TSTP Solution File: ITP101^2 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP101^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 : Mon May 20 22:22:55 EDT 2024
% Result : Theorem 37.78s 23.89s
% Output : Refutation 38.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 315
% Syntax : Number of formulae : 592 ( 107 unt; 40 typ; 0 def)
% Number of atoms : 2023 ( 467 equ; 8 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 7279 ( 172 ~; 49 |; 100 &;5922 @)
% ( 0 <=>;1036 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 200 ( 200 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 40 usr; 8 con; 0-4 aty)
% Number of variables : 2032 ( 106 ^1813 !; 80 ?;2032 :)
% ( 33 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(size_type,type,
size:
!>[TA: $tType] : $o ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(no_bot_type,type,
no_bot:
!>[TA: $tType] : $o ).
thf(no_top_type,type,
no_top:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(dense_order_type,type,
dense_order:
!>[TA: $tType] : $o ).
thf(dense_linorder_type,type,
dense_linorder:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(condit1037483654norder_type,type,
condit1037483654norder:
!>[TA: $tType] : $o ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(list_asc_type,type,
list_asc:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(list_desc_type,type,
list_desc:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(list_strict_asc_type,type,
list_strict_asc:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(list_strict_desc_type,type,
list_strict_desc:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(listIn521021761append_type,type,
listIn521021761append:
!>[TA: $tType] : ( ( list @ TA ) > ( nat > TA ) > nat > TA ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(butlast_type,type,
butlast:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) ) ).
thf(set2_type,type,
set2:
!>[TA: $tType] : ( ( list @ TA ) > ( set @ TA ) ) ).
thf(list_ex_type,type,
list_ex:
!>[TA: $tType] : ( ( TA > $o ) > ( list @ TA ) > $o ) ).
thf(list_update_type,type,
list_update:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA > ( list @ TA ) ) ).
thf(nth_type,type,
nth:
!>[TA: $tType] : ( ( list @ TA ) > nat > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_type,type,
f: nat > a ).
thf(g_type,type,
g: nat > a ).
thf(x_type,type,
x: nat ).
thf(xs_type,type,
xs: list @ a ).
thf(ys_type,type,
ys: list @ a ).
thf(113,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_minf_I6_J) ).
thf(645,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( minus_minus @ nat @ C @ B ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_nat__diff__right__cancel__eq2) ).
thf(1036,plain,
! [A: nat,B: nat,C: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( minus_minus @ nat @ C @ B ) )
=> ( ( ord_less @ nat @ B @ C )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(184,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ A @ C ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_nat__diff__left__cancel__le1) ).
thf(846,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ A @ C ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(238,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_dense__ge) ).
thf(1031,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(200,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_less__not__sym) ).
thf(893,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(213,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_diff__less__mono2) ).
thf(941,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
=> ( ( ord_less_eq @ nat @ D @ C )
=> ( ord_less_eq @ nat @ A @ ( minus_minus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_le__diff__le__imp__le) ).
thf(666,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
=> ( ( ord_less_eq @ nat @ D @ C )
=> ( ord_less_eq @ nat @ A @ ( minus_minus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(19,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_linorder__wlog) ).
thf(352,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(61,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_12) ).
thf(479,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(259,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_asc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ C ) @ ( nth @ TA @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_list__asc__trans) ).
thf(1105,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_asc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ C ) @ ( nth @ TA @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_le__diff__iff) ).
thf(777,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(82,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_5) ).
thf(555,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(226,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ C @ B ) )
=> ( ord_less @ nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_nat__diff__right__cancel__less) ).
thf(1005,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ C @ B ) )
=> ( ord_less @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(222,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_order_Ostrict__trans1) ).
thf(994,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_order__less__subst2) ).
thf(308,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(248,axiom,
! [TA: $tType] :
( ( list_ex @ TA )
= ( ^ [A: TA > $o,B: list @ TA] :
? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_list__ex__length) ).
thf(1073,plain,
! [TA: $tType] :
( ( list_ex @ TA )
= ( ^ [A: TA > $o,B: list @ TA] :
? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( A @ ( nth @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(47,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_pinf_I7_J) ).
thf(440,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(117,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_less__asym_H) ).
thf(655,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(71,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_minf_I1_J) ).
thf(511,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(80,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_order_Oorder__iff__strict) ).
thf(550,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_le__fun__def) ).
thf(472,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(172,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_order__refl) ).
thf(814,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(34,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_minf_I7_J) ).
thf(404,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(225,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_dense__ge__bounded) ).
thf(1001,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(137,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_diff__strict__right__mono) ).
thf(709,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(197,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_le__antisym) ).
thf(885,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)],[197]) ).
thf(4,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_antisym__conv) ).
thf(288,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_ord__less__eq__trans) ).
thf(301,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_neq__iff) ).
thf(389,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(142,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_neq__if__length__neq) ).
thf(724,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
!= ( size_size @ ( list @ TA ) @ B ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(150,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( list_update @ TA @ A @ B @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_list__update__beyond) ).
thf(751,plain,
! [TA: $tType,A: list @ TA,B: nat,C: TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( list_update @ TA @ A @ B @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(210,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_verit__comp__simplify1_I3_J) ).
thf(934,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ C @ B )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_minf_I11_J) ).
thf(357,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_linorder__cases) ).
thf(542,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(55,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_order_Ostrict__implies__not__eq) ).
thf(460,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(202,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA,E: TA] :
( ( A != B )
=> ( ( list_update @ TA @ ( list_update @ TA @ C @ A @ D ) @ B @ E )
= ( list_update @ TA @ ( list_update @ TA @ C @ B @ E ) @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_list__update__swap) ).
thf(902,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA,E: TA] :
( ( A != B )
=> ( ( list_update @ TA @ ( list_update @ TA @ C @ A @ D ) @ B @ E )
= ( list_update @ TA @ ( list_update @ TA @ C @ B @ E ) @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_not__less) ).
thf(638,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_le__funD) ).
thf(421,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(230,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_minf_I8_J) ).
thf(1013,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(51,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_one__reorient) ).
thf(448,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(60,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_minf_I3_J) ).
thf(475,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ord__eq__le__subst) ).
