TSTP Solution File: ITP104^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP104^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:51 EDT 2024
% Result : Theorem 16.14s 4.51s
% Output : Refutation 16.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 303
% Syntax : Number of formulae : 544 ( 166 unt; 64 typ; 0 def)
% Number of atoms : 1424 ( 471 equ; 12 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 4381 ( 192 ~; 36 |; 88 &;3325 @)
% ( 0 <=>; 740 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 18 ( 17 usr)
% Number of type conns : 197 ( 197 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 48 usr; 7 con; 0-3 aty)
% Number of variables : 1476 ( 104 ^1280 !; 92 ?;1476 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_l2071841302list_a_type,type,
list_l2071841302list_a: $tType ).
thf(list_list_list_nat_type,type,
list_list_list_nat: $tType ).
thf(list_list_list_a_type,type,
list_list_list_a: $tType ).
thf(set_list_list_a_type,type,
set_list_list_a: $tType ).
thf(list_set_list_a_type,type,
list_set_list_a: $tType ).
thf(list_list_nat_type,type,
list_list_nat: $tType ).
thf(set_list_nat_type,type,
set_list_nat: $tType ).
thf(list_set_nat_type,type,
list_set_nat: $tType ).
thf(list_list_a_type,type,
list_list_a: $tType ).
thf(set_list_a_type,type,
set_list_a: $tType ).
thf(list_set_a_type,type,
list_set_a: $tType ).
thf(list_nat_type,type,
list_nat: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(list_a_type,type,
list_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(f_image_list_a_type,type,
f_image_list_a: list_list_a > set_nat > set_list_a ).
thf(f_image_a_type,type,
f_image_a: list_a > set_nat > set_a ).
thf(list_asc_set_list_a_type,type,
list_asc_set_list_a: list_set_list_a > $o ).
thf(list_asc_set_a_type,type,
list_asc_set_a: list_set_a > $o ).
thf(list_desc_set_list_a_type,type,
list_desc_set_list_a: list_set_list_a > $o ).
thf(list_desc_set_a_type,type,
list_desc_set_a: list_set_a > $o ).
thf(listSl703198822list_a_type,type,
listSl703198822list_a: list_list_a > nat > list_list_list_a ).
thf(listSl1174287072ice2_a_type,type,
listSl1174287072ice2_a: list_a > nat > list_list_a ).
thf(listSl162220270list_a_type,type,
listSl162220270list_a: list_list_a > nat > list_list_list_a ).
thf(listSl97544552lice_a_type,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(listSl856612276list_a_type,type,
listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
thf(listSl1495374126_aux_a_type,type,
listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
thf(butlast_list_a_type,type,
butlast_list_a: list_list_a > list_list_a ).
thf(butlast_a_type,type,
butlast_a: list_a > list_a ).
thf(distinct_list_a_type,type,
distinct_list_a: list_list_a > $o ).
thf(distinct_a_type,type,
distinct_a: list_a > $o ).
thf(set_list_a2_type,type,
set_list_a2: list_list_a > set_list_a ).
thf(set_a2_type,type,
set_a2: list_a > set_a ).
thf(list_ex_list_a_type,type,
list_ex_list_a: ( list_a > $o ) > list_list_a > $o ).
thf(list_ex_a_type,type,
list_ex_a: ( a > $o ) > list_a > $o ).
thf(list_update_list_a_type,type,
list_update_list_a: list_list_a > nat > list_a > list_list_a ).
thf(list_update_a_type,type,
list_update_a: list_a > nat > a > list_a ).
thf(nth_list_list_a_type,type,
nth_list_list_a: list_list_list_a > nat > list_list_a ).
thf(nth_list_a_type,type,
nth_list_a: list_list_a > nat > list_a ).
thf(nth_set_list_a_type,type,
nth_set_list_a: list_set_list_a > nat > set_list_a ).
thf(nth_set_a_type,type,
nth_set_a: list_set_a > nat > set_a ).
thf(nth_a_type,type,
nth_a: list_a > nat > a ).
thf(size_s575106428list_a_type,type,
size_s575106428list_a: list_list_list_a > nat ).
thf(size_s1427607542list_a_type,type,
size_s1427607542list_a: list_list_a > nat ).
thf(size_s1635937238list_a_type,type,
size_s1635937238list_a: list_set_list_a > nat ).
thf(size_size_list_set_a_type,type,
size_size_list_set_a: list_set_a > nat ).
thf(size_size_list_a_type,type,
size_size_list_a: list_a > nat ).
thf(ord_less_nat_type,type,
ord_less_nat: nat > nat > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_le1301786372list_a_type,type,
ord_le1301786372list_a: set_list_a > set_list_a > $o ).
thf(ord_less_eq_set_a_type,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(top_top_set_nat_type,type,
top_top_set_nat: set_nat ).
thf(divide_divide_nat_type,type,
divide_divide_nat: nat > nat > nat ).
thf(collect_list_a_type,type,
collect_list_a: ( list_a > $o ) > set_list_a ).
thf(collect_nat_type,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(member_list_a_type,type,
member_list_a: list_a > set_list_a > $o ).
thf(member_nat_type,type,
member_nat: nat > set_nat > $o ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(k_type,type,
k: nat ).
thf(m_type,type,
m: nat ).
thf(xs_type,type,
xs: list_a ).
thf(114,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_le__trans) ).
thf(645,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(236,axiom,
! [A: nat,B: list_list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ ( butlast_list_a @ B ) ) )
=> ( ( nth_list_a @ ( butlast_list_a @ B ) @ A )
= ( nth_list_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_nth__butlast) ).
thf(1105,plain,
! [A: nat,B: list_list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ ( butlast_list_a @ B ) ) )
=> ( ( nth_list_a @ ( butlast_list_a @ B ) @ A )
= ( nth_list_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(183,axiom,
! [A: a,B: list_a,C: nat,D: set_nat] :
( ( A
= ( nth_a @ B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( member_a @ A @ ( f_image_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_f__image__eqI) ).
thf(909,plain,
! [A: a,B: list_a,C: nat,D: set_nat] :
( ( A
= ( nth_a @ B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( member_a @ A @ ( f_image_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(78,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_ord__eq__le__subst) ).
thf(518,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_less__trans) ).
thf(481,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(29,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_dual__order_Ostrict__iff__order) ).
thf(352,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(200,axiom,
! [A: a,B: list_a] :
( ( member_a @ A @ ( set_a2 @ B ) )
= ( ? [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
& ( ( nth_a @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_in__set__conv__nth) ).
thf(977,plain,
! [A: a,B: list_a] :
( ( member_a @ A @ ( set_a2 @ B ) )
= ( ? [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
& ( ( nth_a @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_less__not__sym) ).
thf(730,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(225,axiom,
! [A: nat,B: list_a,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ ( size_size_list_a @ B ) @ C ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ B @ C ) @ A )
= ( nth_list_a @ ( listSl97544552lice_a @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_list__slice2__list__slice__nth) ).
thf(1068,plain,
! [A: nat,B: list_a,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ ( size_size_list_a @ B ) @ C ) )
=> ( ( nth_list_a @ ( listSl1174287072ice2_a @ B @ C ) @ A )
= ( nth_list_a @ ( listSl97544552lice_a @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(204,axiom,
! [A: a,B: list_a,C: nat] :
( ( A
= ( nth_a @ B @ C ) )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( member_a @ A @ ( f_image_a @ B @ top_top_set_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_f__range__eqI) ).
thf(994,plain,
! [A: a,B: list_a,C: nat] :
( ( A
= ( nth_a @ B @ C ) )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( member_a @ A @ ( f_image_a @ B @ top_top_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(227,axiom,
! [A: set_nat,B: list_list_a,C: set_list_a] :
( ! [D: nat] :
( ( ( member_nat @ D @ A )
& ( ord_less_nat @ D @ ( size_s1427607542list_a @ B ) ) )
=> ( member_list_a @ ( nth_list_a @ B @ D ) @ C ) )
=> ( ord_le1301786372list_a @ ( f_image_list_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_f__image__subsetI) ).
thf(1073,plain,
! [A: set_nat,B: list_list_a,C: set_list_a] :
( ! [D: nat] :
( ( ( member_nat @ D @ A )
& ( ord_less_nat @ D @ ( size_s1427607542list_a @ B ) ) )
=> ( member_list_a @ ( nth_list_a @ B @ D ) @ C ) )
=> ( ord_le1301786372list_a @ ( f_image_list_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(174,axiom,
! [A: list_a,B: a] :
( ( distinct_a @ A )
=> ( ( member_a @ B @ ( set_a2 @ A ) )
=> ? [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
& ( ( nth_a @ A @ C )
= B )
& ! [D: nat] :
( ( ( ord_less_nat @ D @ ( size_size_list_a @ A ) )
& ( ( nth_a @ A @ D )
= B ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_distinct__Ex1) ).
thf(873,plain,
! [A: list_a,B: a] :
( ( distinct_a @ A )
=> ( ( member_a @ B @ ( set_a2 @ A ) )
=> ? [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
& ( ( nth_a @ A @ C )
= B )
& ! [D: nat] :
( ( ( ord_less_nat @ D @ ( size_size_list_a @ A ) )
& ( ( nth_a @ A @ D )
= B ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(37,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_minf_I5_J) ).
