__zero__iff__single__add__less__zero, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_65_mod__add__cong, help_COMBC_1_1_U, help_fequal_2_1_T, fact_5_mod__mult__self1, arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, help_fconj_1_1_U, fact_75_Collect__def, fact_41_add__0__left, fact_43_add__less__imp__less__right, fact_24_div__0, help_fFalse_1_1_U, fact_0_norm, arity_Int_Oint___Groups_Oab__semigroup__add, arity_Int_Oint___Groups_Oordered__ab__group__add, fact_31_ab__semigroup__mult__class_Omult__ac_I1_J, fact_77_mod__diff__right__eq, fact_39_add__0__right, fact_90_div__mult__mult2, help_pp_1_1_U, fact_14_add__left__cancel, fact_2_iprod__assoc, fact_19_add__less__cancel__right, fact_86_add__neg__neg, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_7_div__mult__mult1__if, fact_44_add__strict__mono, fact_8_mod__mult__self2__is__0, fact_23_div__by__0, arity_Int_Oint___Divides_Osemiring__div, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_59_zmod__simps_I4_J, fact_72_mod__diff__eq, fact_61_mod__mult__mult1, fact_33_add__imp__eq, arity_Int_Oint___Groups_Ozero, fact_42_add__less__imp__less__left, fact_22_mod__0, help_pp_2_1_U, fact_82_zdiff__zmod__right, fact_56_diff__add__cancel, fact_32_add__right__imp__eq, fact_95_neg__mod__bound, help_fEx_1_1_U, fact_92_div__mult__self2__is__id, arity_Int_Oint___Groups_Ocomm__monoid__mult
% 47.56/34.44 % No. of inferences in proof: 270
% 47.56/34.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 33914 ms resp. 33368 ms w/o parsing
% 48.30/34.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 48.30/34.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------