thf(321,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(105,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: list @ TA] :
( ( list_strict_asc @ TA @ A )
=> ( list_asc @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_list__strict__asc__imp__list__asc) ).
thf(623,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: list @ TA] :
( ( list_strict_asc @ TA @ A )
=> ( list_asc @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(180,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(834,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_less__imp__le__nat) ).
thf(937,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(17,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_dual__order_Orefl) ).
thf(348,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(245,axiom,
! [A: nat] :
( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( nth @ a @ xs @ A )
= ( nth @ a @ ys @ A ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( f @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ a ) @ xs ) ) )
= ( nth @ a @ ys @ A ) ) ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( nth @ a @ xs @ A )
= ( g @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) ) ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( f @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ a ) @ xs ) ) )
= ( g @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(1051,plain,
! [A: nat] :
( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( nth @ a @ xs @ A )
= ( nth @ a @ ys @ A ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( f @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ a ) @ xs ) ) )
= ( nth @ a @ ys @ A ) ) ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( nth @ a @ xs @ A )
= ( g @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) ) ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) )
=> ( ( f @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ a ) @ xs ) ) )
= ( g @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ a ) @ ys ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',fact_69_Nat_Oex__has__greatest__nat) ).
thf(905,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)],[203]) ).
thf(62,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_order__class_Oorder_Oantisym) ).
thf(480,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(30,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_6) ).
thf(397,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(195,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_antisym__conv1) ).
thf(877,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(145,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( A != C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_le__greater__neq__conv) ).
thf(734,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( A != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(224,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(998,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(220,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_less__le) ).
thf(988,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ord__le__eq__subst) ).
thf(428,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(70,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_ord__eq__le__trans) ).
thf(507,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(73,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_neqE) ).
thf(527,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(263,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o,C: TA] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ ( size_size @ ( list @ TA ) @ A ) )
=> ( B @ ( nth @ TA @ A @ D ) ) )
=> ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_all__nth__imp__all__set) ).
thf(1119,plain,
! [TA: $tType,A: list @ TA,B: TA > $o,C: TA] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ ( size_size @ ( list @ TA ) @ A ) )
=> ( B @ ( nth @ TA @ A @ D ) ) )
=> ( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_diff__less__mono) ).
thf(774,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(46,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_11) ).
thf(439,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(126,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_order_Ostrict__iff__order) ).
thf(678,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(164,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
| ( ( size_size @ ( list @ TA ) @ C )
= ( size_size @ ( list @ TA ) @ D ) ) )
=> ( ( ( append @ TA @ A @ C )
= ( append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_append__eq__append__conv) ).
thf(793,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
| ( ( size_size @ ( list @ TA ) @ C )
= ( size_size @ ( list @ TA ) @ D ) ) )
=> ( ( ( append @ TA @ A @ C )
= ( append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(170,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_leI) ).
thf(810,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(247,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: nat,D: TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ( A = C )
=> ( ( nth @ TA @ ( list_update @ TA @ B @ A @ D ) @ C )
= D ) )
& ( ( A != C )
=> ( ( nth @ TA @ ( list_update @ TA @ B @ A @ D ) @ C )
= ( nth @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_nth__list__update) ).
thf(1067,plain,
! [TA: $tType,A: nat,B: list @ TA,C: nat,D: TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ( A = C )
=> ( ( nth @ TA @ ( list_update @ TA @ B @ A @ D ) @ C )
= D ) )
& ( ( A != C )
=> ( ( nth @ TA @ ( list_update @ TA @ B @ A @ D ) @ C )
= ( nth @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(275,axiom,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( B @ C ) ) )
= ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( B @ ( nth @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_all__set__conv__all__nth) ).
thf(1153,plain,
! [TA: $tType,A: list @ TA,B: TA > $o] :
( ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( B @ C ) ) )
= ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( B @ ( nth @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_le__neq__implies__less) ).
thf(761,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)],[154]) ).
thf(244,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_less__diff__iff) ).
thf(1047,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(165,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_pinf_I6_J) ).
thf(798,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(254,axiom,
( ( size_size @ ( list @ a ) @ xs )
= ( size_size @ ( list @ a ) @ ys ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1091,plain,
( ( size_size @ ( list @ a ) @ xs )
= ( size_size @ ( list @ a ) @ ys ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(97,axiom,
! [TA: $tType,A: TA > $o,B: list @ TA,C: list @ TA] :
( ( list_ex @ TA @ A @ ( append @ TA @ B @ C ) )
= ( ( list_ex @ TA @ A @ B )
| ( list_ex @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_list__ex__append) ).
thf(598,plain,
! [TA: $tType,A: TA > $o,B: list @ TA,C: list @ TA] :
( ( list_ex @ TA @ A @ ( append @ TA @ B @ C ) )
= ( ( list_ex @ TA @ A @ B )
| ( list_ex @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(28,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_verit__la__disequality) ).
thf(392,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',fact_63_le__trans) ).
thf(1042,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)],[242]) ).
thf(216,axiom,
! [TA: $tType] :
( ( condit1037483654norder @ TA )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_complete__interval) ).
thf(952,plain,
! [TA: $tType] :
( ( condit1037483654norder @ TA )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(106,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_dual__order_Ostrict__trans1) ).
thf(625,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(44,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_antisym) ).
thf(435,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(178,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_diff__strict__left__mono) ).
thf(830,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(152,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ B ) ) )
=> ( member @ TA @ A @ ( set2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_in__set__butlastD) ).
thf(757,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ B ) ) )
=> ( member @ TA @ A @ ( set2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(266,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: list @ TA] :
( ( list_strict_asc @ TA @ A )
=> ! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ C ) @ ( nth @ TA @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_list__strict__asc__trans__le) ).
thf(1128,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: list @ TA] :
( ( list_strict_asc @ TA @ A )
=> ! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ C ) @ ( nth @ TA @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(54,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_dual__order_Ostrict__implies__not__eq) ).
thf(456,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(205,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_Ex__list__of__length) ).
thf(916,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(57,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_minf_I5_J) ).
thf(467,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(86,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_diff__right__commute) ).
thf(566,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(64,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_less__imp__not__eq2) ).
thf(484,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(250,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: list @ TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( nth @ TA @ ( append @ TA @ A @ C ) @ B )
= ( nth @ TA @ C @ ( minus_minus @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nth__append2) ).