thf(379,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(76,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_less__induct) ).
thf(511,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(104,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_order__class_Oorder_Oeq__iff) ).
thf(614,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(171,axiom,
! [A: set_nat,B: list_a,C: set_a] :
( ! [D: nat] :
( ( ( member_nat @ D @ A )
& ( ord_less_nat @ D @ ( size_size_list_a @ B ) ) )
=> ( member_a @ ( nth_a @ B @ D ) @ C ) )
=> ( ord_less_eq_set_a @ ( f_image_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_f__image__subsetI) ).
thf(861,plain,
! [A: set_nat,B: list_a,C: set_a] :
( ! [D: nat] :
( ( ( member_nat @ D @ A )
& ( ord_less_nat @ D @ ( size_size_list_a @ B ) ) )
=> ( member_a @ ( nth_a @ B @ D ) @ C ) )
=> ( ord_less_eq_set_a @ ( f_image_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_less__asym) ).
thf(582,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_le__imp__less__or__eq) ).
thf(762,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(39,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_pinf_I6_J) ).
thf(384,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(87,axiom,
! [A: nat,B: nat,C: list_a,D: a,E: a] :
( ( A != B )
=> ( ( list_update_a @ ( list_update_a @ C @ A @ D ) @ B @ E )
= ( list_update_a @ ( list_update_a @ C @ B @ E ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_list__update__swap) ).
thf(550,plain,
! [A: nat,B: nat,C: list_a,D: a,E: a] :
( ( A != B )
=> ( ( list_update_a @ ( list_update_a @ C @ A @ D ) @ B @ E )
= ( list_update_a @ ( list_update_a @ C @ B @ E ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(136,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_minf_I7_J) ).
thf(715,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(27,axiom,
! [A: nat,B: nat > $o,C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ A @ D )
=> ( B @ D ) )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ D @ A )
=> ( ! [E: nat] :
( ( ord_less_nat @ D @ E )
=> ( B @ E ) )
=> ( B @ D ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_nat__descend__induct) ).
thf(340,plain,
! [A: nat,B: nat > $o,C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ A @ D )
=> ( B @ D ) )
=> ( ! [D: nat] :
( ( ord_less_eq_nat @ D @ A )
=> ( ! [E: nat] :
( ( ord_less_nat @ D @ E )
=> ( B @ E ) )
=> ( B @ D ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(180,axiom,
! [A: nat,B: list_list_a,C: list_a > $o] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ! [D: list_a] :
( ( member_list_a @ D @ ( set_list_a2 @ B ) )
=> ( C @ D ) )
=> ( C @ ( nth_list_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_list__ball__nth) ).
thf(898,plain,
! [A: nat,B: list_list_a,C: list_a > $o] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ! [D: list_a] :
( ( member_list_a @ D @ ( set_list_a2 @ B ) )
=> ( C @ D ) )
=> ( C @ ( nth_list_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_le__antisym) ).
thf(288,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(116,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_dual__order_Oirrefl) ).
thf(651,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(169,axiom,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: nat] :
( ( ord_less_eq_nat @ A @ D )
& ( ord_less_eq_nat @ D @ B )
& ! [E: nat] :
( ( ( ord_less_eq_nat @ A @ E )
& ( ord_less_nat @ E @ D ) )
=> ( C @ E ) )
& ! [E: nat] :
( ! [F: nat] :
( ( ( ord_less_eq_nat @ A @ F )
& ( ord_less_nat @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_complete__interval) ).
thf(829,plain,
! [A: nat,B: nat,C: nat > $o] :
( ( ord_less_nat @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: nat] :
( ( ord_less_eq_nat @ A @ D )
& ( ord_less_eq_nat @ D @ B )
& ! [E: nat] :
( ( ( ord_less_eq_nat @ A @ E )
& ( ord_less_nat @ E @ D ) )
=> ( C @ E ) )
& ! [E: nat] :
( ! [F: nat] :
( ( ( ord_less_eq_nat @ A @ F )
& ( ord_less_nat @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(233,axiom,
! [A: list_a,B: list_list_a,C: set_nat] :
( ( member_list_a @ A @ ( f_image_list_a @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( nth_list_a @ B @ D ) )
=> ( ( member_nat @ D @ C )
=> ~ ( ord_less_nat @ D @ ( size_s1427607542list_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_f__imageE) ).
thf(1095,plain,
! [A: list_a,B: list_list_a,C: set_nat] :
( ( member_list_a @ A @ ( f_image_list_a @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( nth_list_a @ B @ D ) )
=> ( ( member_nat @ D @ C )
=> ~ ( ord_less_nat @ D @ ( size_s1427607542list_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(199,axiom,
! [A: list_list_a,B: nat,C: nat] :
( ( distinct_list_a @ A )
=> ( ( ord_less_nat @ B @ ( size_s1427607542list_a @ A ) )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( ( ( nth_list_a @ A @ B )
= ( nth_list_a @ A @ C ) )
= ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_nth__eq__iff__index__eq) ).
thf(973,plain,
! [A: list_list_a,B: nat,C: nat] :
( ( distinct_list_a @ A )
=> ( ( ord_less_nat @ B @ ( size_s1427607542list_a @ A ) )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( ( ( nth_list_a @ A @ B )
= ( nth_list_a @ A @ C ) )
= ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(176,axiom,
! [A: list_a,B: a > $o,C: a] :
( ! [D: nat] :
( ( ord_less_nat @ D @ ( size_size_list_a @ A ) )
=> ( B @ ( nth_a @ A @ D ) ) )
=> ( ( member_a @ C @ ( set_a2 @ A ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_all__nth__imp__all__set) ).
thf(885,plain,
! [A: list_a,B: a > $o,C: a] :
( ! [D: nat] :
( ( ord_less_nat @ D @ ( size_size_list_a @ A ) )
=> ( B @ ( nth_a @ A @ D ) ) )
=> ( ( member_a @ C @ ( set_a2 @ A ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(217,axiom,
( ( (=) @ list_list_a )
= ( ^ [A: list_list_a,B: list_list_a] :
( ( ( size_s1427607542list_a @ A )
= ( size_s1427607542list_a @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( ( nth_list_a @ A @ C )
= ( nth_list_a @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_list__eq__iff__nth__eq) ).
thf(1046,plain,
( ( (=) @ list_list_a )
= ( ^ [A: list_list_a,B: list_list_a] :
( ( ( size_s1427607542list_a @ A )
= ( size_s1427607542list_a @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( ( nth_list_a @ A @ C )
= ( nth_list_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(220,axiom,
! [A: nat,B: list_a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ ( butlast_a @ B ) ) )
=> ( ( nth_a @ ( butlast_a @ B ) @ A )
= ( nth_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_nth__butlast) ).
thf(1055,plain,
! [A: nat,B: list_a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ ( butlast_a @ B ) ) )
=> ( ( nth_a @ ( butlast_a @ B ) @ A )
= ( nth_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ( ord_less_nat @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_not__less__iff__gr__or__eq) ).
thf(619,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ( ord_less_nat @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_order__class_Oorder_Oantisym) ).
thf(357,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(222,axiom,
! [A: nat,B: list_list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ ( nth_list_a @ B @ A ) @ ( set_list_a2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_nth__mem) ).
thf(1059,plain,
! [A: nat,B: list_list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ ( nth_list_a @ B @ A ) @ ( set_list_a2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(181,axiom,
! [A: nat] :
? [B: list_a] :
( ( size_size_list_a @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Ex__list__of__length) ).
thf(902,plain,
! [A: nat] :
? [B: list_a] :
( ( size_size_list_a @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(175,axiom,
! [A: list_a,B: list_list_a,C: nat] :
( ( A
= ( nth_list_a @ B @ C ) )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ A @ ( f_image_list_a @ B @ top_top_set_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_f__range__eqI) ).
thf(881,plain,
! [A: list_a,B: list_list_a,C: nat] :
( ( A
= ( nth_list_a @ B @ C ) )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ A @ ( f_image_list_a @ B @ top_top_set_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(24,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_less__irrefl__nat) ).
thf(316,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(234,axiom,
! [A: list_list_a,B: set_nat,C: set_list_a] :
( ( ord_le1301786372list_a @ ( f_image_list_a @ A @ B ) @ C )
= ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ D @ ( size_s1427607542list_a @ A ) )
=> ( member_list_a @ ( nth_list_a @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_f__image__subset__iff) ).
thf(1100,plain,
! [A: list_list_a,B: set_nat,C: set_list_a] :
( ( ord_le1301786372list_a @ ( f_image_list_a @ A @ B ) @ C )
= ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ D @ ( size_s1427607542list_a @ A ) )
=> ( member_list_a @ ( nth_list_a @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(198,axiom,
! [A: nat,B: list_a,C: nat] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( ( set_a2 @ ( list_update_a @ ( list_update_a @ B @ A @ ( nth_a @ B @ C ) ) @ C @ ( nth_a @ B @ A ) ) )
= ( set_a2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_set__swap) ).
thf(969,plain,
! [A: nat,B: list_a,C: nat] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( ( set_a2 @ ( list_update_a @ ( list_update_a @ B @ A @ ( nth_a @ B @ C ) ) @ C @ ( nth_a @ B @ A ) ) )
= ( set_a2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(101,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( A != C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_le__greater__neq__conv) ).