thf(1079,plain,
! [TA: $tType,A: list @ TA,B: nat,C: list @ TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( nth @ TA @ ( append @ TA @ A @ C ) @ B )
= ( nth @ TA @ C @ ( minus_minus @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(236,axiom,
condit1037483654norder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder) ).
thf(1027,plain,
condit1037483654norder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(133,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_ex__has__least__nat) ).
thf(697,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat] :
( ( A @ B )
=> ? [D: TA] :
( ( A @ D )
& ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ nat @ ( C @ D ) @ ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(103,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA,D: TA] :
( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( list_update @ TA @ ( append @ TA @ B @ C ) @ A @ D )
= ( append @ TA @ ( list_update @ TA @ B @ A @ D ) @ C ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( list_update @ TA @ ( append @ TA @ B @ C ) @ A @ D )
= ( append @ TA @ B @ ( list_update @ TA @ C @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_list__update__append) ).
thf(615,plain,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA,D: TA] :
( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( list_update @ TA @ ( append @ TA @ B @ C ) @ A @ D )
= ( append @ TA @ ( list_update @ TA @ B @ A @ D ) @ C ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( list_update @ TA @ ( append @ TA @ B @ C ) @ A @ D )
= ( append @ TA @ B @ ( list_update @ TA @ C @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(246,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( set2 @ TA @ ( list_update @ TA @ ( list_update @ TA @ B @ A @ ( nth @ TA @ B @ C ) ) @ C @ ( nth @ TA @ B @ A ) ) )
= ( set2 @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_set__swap) ).
thf(1064,plain,
! [TA: $tType,A: nat,B: list @ TA,C: nat] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( set2 @ TA @ ( list_update @ TA @ ( list_update @ TA @ B @ A @ ( nth @ TA @ B @ C ) ) @ C @ ( nth @ TA @ B @ A ) ) )
= ( set2 @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(217,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_not__le) ).
thf(980,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(256,axiom,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Skolem__list__nth) ).
thf(1096,plain,
! [TA: $tType,A: nat,B: nat > TA > $o] :
( ( ! [C: nat] :
( ( ord_less @ nat @ C @ A )
=> ? [D: TA] : ( B @ C @ D ) ) )
= ( ? [C: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ C )
= A )
& ! [D: nat] :
( ( ord_less @ nat @ D @ A )
=> ( B @ D @ ( nth @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(192,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_pinf_I8_J) ).
thf(869,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(39,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3) ).
thf(420,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(67,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_order__class_Oorder_Oeq__iff) ).
thf(499,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(188,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_diff__commute) ).
thf(857,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(194,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less_eq @ TA @ C @ A )
=> ( B != C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_greater__le__neq__conv) ).
thf(874,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less_eq @ TA @ C @ A )
=> ( B != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(271,axiom,
! [TA: $tType] :
( ( listIn521021761append @ TA )
= ( ^ [A: list @ TA,B: nat > TA,C: nat] : ( if @ TA @ ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) ) @ ( nth @ TA @ A @ C ) @ ( B @ ( minus_minus @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_i__append__def) ).
thf(1143,plain,
! [TA: $tType] :
( ( listIn521021761append @ TA )
= ( ^ [A: list @ TA,B: nat > TA,C: nat] : ( if @ TA @ ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) ) @ ( nth @ TA @ A @ C ) @ ( B @ ( minus_minus @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(14,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_le__cases3) ).
thf(328,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_minf_I2_J) ).
thf(488,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less_eq @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_le__diff__iff_H) ).
thf(669,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less_eq @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(129,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_dual__order_Ostrict__trans2) ).
thf(686,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(112,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_linorder__neqE__nat) ).
thf(642,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)],[112]) ).
thf(232,axiom,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ B ) ) )
| ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ C ) ) ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ ( append @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_in__set__butlast__appendI) ).
thf(1016,plain,
! [TA: $tType,A: TA,B: list @ TA,C: list @ TA] :
( ( ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ B ) ) )
| ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ C ) ) ) )
=> ( member @ TA @ A @ ( set2 @ TA @ ( butlast @ TA @ ( append @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(241,axiom,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( butlast @ TA @ A ) )
= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_length__butlast) ).
thf(1039,plain,
! [TA: $tType,A: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( butlast @ TA @ A ) )
= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(79,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( minus_minus @ nat @ A @ C ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_nat__diff__left__cancel__eq1) ).
thf(547,plain,
! [A: nat,B: nat,C: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( minus_minus @ nat @ A @ C ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(237,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_append_Oassoc) ).
thf(1028,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(251,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: TA > $o] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ B ) )
=> ( C @ D ) )
=> ( C @ ( nth @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_list__ball__nth) ).
thf(1082,plain,
! [TA: $tType,A: nat,B: list @ TA,C: TA > $o] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( set2 @ TA @ B ) )
=> ( C @ D ) )
=> ( C @ ( nth @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(181,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(837,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(114,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_nat__less__le) ).
thf(647,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(257,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_strict_asc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ TA @ ( nth @ TA @ A @ C ) @ ( nth @ TA @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_list__strict__asc__trans) ).
thf(1099,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_strict_asc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ TA @ ( nth @ TA @ A @ C ) @ ( nth @ TA @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(204,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_less__or__eq__imp__le) ).
thf(911,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)],[204]) ).
thf(87,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_dual__order_Ostrict__iff__order) ).
thf(569,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(22,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_ord__eq__less__trans) ).
thf(360,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_order__less__le__subst2) ).
thf(805,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_ord__le__eq__trans) ).
thf(311,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(118,axiom,
! [TA: $tType] :
( ( no_bot @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_lt__ex) ).
thf(657,plain,
! [TA: $tType] :
( ( no_bot @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(74,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_pinf_I5_J) ).
thf(530,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_diff__eq__diff__less) ).
thf(586,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(198,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_diff__left__mono) ).
thf(888,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(269,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA] :
( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( append @ TA @ B @ C ) @ A )
= ( nth @ TA @ B @ A ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( append @ TA @ B @ C ) @ A )
= ( nth @ TA @ C @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_nth__append) ).
thf(1135,plain,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA] :
( ( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( append @ TA @ B @ C ) @ A )
= ( nth @ TA @ B @ A ) ) )
& ( ~ ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( append @ TA @ B @ C ) @ A )
= ( nth @ TA @ C @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(42,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_not__less__iff__gr__or__eq) ).
thf(425,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(272,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ( list_update @ TA @ B @ A @ C )
= B )
= ( ( nth @ TA @ B @ A )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_list__update__same__conv) ).
thf(1146,plain,
! [TA: $tType,A: nat,B: list @ TA,C: TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ( list_update @ TA @ B @ A @ C )
= B )
= ( ( nth @ TA @ B @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(176,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA,D: TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( list_update @ TA @ ( append @ TA @ B @ C ) @ A @ D )
= ( append @ TA @ ( list_update @ TA @ B @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_list__update__append1) ).
thf(824,plain,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA,D: TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( list_update @ TA @ ( append @ TA @ B @ C ) @ A @ D )
= ( append @ TA @ ( list_update @ TA @ B @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(3,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_pinf_I1_J) ).
thf(279,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(98,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: TA,D: TA] :
( ( list_update @ TA @ ( list_update @ TA @ A @ B @ C ) @ B @ D )
= ( list_update @ TA @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_list__update__overwrite) ).
thf(601,plain,
! [TA: $tType,A: list @ TA,B: nat,C: TA,D: TA] :
( ( list_update @ TA @ ( list_update @ TA @ A @ B @ C ) @ B @ D )
= ( list_update @ TA @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(92,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_dual__order_Ostrict__implies__order) ).
thf(584,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(174,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: TA] :
( ( size_size @ ( list @ TA ) @ ( list_update @ TA @ A @ B @ C ) )
= ( size_size @ ( list @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_length__list__update) ).
thf(819,plain,
! [TA: $tType,A: list @ TA,B: nat,C: TA] :
( ( size_size @ ( list @ TA ) @ ( list_update @ TA @ A @ B @ C ) )
= ( size_size @ ( list @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(41,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_le__cases) ).
thf(423,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(402,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(148,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: TA] :
( ( ( A
= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ B ) @ ( one_one @ nat ) ) )
=> ( ( butlast @ TA @ ( list_update @ TA @ B @ A @ C ) )
= ( butlast @ TA @ B ) ) )
& ( ( A
!= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ B ) @ ( one_one @ nat ) ) )
=> ( ( butlast @ TA @ ( list_update @ TA @ B @ A @ C ) )
= ( list_update @ TA @ ( butlast @ TA @ B ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_butlast__list__update) ).
thf(743,plain,
! [TA: $tType,A: nat,B: list @ TA,C: TA] :
( ( ( A
= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ B ) @ ( one_one @ nat ) ) )
=> ( ( butlast @ TA @ ( list_update @ TA @ B @ A @ C ) )
= ( butlast @ TA @ B ) ) )
& ( ( A
!= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ B ) @ ( one_one @ nat ) ) )
=> ( ( butlast @ TA @ ( list_update @ TA @ B @ A @ C ) )
= ( list_update @ TA @ ( butlast @ TA @ B ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(138,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_14) ).
thf(711,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(5,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_pinf_I2_J) ).
thf(291,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(78,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_le__less__trans) ).
thf(545,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(227,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_less__imp__triv) ).
thf(1007,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(132,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ A @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_antisym__conv2) ).
thf(694,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ A @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(183,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_append__eq__append__conv2) ).
thf(843,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(265,axiom,
! [TA: $tType,A: list @ TA,B: nat] :
( ( list_update @ TA @ A @ B @ ( nth @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_list__update__id) ).
thf(1125,plain,
! [TA: $tType,A: list @ TA,B: nat] :
( ( list_update @ TA @ A @ B @ ( nth @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(111,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(641,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(49,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(445,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_order__less__le__subst1) ).
thf(572,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(139,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_less__not__refl) ).
thf(713,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',fact_118_nat__descend__induct) ).
thf(919,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)],[206]) ).
thf(135,axiom,
no_top @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top) ).
thf(704,plain,
no_top @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(215,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat,D: nat] :
( ( A @ B )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less @ nat @ ( C @ E ) @ D ) )
=> ? [E: TA] :
( ( A @ E )
& ! [F: TA] :
( ( A @ F )
=> ( ord_less_eq @ nat @ ( C @ F ) @ ( C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Lattices__Big_Oex__has__greatest__nat) ).
thf(947,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat,D: nat] :
( ( A @ B )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less @ nat @ ( C @ E ) @ D ) )
=> ? [E: TA] :
( ( A @ E )
& ! [F: TA] :
( ( A @ F )
=> ( ord_less_eq @ nat @ ( C @ F ) @ ( C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(18,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_7) ).
thf(350,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(101,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_order__trans) ).
thf(611,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nat__neq__iff) ).
thf(787,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)],[162]) ).
thf(35,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_pinf_I3_J) ).
thf(406,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(127,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_order_Onot__eq__order__implies__strict) ).
thf(681,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(161,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( B != C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_ge__less__neq__conv) ).
thf(784,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( B != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(229,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_diff__le__self) ).
thf(1011,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(223,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_less__imp__le) ).
thf(996,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(52,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_dual__order_Oantisym) ).
thf(451,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(146,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_less__le__not__le) ).
thf(737,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(264,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_strict_desc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ TA @ ( nth @ TA @ A @ B ) @ ( nth @ TA @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_list__strict__desc__trans) ).
thf(1122,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_strict_desc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ TA @ ( nth @ TA @ A @ B ) @ ( nth @ TA @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(190,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_dense__le__bounded) ).
thf(863,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
=> ( ( ord_less_eq @ nat @ D @ C )
=> ( ord_less @ nat @ A @ ( minus_minus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_less__diff__le__imp__less) ).
thf(764,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
=> ( ( ord_less_eq @ nat @ D @ C )
=> ( ord_less @ nat @ A @ ( minus_minus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_eq__imp__le) ).
thf(604,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(196,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_infinite__descent) ).
thf(880,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)],[196]) ).
thf(115,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_eq__refl) ).
thf(649,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(199,axiom,
! [TA: $tType] :
( ( dense_order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_dense) ).