thf(606,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( A != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(149,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_less__irrefl) ).
thf(756,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(157,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_neqE) ).
thf(789,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(210,axiom,
! [A: a,B: list_a,C: set_nat] :
( ( member_a @ A @ ( f_image_a @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( ord_less_nat @ D @ ( size_size_list_a @ B ) )
& ( A
= ( nth_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_f__image__iff) ).
thf(1020,plain,
! [A: a,B: list_a,C: set_nat] :
( ( member_a @ A @ ( f_image_a @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( ord_less_nat @ D @ ( size_size_list_a @ B ) )
& ( A
= ( nth_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(162,axiom,
! [A: nat,B: nat,C: list_list_a,D: list_a,E: list_a] :
( ( A != B )
=> ( ( list_update_list_a @ ( list_update_list_a @ C @ A @ D ) @ B @ E )
= ( list_update_list_a @ ( list_update_list_a @ C @ B @ E ) @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_list__update__swap) ).
thf(806,plain,
! [A: nat,B: nat,C: list_list_a,D: list_a,E: list_a] :
( ( A != B )
=> ( ( list_update_list_a @ ( list_update_list_a @ C @ A @ D ) @ B @ E )
= ( list_update_list_a @ ( list_update_list_a @ C @ B @ E ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(182,axiom,
! [A: nat,B: list_a,C: a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ( list_update_a @ B @ A @ C )
= B )
= ( ( nth_a @ B @ A )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_list__update__same__conv) ).
thf(905,plain,
! [A: nat,B: list_a,C: a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ( list_update_a @ B @ A @ C )
= B )
= ( ( nth_a @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(111,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_eq__iff) ).
thf(634,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(58,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_order_Oorder__iff__strict) ).
thf(453,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(240,axiom,
! [A: list_a,B: list_list_a,C: set_nat] :
( ( member_list_a @ A @ ( f_image_list_a @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( ord_less_nat @ D @ ( size_s1427607542list_a @ B ) )
& ( A
= ( nth_list_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_f__image__iff) ).
thf(1119,plain,
! [A: list_a,B: list_list_a,C: set_nat] :
( ( member_list_a @ A @ ( f_image_list_a @ B @ C ) )
= ( ? [D: nat] :
( ( member_nat @ D @ C )
& ( ord_less_nat @ D @ ( size_s1427607542list_a @ B ) )
& ( A
= ( nth_list_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(205,axiom,
! [A: nat,B: set_nat,C: list_list_a,D: list_a] :
( ( member_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( size_s1427607542list_a @ C ) )
=> ( ( D
= ( nth_list_a @ C @ A ) )
=> ( member_list_a @ D @ ( f_image_list_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_rev__f__imageI) ).
thf(998,plain,
! [A: nat,B: set_nat,C: list_list_a,D: list_a] :
( ( member_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( size_s1427607542list_a @ C ) )
=> ( ( D
= ( nth_list_a @ C @ A ) )
=> ( member_list_a @ D @ ( f_image_list_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(202,axiom,
! [A: nat,B: list_list_a,C: list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( nth_list_a @ ( list_update_list_a @ B @ A @ C ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_nth__list__update__eq) ).
thf(988,plain,
! [A: nat,B: list_list_a,C: list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( nth_list_a @ ( list_update_list_a @ B @ A @ C ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(3,axiom,
! [A: list_list_list_a > $o,B: list_list_list_a] :
( ! [C: list_list_list_a] :
( ! [D: list_list_list_a] :
( ( ord_less_nat @ ( size_s575106428list_a @ D ) @ ( size_s575106428list_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_length__induct) ).
thf(243,plain,
! [A: list_list_list_a > $o,B: list_list_list_a] :
( ! [C: list_list_list_a] :
( ! [D: list_list_list_a] :
( ( ord_less_nat @ ( size_s575106428list_a @ D ) @ ( size_s575106428list_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(53,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_dual__order_Ostrict__implies__order) ).
thf(428,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(9,axiom,
( ( (=) @ list_list_list_a )
= ( ^ [A: list_list_list_a,B: list_list_list_a] :
( ( ( size_s575106428list_a @ A )
= ( size_s575106428list_a @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s575106428list_a @ A ) )
=> ( ( nth_list_list_a @ A @ C )
= ( nth_list_list_a @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_list__eq__iff__nth__eq) ).
thf(265,plain,
( ( (=) @ list_list_list_a )
= ( ^ [A: list_list_list_a,B: list_list_list_a] :
( ( ( size_s575106428list_a @ A )
= ( size_s575106428list_a @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s575106428list_a @ A ) )
=> ( ( nth_list_list_a @ A @ C )
= ( nth_list_list_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_minf_I8_J) ).
thf(397,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_antisym__conv1) ).
thf(687,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(18,axiom,
( ( '?' @ nat )
= ( ^ [A: nat > $o] :
? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_exists__least__iff) ).
thf(293,plain,
( ( '?' @ nat )
= ( ^ [A: nat > $o] :
? [B: nat] :
( ( A @ B )
& ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ~ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(194,axiom,
( list_ex_list_a
= ( ^ [A: list_a > $o,B: list_list_a] :
? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
& ( A @ ( nth_list_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_list__ex__length) ).
thf(956,plain,
( list_ex_list_a
= ( ^ [A: list_a > $o,B: list_list_a] :
? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
& ( A @ ( nth_list_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(21,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_nat__less__le) ).
thf(307,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: list_list_list_a,B: list_list_list_a] :
( ( ( size_s575106428list_a @ A )
!= ( size_s575106428list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_size__neq__size__imp__neq) ).
thf(248,plain,
! [A: list_list_list_a,B: list_list_list_a] :
( ( ( size_s575106428list_a @ A )
!= ( size_s575106428list_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(122,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_less__imp__le__nat) ).
thf(678,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(80,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_order_Ostrict__iff__order) ).
thf(529,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_le__cases3) ).
thf(661,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_less__asym_H) ).
thf(810,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_dual__order_Otrans) ).
thf(381,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_antisym__conv3) ).
thf(534,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(179,axiom,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_neq__if__length__neq) ).
thf(894,plain,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(216,axiom,
! [A: a,B: list_a] :
( ( member_a @ A @ ( f_image_a @ B @ top_top_set_nat ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( A
!= ( nth_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_f__rangeE) ).
thf(1042,plain,
! [A: a,B: list_a] :
( ( member_a @ A @ ( f_image_a @ B @ top_top_set_nat ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( A
!= ( nth_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(28,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_dual__order_Ostrict__trans2) ).
thf(349,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_linorder__cases) ).
thf(392,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(20,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_minf_I2_J) ).
thf(297,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(128,axiom,
! [A: nat] :
? [B: nat] : ( ord_less_nat @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_gt__ex) ).
thf(693,plain,
! [A: nat] :
? [B: nat] : ( ord_less_nat @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_leI) ).
thf(275,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(67,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_less__le) ).
thf(484,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(5,axiom,
! [A: list_list_list_a,B: list_list_list_a] :
( ( ( size_s575106428list_a @ A )
!= ( size_s575106428list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_neq__if__length__neq) ).
thf(252,plain,
! [A: list_list_list_a,B: list_list_list_a] :
( ( ( size_s575106428list_a @ A )
!= ( size_s575106428list_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(56,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_pinf_I1_J) ).
thf(435,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(177,axiom,
( list_ex_a
= ( ^ [A: a > $o,B: list_a] :
? [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
& ( A @ ( nth_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_list__ex__length) ).
thf(889,plain,
( list_ex_a
= ( ^ [A: a > $o,B: list_a] :
? [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
& ( A @ ( nth_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(229,axiom,
! [A: list_a,B: a > $o] :
( ( ! [C: a] :
( ( member_a @ C @ ( set_a2 @ A ) )
=> ( B @ C ) ) )
= ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( B @ ( nth_a @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_all__set__conv__all__nth) ).
thf(1079,plain,
! [A: list_a,B: a > $o] :
( ( ! [C: a] :
( ( member_a @ C @ ( set_a2 @ A ) )
=> ( B @ C ) ) )
= ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( B @ ( nth_a @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_le__neq__trans) ).
thf(682,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(134,axiom,
( list_desc_set_a
= ( ^ [A: list_set_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_size_list_set_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_eq_set_a @ ( nth_set_a @ A @ B ) @ ( nth_set_a @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_list__desc__trans) ).
thf(710,plain,
( list_desc_set_a
= ( ^ [A: list_set_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_size_list_set_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_eq_set_a @ ( nth_set_a @ A @ B ) @ ( nth_set_a @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(15,axiom,
! [A: set_list_a] :
( ( collect_list_a
@ ^ [B: list_a] : ( member_list_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Collect__mem__eq) ).
thf(285,plain,
! [A: set_list_a] :
( ( collect_list_a
@ ^ [B: list_a] : ( member_list_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(130,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_minf_I4_J) ).
thf(697,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(193,axiom,
! [A: nat,B: list_a,C: nat,D: a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ( A = C )
=> ( ( nth_a @ ( list_update_a @ B @ A @ D ) @ C )
= D ) )
& ( ( A != C )
=> ( ( nth_a @ ( list_update_a @ B @ A @ D ) @ C )
= ( nth_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_nth__list__update) ).