thf(890,plain,
! [TA: $tType] :
( ( dense_order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(26,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_order_Oasym) ).
thf(387,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_less__linear) ).
thf(367,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(173,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_diff__diff__cancel) ).
thf(816,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(63,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2) ).
thf(483,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(201,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( list_ex @ TA @ C @ A )
= ( list_ex @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_list__ex__cong) ).
thf(895,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( set2 @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( list_ex @ TA @ C @ A )
= ( list_ex @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(273,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( list_update @ TA @ B @ A @ C ) @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_nth__list__update__eq) ).
thf(1149,plain,
! [TA: $tType,A: nat,B: list @ TA,C: TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( list_update @ TA @ B @ A @ C ) @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(234,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
=> ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__diff__imp__less) ).
thf(1022,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
=> ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(209,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ C @ B ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_nat__diff__right__cancel__le2) ).
thf(932,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ C @ B ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(185,axiom,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_length__induct) ).
thf(848,plain,
! [TA: $tType,A: ( list @ TA ) > $o,B: list @ TA] :
( ! [C: list @ TA] :
( ! [D: list @ TA] :
( ( ord_less @ nat @ ( size_size @ ( list @ TA ) @ D ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ C ) @ A )
= ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_le__diff__swap) ).
thf(700,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ C ) @ A )
= ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_ord__eq__less__subst) ).
thf(520,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_order__le__less__subst2) ).
thf(983,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(31,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(399,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(177,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_le__imp__diff__le) ).
thf(827,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(231,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone) ).
thf(1015,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(100,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_diff__le__mono) ).
thf(608,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(219,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_diff__mono) ).
thf(986,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(261,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( append @ TA @ B @ C ) @ A )
= ( nth @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_nth__append1) ).
thf(1113,plain,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( append @ TA @ B @ C ) @ A )
= ( nth @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(116,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_less__le__trans) ).
thf(653,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_less__not__refl2) ).
thf(851,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(258,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA] :
( ( A != B )
=> ( ( nth @ TA @ ( list_update @ TA @ C @ A @ D ) @ B )
= ( nth @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_nth__list__update__neq) ).
thf(1102,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA,D: TA] :
( ( A != B )
=> ( ( nth @ TA @ ( list_update @ TA @ C @ A @ D ) @ B )
= ( nth @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(505,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(45,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_10) ).
thf(438,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(249,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ ( butlast @ TA @ B ) ) )
=> ( ( nth @ TA @ ( butlast @ TA @ B ) @ A )
= ( nth @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_nth__butlast) ).
thf(1076,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ ( butlast @ TA @ B ) ) )
=> ( ( nth @ TA @ ( butlast @ TA @ B ) @ A )
= ( nth @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(239,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ C @ B ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_nat__diff__right__cancel__le1) ).
thf(1034,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ C @ B ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le__diff__imp__le) ).
thf(589,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(214,axiom,
! [TA: $tType,A: list @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_subset__code_I1_J) ).
thf(944,plain,
! [TA: $tType,A: list @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( set2 @ TA @ A ) )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(120,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_9) ).
thf(663,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(171,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_diff__strict__mono) ).
thf(812,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(149,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_le__less__linear) ).
thf(749,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(212,axiom,
! [TA: $tType,A: list @ TA,B: set @ TA,C: TA,D: nat] :
( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
=> ( ( member @ TA @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ ( list_update @ TA @ A @ D @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_set__update__subsetI) ).
thf(939,plain,
! [TA: $tType,A: list @ TA,B: set @ TA,C: TA,D: nat] :
( ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ A ) @ B )
=> ( ( member @ TA @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( set2 @ TA @ ( list_update @ TA @ A @ D @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(15,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_less__imp__neq) ).
thf(342,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(151,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_infinite__descent__measure) ).
thf(754,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_nat__le__linear) ).
thf(553,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)],[81]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( minus_minus @ nat @ A @ C ) )
=> ( ( ord_less @ nat @ C @ A )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_nat__diff__left__cancel__eq2) ).
thf(557,plain,
! [A: nat,B: nat,C: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( minus_minus @ nat @ A @ C ) )
=> ( ( ord_less @ nat @ C @ A )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(187,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_le__eq__less__or__eq) ).
thf(855,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ B @ C ) )
= ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_eq__diff__left__iff) ).
thf(690,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ B @ C ) )
= ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(235,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_order_Ostrict__trans2) ).
thf(1025,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(37,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_pinf_I4_J) ).
thf(414,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(136,axiom,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_size__neq__size__imp__neq) ).
thf(705,plain,
! [TA: $tType] :
( ( size @ TA )
=> ! [A: TA,B: TA] :
( ( ( size_size @ TA @ A )
!= ( size_size @ TA @ B ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(276,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( ( nth @ TA @ B @ C )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_in__set__conv__nth) ).
thf(1156,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( member @ TA @ A @ ( set2 @ TA @ B ) )
= ( ? [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ B ) )
& ( ( nth @ TA @ B @ C )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(124,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_dual__order_Oorder__iff__strict) ).
thf(673,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(25,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA] : ( A @ D @ D )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_linorder__less__wlog) ).
thf(370,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA] : ( A @ D @ D )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_order__subst2) ).
thf(502,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(182,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_append__assoc) ).
thf(840,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( append @ TA @ ( append @ TA @ A @ B ) @ C )
= ( append @ TA @ A @ ( append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(169,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_not__le__imp__less) ).
thf(808,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(267,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: nat > TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( listIn521021761append @ TA @ B @ C @ A )
= ( nth @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_i__append__nth1) ).
thf(1130,plain,
! [TA: $tType,A: nat,B: list @ TA,C: nat > TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( listIn521021761append @ TA @ B @ C @ A )
= ( nth @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(252,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_list__eq__iff__nth__eq) ).
thf(1085,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
& ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(90,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_nat__less__induct) ).
thf(576,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)],[90]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(613,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(270,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_desc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ B ) @ ( nth @ TA @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_list__desc__trans__le) ).
thf(1140,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_desc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ B ) @ ( nth @ TA @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(50,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_order_Otrans) ).
thf(446,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
& ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_less__fun__def) ).
thf(595,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
& ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(66,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_dual__order_Oasym) ).
thf(497,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(221,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_append__same__eq) ).
thf(991,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( minus_minus @ nat @ A @ C )
= ( minus_minus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_eq__imp__diff__eq) ).
thf(627,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( minus_minus @ nat @ A @ C )
= ( minus_minus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(76,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_dual__order_Oeq__iff) ).
thf(539,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(130,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_leD) ).
thf(688,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_order__le__less__subst1) ).
thf(581,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(153,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ A @ C ) )
=> ( ord_less @ nat @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_nat__diff__left__cancel__less) ).
thf(759,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ A @ C ) )
=> ( ord_less @ nat @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(157,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_le__imp__less__or__eq) ).
thf(771,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(260,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_nth__equalityI) ).
thf(1108,plain,
! [TA: $tType,A: list @ TA,B: list @ TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) )
=> ( ( nth @ TA @ A @ C )
= ( nth @ TA @ B @ C ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(12,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_dual__order_Oirrefl) ).
thf(319,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(108,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( minus_minus @ nat @ C @ B ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_nat__diff__right__cancel__eq1) ).
thf(632,plain,
! [A: nat,B: nat,C: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( minus_minus @ nat @ C @ B ) )
=> ( ( ord_less @ nat @ B @ A )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(160,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_le__neq__trans) ).
thf(781,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(144,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_diff__eq__diff__eq) ).
thf(731,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(38,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_dual__order_Ostrict__trans) ).
thf(418,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(208,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_dense__le) ).
thf(929,plain,
! [TA: $tType] :
( ( dense_linorder @ TA )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(16,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_order_Ostrict__trans) ).
thf(346,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(243,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_le__refl) ).
thf(1045,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(179,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: list @ TA] :
( ( list_strict_desc @ TA @ A )
=> ( list_desc @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_list__strict__desc__imp__list__desc) ).
thf(832,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: list @ TA] :
( ( list_strict_desc @ TA @ A )
=> ( list_desc @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(128,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_less__trans) ).
thf(684,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(140,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_append__eq__appendI) ).
thf(716,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: list @ TA,E: list @ TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( append @ TA @ B @ E ) )
=> ( ( append @ TA @ A @ D )
= ( append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(800,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(262,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_asc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ C ) @ ( nth @ TA @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_list__asc__trans__le) ).
thf(1116,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_asc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ C ) @ ( nth @ TA @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(268,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( member @ TA @ ( nth @ TA @ B @ A ) @ ( set2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_nth__mem) ).
thf(1133,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( member @ TA @ ( nth @ TA @ B @ A ) @ ( set2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ B @ C )
=> ( A = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_pinf_I11_J) ).
thf(300,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(104,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less_eq @ TA @ B @ C )
=> ( A != C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_less__ge__neq__conv) ).
thf(620,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
! [C: TA] :
( ( ord_less_eq @ TA @ B @ C )
=> ( A != C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(11,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_less__imp__not__eq) ).
thf(315,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_minf_I4_J) ).
thf(410,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(163,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: nat > TA] :
( ( listIn521021761append @ TA @ A @ ( listIn521021761append @ TA @ B @ C ) )
= ( listIn521021761append @ TA @ ( append @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_i__append__assoc) ).
thf(790,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: nat > TA] :
( ( listIn521021761append @ TA @ A @ ( listIn521021761append @ TA @ B @ C ) )
= ( listIn521021761append @ TA @ ( append @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(191,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_less__asym) ).
thf(867,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(85,axiom,
! [TA: $tType] :
( ( no_top @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_gt__ex) ).
thf(564,plain,
! [TA: $tType] :
( ( no_top @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(8,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_antisym__conv3) ).
thf(305,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_linear) ).
thf(358,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( minus_minus @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Nat_Odiff__diff__eq) ).
thf(767,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( minus_minus @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( minus_minus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(121,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_order_Ostrict__implies__order) ).
thf(664,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_le__funE) ).
thf(400,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(109,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_le__less) ).
thf(635,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_ord__less__eq__subst) ).
thf(532,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_87_less__mono__imp__le__mono) ).
thf(720,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)],[141]) ).
thf(207,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1) ).
thf(928,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(56,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(464,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(89,axiom,
size @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(575,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(274,axiom,
ord_less @ nat @ x @ ( size_size @ ( list @ a ) @ ys ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(1152,plain,
ord_less @ nat @ x @ ( size_size @ ( list @ a ) @ ys ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(189,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_diff__eq__diff__less__eq) ).
thf(860,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(233,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_same__append__eq) ).
thf(1019,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA] :
( ( ( append @ TA @ A @ B )
= ( append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(175,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_less__imp__not__less) ).
thf(822,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(1,conjecture,
( ( nth @ a @ xs @ x )
= ( nth @ a @ ys @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(2,negated_conjecture,
( ( nth @ a @ xs @ x )
!= ( nth @ a @ ys @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(277,plain,
( ( nth @ a @ xs @ x )
!= ( nth @ a @ ys @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_order__subst1) ).
thf(442,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(193,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: nat > TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( listIn521021761append @ TA @ A @ C @ B )
= ( C @ ( minus_minus @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_i__append__nth2) ).
thf(871,plain,
! [TA: $tType,A: list @ TA,B: nat,C: nat > TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( listIn521021761append @ TA @ A @ C @ B )
= ( C @ ( minus_minus @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(255,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_desc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ B ) @ ( nth @ TA @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_list__desc__trans) ).
thf(1093,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ( ( list_desc @ TA )
= ( ^ [A: list @ TA] :
! [B: nat] :
( ( ord_less @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) )
=> ! [C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less_eq @ TA @ ( nth @ TA @ A @ B ) @ ( nth @ TA @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(29,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_dual__order_Otrans) ).
thf(395,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(143,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_diff__le__mono2) ).
thf(728,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(147,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_less__imp__diff__less) ).
thf(740,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(167,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_diff__right__mono) ).
thf(803,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(58,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_eq__iff) ).
thf(469,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(228,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_less__irrefl) ).
thf(1009,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_less__not__refl3) ).
thf(659,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_eq__diff__iff) ).
thf(560,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(125,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ A @ C ) )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less_eq @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_nat__diff__left__cancel__le2) ).