thf(948,plain,
! [A: nat,B: list_a,C: nat,D: a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ( A = C )
=> ( ( nth_a @ ( list_update_a @ B @ A @ D ) @ C )
= D ) )
& ( ( A != C )
=> ( ( nth_a @ ( list_update_a @ B @ A @ D ) @ C )
= ( nth_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(207,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( size_s1427607542list_a @ A )
= ( size_s1427607542list_a @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( ( nth_list_a @ A @ C )
= ( nth_list_a @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nth__equalityI) ).
thf(1006,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( size_s1427607542list_a @ A )
= ( size_s1427607542list_a @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( ( nth_list_a @ A @ C )
= ( nth_list_a @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(173,axiom,
! [A: nat,B: nat,C: list_list_a,D: list_a] :
( ( A != B )
=> ( ( nth_list_a @ ( list_update_list_a @ C @ A @ D ) @ B )
= ( nth_list_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_nth__list__update__neq) ).
thf(869,plain,
! [A: nat,B: nat,C: list_list_a,D: list_a] :
( ( A != B )
=> ( ( nth_list_a @ ( list_update_list_a @ C @ A @ D ) @ B )
= ( nth_list_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_dual__order_Ostrict__implies__not__eq) ).
thf(499,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(201,axiom,
! [A: list_list_a,B: list_a] :
( ( distinct_list_a @ A )
=> ( ( member_list_a @ B @ ( set_list_a2 @ A ) )
=> ? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
& ( ( nth_list_a @ A @ C )
= B )
& ! [D: nat] :
( ( ( ord_less_nat @ D @ ( size_s1427607542list_a @ A ) )
& ( ( nth_list_a @ A @ D )
= B ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_distinct__Ex1) ).
thf(980,plain,
! [A: list_list_a,B: list_a] :
( ( distinct_list_a @ A )
=> ( ( member_list_a @ B @ ( set_list_a2 @ A ) )
=> ? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
& ( ( nth_list_a @ A @ C )
= B )
& ! [D: nat] :
( ( ( ord_less_nat @ D @ ( size_s1427607542list_a @ A ) )
& ( ( nth_list_a @ A @ D )
= B ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(46,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_less__not__refl) ).
thf(403,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(6,axiom,
! [A: nat] :
? [B: list_list_list_a] :
( ( size_s575106428list_a @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Ex__list__of__length) ).
thf(256,plain,
! [A: nat] :
? [B: list_list_list_a] :
( ( size_s575106428list_a @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(230,axiom,
! [A: nat,B: list_list_a,C: nat,D: list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( ( A = C )
=> ( ( nth_list_a @ ( list_update_list_a @ B @ A @ D ) @ C )
= D ) )
& ( ( A != C )
=> ( ( nth_list_a @ ( list_update_list_a @ B @ A @ D ) @ C )
= ( nth_list_a @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_nth__list__update) ).
thf(1082,plain,
! [A: nat,B: list_list_a,C: nat,D: list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( ( A = C )
=> ( ( nth_list_a @ ( list_update_list_a @ B @ A @ D ) @ C )
= D ) )
& ( ( A != C )
=> ( ( nth_list_a @ ( list_update_list_a @ B @ A @ D ) @ C )
= ( nth_list_a @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_order_Onot__eq__order__implies__strict) ).
thf(488,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__not__refl2) ).
thf(537,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_ord__le__eq__trans) ).
thf(476,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(79,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_less__le__trans) ).
thf(526,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(86,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_mem__Collect__eq) ).
thf(547,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(88,axiom,
! [A: list_list_a,B: nat,C: list_a,D: list_a] :
( ( list_update_list_a @ ( list_update_list_a @ A @ B @ C ) @ B @ D )
= ( list_update_list_a @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_list__update__overwrite) ).
thf(554,plain,
! [A: list_list_a,B: nat,C: list_a,D: list_a] :
( ( list_update_list_a @ ( list_update_list_a @ A @ B @ C ) @ B @ D )
= ( list_update_list_a @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_antisym__conv) ).
thf(753,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(107,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_order__refl) ).
thf(622,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_order__subst2) ).
thf(701,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_ord__eq__less__trans) ).
thf(738,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(117,axiom,
! [A: nat,B: nat,C: $o] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_less__imp__triv) ).
thf(654,plain,
! [A: nat,B: nat,C: $o] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_linear) ).
thf(457,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(138,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_nat__le__linear) ).
thf(721,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(154,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_dual__order_Oeq__iff) ).
thf(779,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(73,axiom,
! [A: nat] :
? [B: list_list_a] :
( ( size_s1427607542list_a @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_Ex__list__of__length) ).
thf(503,plain,
! [A: nat] :
? [B: list_list_a] :
( ( size_s1427607542list_a @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(158,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__neq__implies__less) ).
thf(792,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_order_Ostrict__trans2) ).
thf(360,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(75,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Collect__mem__eq) ).
thf(508,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B )
| ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_less__linear) ).
thf(541,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B )
| ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(118,axiom,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ~ ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_less__le__not__le) ).
thf(657,plain,
( ord_less_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ~ ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(152,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_pinf_I4_J) ).
thf(765,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(226,axiom,
( distinct_list_a
= ( ^ [A: list_list_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1427607542list_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( ( B != C )
=> ( ( nth_list_a @ A @ B )
!= ( nth_list_a @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_distinct__conv__nth) ).
thf(1071,plain,
( distinct_list_a
= ( ^ [A: list_list_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1427607542list_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( ( B != C )
=> ( ( nth_list_a @ A @ B )
!= ( nth_list_a @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(212,axiom,
! [A: list_list_a,B: nat] :
( ( list_update_list_a @ A @ B @ ( nth_list_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_list__update__id) ).
thf(1026,plain,
! [A: list_list_a,B: nat] :
( ( list_update_list_a @ A @ B @ ( nth_list_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(197,axiom,
! [A: nat,B: list_a,C: a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( nth_a @ ( list_update_a @ B @ A @ C ) @ A )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_nth__list__update__eq) ).
thf(965,plain,
! [A: nat,B: list_a,C: a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( nth_a @ ( list_update_a @ B @ A @ C ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(54,axiom,
! [A: list_list_a,B: nat,C: list_a] :
( ( size_s1427607542list_a @ ( list_update_list_a @ A @ B @ C ) )
= ( size_s1427607542list_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_length__list__update) ).
thf(430,plain,
! [A: list_list_a,B: nat,C: list_a] :
( ( size_s1427607542list_a @ ( list_update_list_a @ A @ B @ C ) )
= ( size_s1427607542list_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(235,axiom,
! [A: nat,B: list_a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( member_a @ ( nth_a @ B @ A ) @ ( f_image_a @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_f__rangeI) ).
thf(1103,plain,
! [A: nat,B: list_a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( member_a @ ( nth_a @ B @ A ) @ ( f_image_a @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__imp__neq) ).
thf(745,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(99,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_dual__order_Ostrict__trans) ).
thf(601,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(94,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_order__less__subst1) ).
thf(584,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(142,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_order_Ostrict__implies__not__eq) ).
thf(732,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(145,axiom,
( list_asc_set_list_a
= ( ^ [A: list_set_list_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1635937238list_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_le1301786372list_a @ ( nth_set_list_a @ A @ C ) @ ( nth_set_list_a @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_list__asc__trans) ).
thf(743,plain,
( list_asc_set_list_a
= ( ^ [A: list_set_list_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1635937238list_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_le1301786372list_a @ ( nth_set_list_a @ A @ C ) @ ( nth_set_list_a @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(168,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_neq__iff) ).
thf(826,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(195,axiom,
! [A: list_a,B: set_nat,C: set_a] :
( ( ord_less_eq_set_a @ ( f_image_a @ A @ B ) @ C )
= ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ D @ ( size_size_list_a @ A ) )
=> ( member_a @ ( nth_a @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_f__image__subset__iff) ).
thf(958,plain,
! [A: list_a,B: set_nat,C: set_a] :
( ( ord_less_eq_set_a @ ( f_image_a @ A @ B ) @ C )
= ( ! [D: nat] :
( ( member_nat @ D @ B )
=> ( ( ord_less_nat @ D @ ( size_size_list_a @ A ) )
=> ( member_a @ ( nth_a @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__not__refl3) ).
thf(281,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: list_list_a,B: nat,C: nat] :
( ( size_s575106428list_a @ ( listSl856612276list_a @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_list__slice__aux__length) ).
thf(259,plain,
! [A: list_list_a,B: nat,C: nat] :
( ( size_s575106428list_a @ ( listSl856612276list_a @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_order_Otrans) ).
thf(579,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_dual__order_Oasym) ).
thf(291,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(103,axiom,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Collect__mem__eq) ).
thf(611,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(221,axiom,
ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1058,plain,
ord_less_nat @ m @ ( divide_divide_nat @ ( size_size_list_a @ xs ) @ k ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(232,axiom,
! [A: list_list_a,B: list_a > $o] :
( ( ! [C: list_a] :
( ( member_list_a @ C @ ( set_list_a2 @ A ) )
=> ( B @ C ) ) )
= ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( B @ ( nth_list_a @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_all__set__conv__all__nth) ).
thf(1092,plain,
! [A: list_list_a,B: list_a > $o] :
( ( ! [C: list_a] :
( ( member_list_a @ C @ ( set_list_a2 @ A ) )
=> ( B @ C ) ) )
= ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( B @ ( nth_list_a @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(231,axiom,
( listSl97544552lice_a
= ( ^ [A: list_a,B: nat] : ( listSl1495374126_aux_a @ A @ B @ ( divide_divide_nat @ ( size_size_list_a @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_list__slice__def) ).
thf(1090,plain,
( listSl97544552lice_a
= ( ^ [A: list_a,B: nat] : ( listSl1495374126_aux_a @ A @ B @ ( divide_divide_nat @ ( size_size_list_a @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(57,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_ord__less__eq__subst) ).
thf(445,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(189,axiom,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_size__neq__size__imp__neq) ).
thf(936,plain,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
!= ( size_size_list_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_not__le__imp__less) ).
thf(604,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(47,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( size_s1427607542list_a @ A )
!= ( size_s1427607542list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_neq__if__length__neq) ).
thf(406,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( size_s1427607542list_a @ A )
!= ( size_s1427607542list_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(239,axiom,
( distinct_a
= ( ^ [A: list_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_size_list_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( ( B != C )
=> ( ( nth_a @ A @ B )
!= ( nth_a @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_distinct__conv__nth) ).
thf(1117,plain,
( distinct_a
= ( ^ [A: list_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_size_list_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( ( B != C )
=> ( ( nth_a @ A @ B )
!= ( nth_a @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(208,axiom,
! [A: nat,B: list_list_a,C: nat] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( ( distinct_list_a @ ( list_update_list_a @ ( list_update_list_a @ B @ A @ ( nth_list_a @ B @ C ) ) @ C @ ( nth_list_a @ B @ A ) ) )
= ( distinct_list_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_distinct__swap) ).
thf(1011,plain,
! [A: nat,B: list_list_a,C: nat] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( ( distinct_list_a @ ( list_update_list_a @ ( list_update_list_a @ B @ A @ ( nth_list_a @ B @ C ) ) @ C @ ( nth_list_a @ B @ A ) ) )
= ( distinct_list_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(36,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_dual__order_Orefl) ).
thf(377,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(90,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_ord__eq__less__subst) ).
thf(567,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(105,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_mem__Collect__eq) ).
thf(616,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(98,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_dual__order_Oorder__iff__strict) ).
thf(599,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(218,axiom,
! [A: list_list_a,B: list_a > $o,C: list_a] :
( ! [D: nat] :
( ( ord_less_nat @ D @ ( size_s1427607542list_a @ A ) )
=> ( B @ ( nth_list_a @ A @ D ) ) )
=> ( ( member_list_a @ C @ ( set_list_a2 @ A ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_all__nth__imp__all__set) ).
thf(1048,plain,
! [A: list_list_a,B: list_a > $o,C: list_a] :
( ! [D: nat] :
( ( ord_less_nat @ D @ ( size_s1427607542list_a @ A ) )
=> ( B @ ( nth_list_a @ A @ D ) ) )
=> ( ( member_list_a @ C @ ( set_list_a2 @ A ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(143,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_pinf_I8_J) ).
thf(736,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_dual__order_Oantisym) ).
thf(631,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(170,axiom,
! [A: nat,B: nat > list_a > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: list_a] : ( B @ C @ D ) ) )
= ( ? [C: list_list_a] :
( ( ( size_s1427607542list_a @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_list_a @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Skolem__list__nth) ).
thf(858,plain,
! [A: nat,B: nat > list_a > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: list_a] : ( B @ C @ D ) ) )
= ( ? [C: list_list_a] :
( ( ( size_s1427607542list_a @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_list_a @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(165,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_le__eq__less__or__eq) ).
thf(816,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(213,axiom,
! [A: list_a,B: list_list_a,C: nat,D: set_nat] :
( ( A
= ( nth_list_a @ B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ A @ ( f_image_list_a @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_f__image__eqI) ).
thf(1029,plain,
! [A: list_a,B: list_list_a,C: nat,D: set_nat] :
( ( A
= ( nth_list_a @ B @ C ) )
=> ( ( member_nat @ C @ D )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ A @ ( f_image_list_a @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(153,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_minf_I1_J) ).
thf(769,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(191,axiom,
! [A: list_a,B: list_list_a] :
( ( member_list_a @ A @ ( set_list_a2 @ B ) )
= ( ? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
& ( ( nth_list_a @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_in__set__conv__nth) ).
thf(943,plain,
! [A: list_a,B: list_list_a] :
( ( member_list_a @ A @ ( set_list_a2 @ B ) )
= ( ? [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
& ( ( nth_list_a @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(62,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_ord__le__eq__subst) ).
thf(462,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(188,axiom,
! [A: list_a,B: list_list_a] :
( ( member_list_a @ A @ ( f_image_list_a @ B @ top_top_set_nat ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( A
!= ( nth_list_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_f__rangeE) ).
thf(932,plain,
! [A: list_a,B: list_list_a] :
( ( member_list_a @ A @ ( f_image_list_a @ B @ top_top_set_nat ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( A
!= ( nth_list_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(223,axiom,
! [A: list_a,B: nat,C: nat] :
( ( distinct_a @ A )
=> ( ( ord_less_nat @ B @ ( size_size_list_a @ A ) )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( ( ( nth_a @ A @ B )
= ( nth_a @ A @ C ) )
= ( B = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_nth__eq__iff__index__eq) ).
thf(1061,plain,
! [A: list_a,B: nat,C: nat] :
( ( distinct_a @ A )
=> ( ( ord_less_nat @ B @ ( size_size_list_a @ A ) )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( ( ( nth_a @ A @ B )
= ( nth_a @ A @ C ) )
= ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(125,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_div__le__dividend) ).
thf(685,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(45,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_order__le__less__subst1) ).
thf(399,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_leD) ).
thf(455,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(209,axiom,
! [A: a,B: list_a,C: set_nat] :
( ( member_a @ A @ ( f_image_a @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( nth_a @ B @ D ) )
=> ( ( member_nat @ D @ C )
=> ~ ( ord_less_nat @ D @ ( size_size_list_a @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_f__imageE) ).
thf(1015,plain,
! [A: a,B: list_a,C: set_nat] :
( ( member_a @ A @ ( f_image_a @ B @ C ) )
=> ~ ! [D: nat] :
( ( A
= ( nth_a @ B @ D ) )
=> ( ( member_nat @ D @ C )
=> ~ ( ord_less_nat @ D @ ( size_size_list_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(102,axiom,
! [A: nat,B: list_list_a,C: list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ C @ ( set_list_a2 @ ( list_update_list_a @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_set__update__memI) ).
thf(608,plain,
! [A: nat,B: list_list_a,C: list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ C @ ( set_list_a2 @ ( list_update_list_a @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(238,axiom,
! [A: list_a,B: nat,C: a] :
( ( ord_less_eq_nat @ ( size_size_list_a @ A ) @ B )
=> ( ( list_update_a @ A @ B @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_list__update__beyond) ).
thf(1113,plain,
! [A: list_a,B: nat,C: a] :
( ( ord_less_eq_nat @ ( size_size_list_a @ A ) @ B )
=> ( ( list_update_a @ A @ B @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(10,axiom,
! [A: list_list_list_a,B: list_list_list_a] :
( ( ( size_s575106428list_a @ A )
= ( size_s575106428list_a @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s575106428list_a @ A ) )
=> ( ( nth_list_list_a @ A @ C )
= ( nth_list_list_a @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_nth__equalityI) ).
thf(267,plain,
! [A: list_list_list_a,B: list_list_list_a] :
( ( ( size_s575106428list_a @ A )
= ( size_s575106428list_a @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s575106428list_a @ A ) )
=> ( ( nth_list_list_a @ A @ C )
= ( nth_list_list_a @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
= k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(241,plain,
( ( size_size_list_a @ ( nth_list_a @ ( listSl1174287072ice2_a @ xs @ k ) @ m ) )
!= k ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(186,axiom,
! [A: list_a,B: set_nat] :
( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( member_nat @ C @ B ) )
=> ( ( f_image_a @ A @ B )
= ( set_a2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_f__image__eq__set) ).
thf(922,plain,
! [A: list_a,B: set_nat] :
( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( member_nat @ C @ B ) )
=> ( ( f_image_a @ A @ B )
= ( set_a2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(112,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_pinf_I3_J) ).
thf(636,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(129,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_eq_nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_minf_I6_J) ).
thf(695,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_eq_nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_nat__neq__iff) ).
thf(473,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(214,axiom,
! [A: nat,B: nat > a > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: a] : ( B @ C @ D ) ) )
= ( ? [C: list_a] :
( ( ( size_size_list_a @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_a @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Skolem__list__nth) ).
thf(1034,plain,
! [A: nat,B: nat > a > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: a] : ( B @ C @ D ) ) )
= ( ? [C: list_a] :
( ( ( size_size_list_a @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_a @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(121,axiom,
! [A: list_a,B: nat] :
( ( list_update_a @ A @ B @ ( nth_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_list__update__id) ).
thf(675,plain,
! [A: list_a,B: nat] :
( ( list_update_a @ A @ B @ ( nth_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_le__less__linear) ).
thf(426,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(81,axiom,
! [A: nat,B: list_list_a,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ ( size_s1427607542list_a @ B ) @ C ) )
=> ( ( size_s1427607542list_a @ ( nth_list_list_a @ ( listSl162220270list_a @ B @ C ) @ A ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_list__slice__nth__length) ).