thf(676,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ ( minus_minus @ nat @ A @ C ) )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less_eq @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(253,axiom,
! [TA: $tType] :
( ( listIn521021761append @ TA )
= ( ^ [A: list @ TA,B: nat > TA,C: nat] : ( if @ TA @ ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) ) @ ( nth @ TA @ A @ C ) @ ( B @ ( minus_minus @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_i__append__nth) ).
thf(1088,plain,
! [TA: $tType] :
( ( listIn521021761append @ TA )
= ( ^ [A: list @ TA,B: nat > TA,C: nat] : ( if @ TA @ ( ord_less @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) ) @ ( nth @ TA @ A @ C ) @ ( B @ ( minus_minus @ nat @ C @ ( size_size @ ( list @ TA ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(95,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_less__irrefl__nat) ).
thf(592,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_le__funI) ).
thf(454,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_order__less__subst1) ).
thf(364,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1159,plain,
$false,
inference(e,[status(thm)],[645,1036,846,1031,893,941,666,352,479,1105,777,555,1005,994,308,1073,440,655,511,550,472,814,404,1001,709,885,288,301,389,724,751,934,357,542,460,902,638,421,1013,448,475,321,623,834,937,348,1051,905,480,397,877,734,998,988,428,507,527,1119,774,439,678,793,810,1067,1153,761,1047,798,1091,598,392,1042,952,625,435,830,757,1128,456,916,467,566,484,1079,1027,697,615,1064,980,1096,869,420,499,857,874,1143,328,488,669,686,642,1016,1039,547,1028,1082,837,647,1099,911,569,360,805,311,657,530,586,888,1135,425,1146,824,279,601,584,819,423,402,743,711,291,545,1007,694,843,1125,641,445,572,713,919,704,947,350,611,787,406,681,784,1011,996,451,737,1122,863,764,604,880,649,890,387,367,816,483,895,1149,1022,932,848,700,520,983,399,827,1015,608,986,1113,653,851,1102,505,438,1076,1034,589,944,663,812,749,939,342,754,553,557,855,690,1025,414,705,1156,673,370,502,840,808,1130,1085,576,613,1140,446,595,497,991,627,539,688,581,759,771,1108,319,632,781,731,418,929,346,1045,832,684,716,800,1116,1133,300,620,315,410,790,867,564,305,358,767,664,400,635,532,720,928,464,575,1152,860,1019,822,277,442,871,1093,395,728,740,803,469,1009,659,560,676,1088,592,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP101^2 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 17:39:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.98/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.80/1.12 % [INFO] Parsing done (258ms).
% 1.80/1.12 % [INFO] Running in sequential loop mode.
% 2.67/1.34 % [INFO] eprover registered as external prover.
% 2.67/1.35 % [INFO] cvc4 registered as external prover.
% 2.67/1.35 % [INFO] Scanning for conjecture ...
% 2.82/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 286 axioms. Running axiom selection ...
% 3.26/1.54 % [INFO] Axiom selection finished. Selected 274 axioms (removed 12 axioms).
% 3.93/1.72 % [INFO] Problem is higher-order (TPTP THF).
% 3.93/1.74 % [INFO] Type checking passed.
% 3.93/1.74 % [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 ...
% 37.78/23.89 % External prover 'e' found a proof!
% 37.78/23.89 % [INFO] Killing All external provers ...
% 37.78/23.89 % Time passed: 23370ms (effective reasoning time: 22762ms)
% 37.78/23.89 % 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)>
% 37.78/23.89 % Axioms used in derivation (274): fact_102_list__update__append, fact_162_less__imp__not__eq, fact_185_pinf_I4_J, fact_186_pinf_I5_J, fact_188_pinf_I11_J, fact_153_less__imp__not__less, fact_88_eq__diff__iff, tcon_Nat_Onat___Orderings_Oorder_2, fact_206_dual__order_Ostrict__trans2, fact_176_gt__ex, fact_167_less__linear, fact_81_le__greater__neq__conv, fact_52_same__append__eq, fact_214_le__imp__less__or__eq, fact_122_le__funE, fact_239_set__swap, fact_121_le__funD, fact_118_nat__descend__induct, fact_69_Nat_Oex__has__greatest__nat, tcon_Nat_Onat___Orderings_Olinorder, fact_246_one__reorient, fact_113_list__desc__trans__le, fact_193_minf_I5_J, tcon_Nat_Onat___Nat_Osize, tcon_Nat_Onat___Orderings_Ono__top, fact_120_minf_I8_J, fact_207_dual__order_Ostrict__trans1, fact_228_order__le__less__subst2, fact_97_le__imp__diff__le, fact_241_length__butlast, fact_30_i__append__def, fact_84_le__eq__less__or__eq, fact_150_dual__order_Ostrict__trans, tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, fact_181_ord__eq__less__subst, fact_177_lt__ex, fact_58_nth__list__update__neq, fact_67_list__update__swap, fact_140_order__class_Oorder_Oantisym, fact_61_list__update__beyond, fact_68_append__eq__appendI, fact_66_nat__le__linear, fact_166_less__irrefl, fact_8_nat__diff__left__cancel__eq1, fact_244_less__fun__def, fact_194_minf_I7_J, fact_70_append__eq__append__conv2, fact_231_le__less, tcon_fun___Orderings_Oord, fact_161_less__not__sym, fact_54_diff__diff__cancel, fact_101_nat__diff__right__cancel__le2, fact_156_linorder__cases, fact_40_list__ex__length, fact_245_in__set__butlastD, fact_32_nat__diff__right__cancel__less, fact_99_le__diff__le__imp__le, fact_39_list__strict__asc__trans, fact_16_linorder__neqE__nat, fact_63_le__trans, fact_108