thf(531,plain,
! [A: nat,B: list_list_a,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ ( size_s1427607542list_a @ B ) @ C ) )
=> ( ( size_s1427607542list_a @ ( nth_list_list_a @ ( listSl162220270list_a @ B @ C ) @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(187,axiom,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( ( nth_a @ A @ C )
= ( nth_a @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_nth__equalityI) ).
thf(927,plain,
! [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
=> ( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( ( nth_a @ A @ C )
= ( nth_a @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(115,axiom,
! [A: list_a,B: nat,C: nat] :
( ( size_s1427607542list_a @ ( listSl1495374126_aux_a @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_list__slice__aux__length) ).
thf(648,plain,
! [A: list_a,B: nat,C: nat] :
( ( size_s1427607542list_a @ ( listSl1495374126_aux_a @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(164,axiom,
! [A: list_list_a,B: list_list_a] :
( ( ( size_s1427607542list_a @ A )
!= ( size_s1427607542list_a @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_size__neq__size__imp__neq) ).
thf(812,plain,
! [A: list_list_a,B: list_list_a] :
( ( ( size_s1427607542list_a @ A )
!= ( size_s1427607542list_a @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(147,axiom,
! [A: list_list_a,B: nat,C: list_a] :
( ( ord_less_eq_nat @ ( size_s1427607542list_a @ A ) @ B )
=> ( ( list_update_list_a @ A @ B @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_list__update__beyond) ).
thf(749,plain,
! [A: list_list_a,B: nat,C: list_a] :
( ( ord_less_eq_nat @ ( size_s1427607542list_a @ A ) @ B )
=> ( ( list_update_list_a @ A @ B @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(77,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_pinf_I7_J) ).
thf(516,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(167,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_dual__order_Ostrict__trans1) ).
thf(823,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(159,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Nat_Oex__has__greatest__nat) ).
thf(795,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(123,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_less__imp__le) ).
thf(680,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(127,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_antisym) ).
thf(690,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_ord__eq__le__trans) ).
thf(640,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(19,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B != C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_ge__less__neq__conv) ).
thf(295,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ( B != C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(132,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_div__le__mono) ).
thf(705,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(49,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_less__mono__imp__le__mono) ).
thf(414,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(135,axiom,
! [A: list_a,B: nat,C: a,D: a] :
( ( list_update_a @ ( list_update_a @ A @ B @ C ) @ B @ D )
= ( list_update_a @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_list__update__overwrite) ).
thf(712,plain,
! [A: list_a,B: nat,C: a,D: a] :
( ( list_update_a @ ( list_update_a @ A @ B @ C ) @ B @ D )
= ( list_update_a @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(89,axiom,
! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_pinf_I2_J) ).
thf(557,plain,
! [A: nat > $o,B: nat > $o,C: nat > $o,D: nat > $o] :
( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: nat] :
! [F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(206,axiom,
! [A: nat,B: list_a,C: a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( member_a @ C @ ( set_a2 @ ( list_update_a @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_set__update__memI) ).
thf(1003,plain,
! [A: nat,B: list_a,C: a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( member_a @ C @ ( set_a2 @ ( list_update_a @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(137,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_eq__imp__le) ).
thf(717,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(63,axiom,
! [A: list_a,B: list_a > $o] :
( ( member_list_a @ A @ ( collect_list_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_mem__Collect__eq) ).
thf(470,plain,
! [A: list_a,B: list_a > $o] :
( ( member_list_a @ A @ ( collect_list_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_order__trans) ).
thf(544,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(211,axiom,
! [A: nat,B: set_nat,C: list_a] :
( ( member_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( size_size_list_a @ C ) )
=> ( member_a @ ( nth_a @ C @ A ) @ ( f_image_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_f__imageI) ).
thf(1023,plain,
! [A: nat,B: set_nat,C: list_a] :
( ( member_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( size_size_list_a @ C ) )
=> ( member_a @ ( nth_a @ C @ A ) @ ( f_image_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(219,axiom,
! [A: nat,B: set_nat,C: list_list_a] :
( ( member_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( size_s1427607542list_a @ C ) )
=> ( member_list_a @ ( nth_list_a @ C @ A ) @ ( f_image_list_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_f__imageI) ).
thf(1052,plain,
! [A: nat,B: set_nat,C: list_list_a] :
( ( member_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( size_s1427607542list_a @ C ) )
=> ( member_list_a @ ( nth_list_a @ C @ A ) @ ( f_image_list_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_less__imp__not__eq) ).
thf(386,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_le__less) ).
thf(314,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(71,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_order_Oasym) ).
thf(497,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(109,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_order__subst1) ).
thf(627,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(33,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_infinite__descent) ).
thf(363,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less_nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_order_Ostrict__trans1) ).
thf(759,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(178,axiom,
! [A: nat,B: list_a,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ ( size_size_list_a @ B ) @ C ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ B @ C ) @ A ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_list__slice__nth__length) ).
thf(891,plain,
! [A: nat,B: list_a,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ ( size_size_list_a @ B ) @ C ) )
=> ( ( size_size_list_a @ ( nth_list_a @ ( listSl97544552lice_a @ B @ C ) @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(34,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_nat__less__induct) ).
thf(368,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(237,axiom,
! [A: list_a > $o,B: list_a] :
( ! [C: list_a] :
( ! [D: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ D ) @ ( size_size_list_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_length__induct) ).
thf(1108,plain,
! [A: list_a > $o,B: list_a] :
( ! [C: list_a] :
( ! [D: list_a] :
( ( ord_less_nat @ ( size_size_list_a @ D ) @ ( size_size_list_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(95,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_order__le__less__subst2) ).
thf(588,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(196,axiom,
! [A: nat,B: list_a,C: a > $o] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ! [D: a] :
( ( member_a @ D @ ( set_a2 @ B ) )
=> ( C @ D ) )
=> ( C @ ( nth_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_list__ball__nth) ).
thf(961,plain,
! [A: nat,B: list_a,C: a > $o] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ! [D: a] :
( ( member_a @ D @ ( set_a2 @ B ) )
=> ( C @ D ) )
=> ( C @ ( nth_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(25,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat] : ( A @ D @ D )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_linorder__less__wlog) ).
thf(319,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat] : ( A @ D @ D )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(192,axiom,
( ( (=) @ list_a )
= ( ^ [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( ( nth_a @ A @ C )
= ( nth_a @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_list__eq__iff__nth__eq) ).
thf(946,plain,
( ( (=) @ list_a )
= ( ^ [A: list_a,B: list_a] :
( ( ( size_size_list_a @ A )
= ( size_size_list_a @ B ) )
& ! [C: nat] :
( ( ord_less_nat @ C @ ( size_size_list_a @ A ) )
=> ( ( nth_a @ A @ C )
= ( nth_a @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_order_Ostrict__implies__order) ).
thf(390,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(155,axiom,
! [A: list_list_a,B: set_nat] :
( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( member_nat @ C @ B ) )
=> ( ( f_image_list_a @ A @ B )
= ( set_list_a2 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_f__image__eq__set) ).
thf(781,plain,
! [A: list_list_a,B: set_nat] :
( ! [C: nat] :
( ( ord_less_nat @ C @ ( size_s1427607542list_a @ A ) )
=> ( member_nat @ C @ B ) )
=> ( ( f_image_list_a @ A @ B )
= ( set_list_a2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(50,axiom,
! [A: nat,B: nat,C: list_a,D: a] :
( ( A != B )
=> ( ( nth_a @ ( list_update_a @ C @ A @ D ) @ B )
= ( nth_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_nth__list__update__neq) ).
thf(418,plain,
! [A: nat,B: nat,C: list_a,D: a] :
( ( A != B )
=> ( ( nth_a @ ( list_update_a @ C @ A @ D ) @ B )
= ( nth_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_linorder__neqE__nat) ).
thf(786,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(184,axiom,
! [A: nat,B: list_list_a,C: list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( ( list_update_list_a @ B @ A @ C )
= B )
= ( ( nth_list_a @ B @ A )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_list__update__same__conv) ).
thf(914,plain,
! [A: nat,B: list_list_a,C: list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( ( list_update_list_a @ B @ A @ C )
= B )
= ( ( nth_list_a @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(55,axiom,
( list_desc_set_list_a
= ( ^ [A: list_set_list_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1635937238list_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_le1301786372list_a @ ( nth_set_list_a @ A @ B ) @ ( nth_set_list_a @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_list__desc__trans) ).
thf(433,plain,
( list_desc_set_list_a
= ( ^ [A: list_set_list_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_s1635937238list_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_le1301786372list_a @ ( nth_set_list_a @ A @ B ) @ ( nth_set_list_a @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(228,axiom,
! [A: nat,B: list_list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ ( nth_list_a @ B @ A ) @ ( f_image_list_a @ B @ top_top_set_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_f__rangeI) ).
thf(1077,plain,
! [A: nat,B: list_list_a] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( member_list_a @ ( nth_list_a @ B @ A ) @ ( f_image_list_a @ B @ top_top_set_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(11,axiom,
! [A: list_list_a,B: nat] :
( ( size_s575106428list_a @ ( listSl162220270list_a @ A @ B ) )
= ( divide_divide_nat @ ( size_s1427607542list_a @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_list__slice__length) ).
thf(272,plain,
! [A: list_list_a,B: nat] :
( ( size_s575106428list_a @ ( listSl162220270list_a @ A @ B ) )
= ( divide_divide_nat @ ( size_s1427607542list_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_eq__refl) ).
thf(410,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(8,axiom,
! [A: nat,B: nat > list_list_a > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: list_list_a] : ( B @ C @ D ) ) )
= ( ? [C: list_list_list_a] :
( ( ( size_s575106428list_a @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_list_list_a @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_Skolem__list__nth) ).
thf(262,plain,
! [A: nat,B: nat > list_list_a > $o] :
( ( ! [C: nat] :
( ( ord_less_nat @ C @ A )
=> ? [D: list_list_a] : ( B @ C @ D ) ) )
= ( ? [C: list_list_list_a] :
( ( ( size_s575106428list_a @ C )
= A )
& ! [D: nat] :
( ( ord_less_nat @ D @ A )
=> ( B @ D @ ( nth_list_list_a @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(166,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__or__eq__imp__le) ).
thf(818,plain,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(51,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_order__less__le__subst1) ).
thf(422,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(172,axiom,
! [A: nat,B: list_list_a,C: nat] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( ( set_list_a2 @ ( list_update_list_a @ ( list_update_list_a @ B @ A @ ( nth_list_a @ B @ C ) ) @ C @ ( nth_list_a @ B @ A ) ) )
= ( set_list_a2 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_set__swap) ).
thf(865,plain,
! [A: nat,B: list_list_a,C: nat] :
( ( ord_less_nat @ A @ ( size_s1427607542list_a @ B ) )
=> ( ( ord_less_nat @ C @ ( size_s1427607542list_a @ B ) )
=> ( ( set_list_a2 @ ( list_update_list_a @ ( list_update_list_a @ B @ A @ ( nth_list_a @ B @ C ) ) @ C @ ( nth_list_a @ B @ A ) ) )
= ( set_list_a2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(35,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_less__imp__not__eq2) ).
thf(373,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(74,axiom,
( list_asc_set_a
= ( ^ [A: list_set_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_size_list_set_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_eq_set_a @ ( nth_set_a @ A @ C ) @ ( nth_set_a @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_list__asc__trans) ).
thf(506,plain,
( list_asc_set_a
= ( ^ [A: list_set_a] :
! [B: nat] :
( ( ord_less_nat @ B @ ( size_size_list_set_a @ A ) )
=> ! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( ord_less_eq_set_a @ ( nth_set_a @ A @ C ) @ ( nth_set_a @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(224,axiom,
! [A: list_a,B: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ A @ B ) )
= ( divide_divide_nat @ ( size_size_list_a @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_list__slice__length) ).
thf(1065,plain,
! [A: list_a,B: nat] :
( ( size_s1427607542list_a @ ( listSl97544552lice_a @ A @ B ) )
= ( divide_divide_nat @ ( size_size_list_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(185,axiom,
! [A: nat,B: list_a,C: nat] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( ( distinct_a @ ( list_update_a @ ( list_update_a @ B @ A @ ( nth_a @ B @ C ) ) @ C @ ( nth_a @ B @ A ) ) )
= ( distinct_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_distinct__swap) ).
thf(918,plain,
! [A: nat,B: list_a,C: nat] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( ( ord_less_nat @ C @ ( size_size_list_a @ B ) )
=> ( ( distinct_a @ ( list_update_a @ ( list_update_a @ B @ A @ ( nth_a @ B @ C ) ) @ C @ ( nth_a @ B @ A ) ) )
= ( distinct_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(160,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ~ ( ord_less_nat @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_pinf_I5_J) ).
thf(801,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ B @ C )
=> ~ ( ord_less_nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(140,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_le__refl) ).
thf(728,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(91,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_order__less__le__subst2) ).
thf(575,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_not__le) ).
thf(596,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_not__less) ).
thf(459,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(203,axiom,
! [A: nat,B: list_a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( member_a @ ( nth_a @ B @ A ) @ ( set_a2 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_nth__mem) ).
thf(992,plain,
! [A: nat,B: list_a] :
( ( ord_less_nat @ A @ ( size_size_list_a @ B ) )
=> ( member_a @ ( nth_a @ B @ A ) @ ( set_a2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(139,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_ord__less__eq__trans) ).
thf(723,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(13,axiom,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( C != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_minf_I3_J) ).
thf(277,plain,
! [A: nat] :
? [B: nat] :
! [C: nat] :
( ( ord_less_nat @ C @ B )
=> ( C != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_le__cases) ).
thf(395,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_antisym__conv2) ).
thf(624,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(68,axiom,
( listSl162220270list_a
= ( ^ [A: list_list_a,B: nat] : ( listSl856612276list_a @ A @ B @ ( divide_divide_nat @ ( size_s1427607542list_a @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_list__slice__def) ).
thf(486,plain,
( listSl162220270list_a
= ( ^ [A: list_list_a,B: nat] : ( listSl856612276list_a @ A @ B @ ( divide_divide_nat @ ( size_s1427607542list_a @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(161,axiom,
! [A: nat,B: list_list_a,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ ( size_s1427607542list_a @ B ) @ C ) )
=> ( ( nth_list_list_a @ ( listSl703198822list_a @ B @ C ) @ A )
= ( nth_list_list_a @ ( listSl162220270list_a @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_list__slice2__list__slice__nth) ).
thf(803,plain,
! [A: nat,B: list_list_a,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ ( size_s1427607542list_a @ B ) @ C ) )
=> ( ( nth_list_list_a @ ( listSl703198822list_a @ B @ C ) @ A )
= ( nth_list_list_a @ ( listSl162220270list_a @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(26,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_le__less__trans) ).
thf(337,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(190,axiom,
! [A: list_a,B: nat,C: a] :
( ( size_size_list_a @ ( list_update_a @ A @ B @ C ) )
= ( size_size_list_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_length__list__update) ).
thf(940,plain,
! [A: list_a,B: nat,C: a] :
( ( size_size_list_a @ ( list_update_a @ A @ B @ C ) )
= ( size_size_list_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(30,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_order_Ostrict__trans) ).
thf(354,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(215,axiom,
! [A: nat,B: set_nat,C: list_a,D: a] :
( ( member_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( size_size_list_a @ C ) )
=> ( ( D
= ( nth_a @ C @ A ) )
=> ( member_a @ D @ ( f_image_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_rev__f__imageI) ).
thf(1037,plain,
! [A: nat,B: set_nat,C: list_a,D: a] :
( ( member_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( size_size_list_a @ C ) )
=> ( ( D
= ( nth_a @ C @ A ) )
=> ( member_a @ D @ ( f_image_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(70,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_linorder__wlog) ).
thf(491,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(96,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_order__less__subst2) ).
thf(592,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_nat @ E @ F )
=> ( ord_less_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(133,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_less__imp__not__less) ).
thf(708,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(22,axiom,
! [A: list_list_a > $o,B: list_list_a] :
( ! [C: list_list_a] :
( ! [D: list_list_a] :
( ( ord_less_nat @ ( size_s1427607542list_a @ D ) @ ( size_s1427607542list_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_length__induct) ).
thf(309,plain,
! [A: list_list_a > $o,B: list_list_a] :
( ! [C: list_list_a] :
( ! [D: list_list_a] :
( ( ord_less_nat @ ( size_s1427607542list_a @ D ) @ ( size_s1427607542list_a @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(119,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ B @ C ) )
=> ( ord_less_eq_nat @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_div__gr__imp__gr__divisor) ).
thf(659,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ A @ ( divide_divide_nat @ B @ C ) )
=> ( ord_less_eq_nat @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(1448,plain,
$false,
inference(cvc4,[status(thm)],[645,1105,909,518,481,352,977,730,1068,994,1073,873,379,511,614,861,582,762,384,550,715,340,898,288,651,829,1095,973,885,1046,1055,619,357,1059,902,881,316,1100,969,606,756,789,1020,806,905,634,453,1119,998,988,243,428,265,397,687,293,956,307,248,678,529,661,810,381,534,894,1042,349,392,297,693,275,484,252,435,889,1079,682,710,285,697,948,1006,869,499,980,403,256,1082,488,537,476,526,547,554,753,622,701,738,654,457,721,779,503,792,360,508,541,657,765,1071,1026,965,430,1103,745,601,584,732,743,826,958,281,259,579,291,611,1058,1092,1090,445,936,604,406,1117,1011,377,567,616,599,1048,736,631,858,816,1029,769,943,462,932,1061,685,399,455,1015,608,1113,267,241,922,636,695,473,1034,675,426,531,927,648,812,749,516,823,795,680,690,640,295,705,414,712,557,1003,717,470,544,1023,1052,386,314,497,627,363,759,891,368,1108,588,961,319,946,390,781,418,786,914,433,1077,272,410,262,818,422,865,373,506,1065,918,801,728,575,596,459,992,723,277,395,624,486,803,337,940,354,1037,491,592,708,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP104^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:25:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/1.12 % [INFO] Parsing done (249ms).
% 1.74/1.12 % [INFO] Running in sequential loop mode.
% 2.74/1.33 % [INFO] eprover registered as external prover.
% 2.74/1.33 % [INFO] cvc4 registered as external prover.
% 2.74/1.34 % [INFO] Scanning for conjecture ...
% 2.90/1.43 % [INFO] Found a conjecture and 349 axioms. Running axiom selection ...
% 3.31/1.52 % [INFO] Axiom selection finished. Selected 238 axioms (removed 111 axioms).
% 3.68/1.65 % [INFO] Problem is higher-order (TPTP THF).
% 3.68/1.67 % [INFO] Type checking passed.
% 3.68/1.67 % [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 ...
% 16.14/4.50 % External prover 'cvc4' found a proof!
% 16.14/4.50 % [INFO] Killing All external provers ...
% 16.14/4.50 % Time passed: 3965ms (effective reasoning time: 3377ms)
% 16.14/4.50 % 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)>
% 16.14/4.51 % Axioms used in derivation (238): fact_214_all__nth__imp__all__set, fact_172_f__rangeI, fact_323_leI, fact_249_antisym__conv, fact_239_dual__order_Oantisym, fact_279_less__not__sym, fact_297_dual__order_Oorder__iff__strict, fact_324_leD, fact_105_f__imageE, fact_311_less__imp__le, fact_89_f__image__iff, fact_309_less__le__trans, fact_215_all__nth__imp__all__set, fact_236_eq__imp__le, fact_55_nat__less__induct, fact_28_list__slice__nth__length, fact_11_list__eq__iff__nth__eq, fact_57_less__not__refl3, fact_127_list__update__swap, fact_268_order_Oasym, fact_269_less__imp__neq, fact_343_pinf_I8_J, fact_79_nth__list__update__eq, fact_217_in__set__conv__nth, fact_329_minf_I8_J, fact_305_not__le__imp__less, fact_298_order_Ostrict__implies__order, fact_278_less__imp__not__eq, fact_283_less__imp__triv, fact_178_f__range__eqI, fact_285_dual__order_Oirrefl, fact_58_less__not__refl2, fact_235_le__antisym, fact_68_list__ex__length, fact_262_ord__less__eq__subst, fact_241_dual__order_Otrans, fact_306_less__le__not__le, fact_38_neq__if__length__neq, fact_144_set__swap, fact_322_le__less, fact_267_neq__iff, fact_139_list__update__same__conv, fact_325_div__gr__imp__gr__divisor, fact_315_not__less, fact_74_f__image__eqI, fact_243_dual__order_Orefl, fact_19_list__slice2__list__slice__nth, fact_321_less__le, fact_53_linorder__neqE__nat, fact_118_list__update__id, fact_240_dual__order_Oeq__iff, fact_33_Ex__list__of__length, fact_237_le__trans, fact_192_le__neq__implies__less, fact_8_Skolem__list__nth, fact_173_f__rangeI, fact_264_order__less__subst2, fact_1_nth__equalityI, fact_341_pinf_I1_J, fact_148_list__desc__trans, fact_52_list__slice__length, fact_94_nth__butlast, fact_152_list__asc__trans, fact_62_list__slice__def, fact_147_list__desc__trans, fact_253_eq__refl, fact_109_list__update__overwrite, fact_159_Collect__mem__eq, fact_85_rev__f__imageI, fact_154_mem__Collect__eq, fact_256_eq__iff, fact_286_order_Ostrict__trans, fact_284_linorder__cases, fact_24_length__induct, fact_328_nat__descend__induct, fact_254_linear, fact_345_complete__interval, fact_316_not__le, fact_333_minf_I3_J, fact_288_exists__least__iff, fact_344_minf_I6_J, fact_342_pinf_I6_J, fact_185_f__image__subset__iff, fact_307_le__imp__less__or__eq, fact_238_le__refl, fact_277_dual__order_Oasym, fact_138_list__update__same__conv, fact_208_distinct__conv__nth, fact_226_set__update__memI, fact_36_Ex__list__of__length, fact_292_order_Ostrict__implies__not__eq, fact_206_nth__eq__iff__index__eq, fact_13_list__eq__iff__nth__eq, fact_302_order_Oorder__iff__strict, fact_133_nth__list__update, fact_108_list__update__overwrite, fact_155_mem__Collect__eq, fact_245_order__class_Oorder_Oantisym, fact_177_f__range__eqI, fact_163_distinct__swap, fact_4_nth__equalityI, fact_248_order__class_Oorder_Oeq__iff, fact_223_nth__mem, fact_270_less__asym, fact_300_dual__order_Ostrict__trans1, fact_294_order_Onot__eq__order__implies__strict, fact_266_neqE, fact_246_ord__le__eq__trans, fact_197_distinct__Ex1, fact_73_f__image__eqI, fact_39_neq__if__length__neq, fact_45_size__neq__size__imp__neq, fact_258_ord__eq__le__subst, fact_191_less__mono__imp__le__mono, fact_289_linorder__less__wlog, fact_182_f__image__subsetI, fact_339_pinf_I3_J, fact_3_nth__equalityI, fact_335_minf_I1_J, fact_271_less__asym_H, fact_43_size__neq__size__imp__neq, fact_296_dual__order_Ostrict__iff__order, fact_99_f__imageI, fact_205_nth__eq__iff__index__eq, fact_130_list__slice__aux__length, fact_59_less__not__refl, fact_134_nth__list__update, fact_272_less__trans, fact_21_length__induct, fact_64_list__slice__def, fact_301_order_Ostrict__iff__order, fact_274_less__irrefl, fact_260_order__subst1, fact_104_f__imageE, fact_337_pinf_I5_J, fact_211_all__set__conv__all__nth, fact_34_Ex__list__of__length, fact_247_ord__eq__le__trans, fact_123_nth__list__update__neq, fact_230_f__image__eq__set, fact_276_ord__less__eq__trans, fact_332_minf_I4_J, fact_156_mem__Collect__eq, fact_304_order_Ostrict__trans1, fact_193_less__or__eq__imp__le, fact_229_f__image__eq__set, fact_255_antisym, fact_299_dual__order_Ostrict__trans2, fact_221_list__ball__nth, fact_209_distinct__conv__nth, fact_198_distinct__Ex1, fact_183_f__image__subsetI, fact_224_nth__mem, fact_80_nth__list__update__eq, fact_129_list__slice__aux__length, fact_188_list__update__beyond, fact_347_ge__less__neq__conv, fact_261_ord__eq__less__subst, fact_220_list__ball__nth, fact_232_order__refl, fact_69_list__ex__length, fact_113_length__list__update, fact_293_dual__order_Ostrict__implies__not__eq, fact_242_linorder__wlog, fact_112_length__list__update, fact_263_order__less__subst1, fact_303_order_Ostrict__trans2, fact_117_list__update__id, fact_346_le__greater__neq__conv, fact_252_le__cases, fact_54_infinite__descent, fact_336_pinf_I7_J, fact_317_order__less__le__subst2, fact_157_Collect__mem__eq, fact_282_less__imp__not__eq2, fact_326_div__le__mono, fact_196_nat__less__le, fact_340_pinf_I2_J, fact_319_order__le__less__subst2, fact_313_antisym__conv1, fact_259_order__subst2, fact_9_Skolem__list__nth, fact_320_order__le__less__subst1, fact_233_Nat_Oex__has__greatest__nat, fact_338_pinf_I4_J, fact_6_Skolem__list__nth, fact_189_list__update__beyond, fact_310_le__less__trans, fact_331_minf_I5_J, fact_290_dual__order_Ostrict__trans, fact_318_order__less__le__subst1, fact_158_Collect__mem__eq, fact_250_le__cases3, fact_251_order_Otrans, fact_227_set__update__memI, fact_126_list__update__swap, fact_195_less__imp__le__nat, fact_330_minf_I7_J, fact_275_ord__eq__less__trans, fact_95_nth__butlast, fact_334_minf_I2_J, fact_218_in__set__conv__nth, fact_56_less__irrefl__nat, fact_167_f__rangeE, fact_14_list__eq__iff__nth__eq, fact_291_not__less__iff__gr__or__eq, fact_257_ord__le__eq__subst, fact_194_le__eq__less__or__eq, fact_84_rev__f__imageI, fact_50_list__slice__length, fact_327_div__le__dividend, fact_234_nat__le__linear, fact_287_less__imp__not__less, fact_314_le__neq__trans, fact_281_antisym__conv3, fact_312_antisym__conv2, fact_295_dual__order_Ostrict__implies__order, fact_308_le__less__linear, fact_151_list__asc__trans, fact_162_distinct__swap, fact_212_all__set__conv__all__nth, fact_168_f__rangeE, conj_0, fact_30_list__slice__nth__length, fact_22_length__induct, fact_273_less__linear, fact_17_list__slice2__list__slice__nth, fact_100_f__imageI, fact_90_f__image__iff, fact_44_size__neq__size__imp__neq, fact_186_f__image__subset__iff, fact_280_less__induct, fact_265_gt__ex, fact_41_neq__if__length__neq, fact_122_nth__list__update__neq, fact_244_order__trans, fact_47_nat__neq__iff, fact_143_set__swap
% 16.14/4.51 % No. of inferences in proof: 480
% 16.14/4.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3965 ms resp. 3377 ms w/o parsing
% 16.33/4.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.33/4.62 % [INFO] Killing All external provers ...
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