_nat__diff__right__cancel__le1, fact_86_le__neq__implies__less, fact_213_less__le__not__le, fact_164_ord__less__eq__trans, fact_251_in__set__conv__nth, fact_235_pinf_I8_J, fact_180_ord__less__eq__subst, fact_33_nat__diff__right__cancel__eq2, fact_219_le__less__trans, fact_242_subset__code_I1_J, fact_201_dual__order_Ostrict__iff__order, fact_56_length__list__update, fact_51_append__same__eq, fact_230_less__le, fact_90_Nat_Odiff__diff__eq, fact_168_less__trans, fact_252_all__nth__imp__all__set, tcon_Nat_Onat___Groups_Oone, fact_163_dual__order_Oasym, fact_4_i__append__nth1, fact_87_less__mono__imp__le__mono, fact_106_less__diff__le__imp__less, fact_49_append_Oassoc, fact_170_less__asym, fact_187_pinf_I7_J, fact_212_not__le__imp__less, fact_123_le__funI, fact_18_nat__less__induct, fact_34_diff__strict__right__mono, fact_46_Collect__mem__eq, fact_15_infinite__descent__measure, fact_173_order_Oasym, fact_192_minf_I4_J, fact_129_eq__iff, fact_172_dense, fact_139_ord__le__eq__trans, tcon_HOL_Obool___Orderings_Oorder_11, fact_184_pinf_I3_J, fact_190_minf_I2_J, tcon_HOL_Obool___Orderings_Olinorder_10, fact_155_dual__order_Oirrefl, fact_1_Skolem__list__nth, fact_128_ord__le__eq__subst, conj_2, fact_221_antisym__conv2, fact_117_order__refl, help_If_1_1_T, fact_78_ge__less__neq__conv, fact_208_order_Ostrict__iff__order, fact_19_less__irrefl__nat, fact_75_list__strict__asc__trans__le, fact_24_size__neq__size__imp__neq, fact_232_leI, fact_157_less__imp__triv, fact_227_order__less__le__subst1, fact_142_dual__order_Orefl, fact_55_append__eq__append__conv, fact_73_diff__right__mono, fact_236_minf_I6_J, fact_130_antisym, fact_136_antisym__conv, fact_250_list__ball__nth, tcon_Set_Oset___Orderings_Oorder_6, fact_182_pinf_I1_J, fact_151_linorder__less__wlog, fact_147_dual__order_Ostrict__implies__not__eq, fact_17_infinite__descent, fact_132_eq__refl, fact_154_order_Ostrict__trans, fact_25_neq__if__length__neq, tcon_Set_Oset___Orderings_Oord_7, fact_29_i__append__nth, fact_45_mem__Collect__eq, fact_44_nth__butlast, fact_205_dense__ge__bounded, fact_43_nth__list__update__eq, fact_233_leD, fact_137_order__class_Oorder_Oeq__iff, fact_223_le__neq__trans, fact_200_dual__order_Ostrict__implies__order, fact_126_order__subst2, fact_174_neq__iff, fact_195_minf_I11_J, fact_100_nat__diff__left__cancel__le2, fact_204_dense__le__bounded, fact_248_in__set__butlast__appendI, fact_93_le__diff__iff_H, fact_114_list__asc__trans__le, tcon_Nat_Onat___Orderings_Oord_3, fact_253_all__set__conv__all__nth, fact_222_antisym__conv1, fact_74_diff__eq__diff__less__eq, fact_80_greater__le__neq__conv, tcon_HOL_Obool___Orderings_Opreorder_9, fact_217_dense__ge, fact_26_Ex__list__of__length, fact_220_less__imp__le, fact_247_list__ex__cong, fact_94_diff__le__mono2, fact_62_le__refl, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_95_le__diff__swap, fact_47_Collect__cong, help_If_3_1_T, fact_91_diff__le__mono, fact_59_list__ex__append, fact_198_list__strict__desc__imp__list__desc, fact_60_i__append__assoc, fact_189_minf_I1_J, tcon_List_Olist___Nat_Osize_14, fact_20_less__not__refl3, fact_42_nth__append, help_If_2_1_T, fact_159_antisym__conv3, fact_96_le__diff__imp__le, fact_72_diff__left__mono, fact_215_le__less__linear, fact_53_list__update__overwrite, fact_125_order__subst1, fact_105_diff__less__mono, fact_216_dense__le, fact_169_less__asym_H, fact_79_less__ge__neq__conv, fact_82_nat__less__le, fact_165_ord__eq__less__trans, fact_158_less__imp__not__eq2, fact_199_order_Onot__eq__order__implies__strict, fact_85_less__or__eq__imp__le, fact_77_nth__append2, fact_131_linear, conj_1, fact_50_append__assoc, tcon_fun___Orderings_Opreorder, fact_2_list__eq__iff__nth__eq, fact_98_eq__diff__left__iff, fact_179_order__less__subst1, fact_119_Lattices__Big_Oex__has__greatest__nat, tcon_Nat_Onat___Orderings_Opreorder_1, fact_234_pinf_I6_J, fact_37_diff__strict__mono, fact_116_list__asc__trans, fact_202_dual__order_Oorder__iff__strict, fact_22_less__not__refl, fact_175_neqE, fact_10_nat__diff__left__cancel__less, fact_135_le__cases3, fact_21_less__not__refl2, fact_76_list__update__append1, fact_211_order_Ostrict__trans1, fact_148_order_Ostrict__implies__not__eq, fact_6_less__imp__diff__less, fact_144_dual__order_Otrans, fact_71_diff__mono, tcon_fun___Orderings_Oorder, fact_210_order_Ostrict__trans2, fact_27_eq__imp__diff__eq, fact_104_less__diff__iff, fact_92_diff__le__self, fact_218_less__le__trans, fact_249_nth__mem, fact_240_butlast__list__update, fact_0_nth__equalityI, fact_133_le__cases, fact_7_less__diff__imp__less, fact_127_ord__eq__le__subst, fact_183_pinf_I2_J, fact_124_le__fun__def, fact_143_linorder__wlog, fact_31_length__induct, fact_65_le__antisym, fact_134_order_Otrans, fact_149_not__less__iff__gr__or__eq, fact_109_nth__list__update, fact_224_not__less, fact_197_list__strict__asc__imp__list__asc, fact_254_verit__la__disequality, fact_38_list__strict__desc__trans, fact_146_dual__order_Oantisym, fact_35_diff__strict__left__mono, tcon_HOL_Obool___Orderings_Oord_12, fact_145_dual__order_Oeq__iff, tcon_Set_Oset___Orderings_Opreorder_5, fact_107_nat__diff__left__cancel__le1, fact_41_i__append__nth2, fact_83_less__imp__le__nat, fact_226_order__less__le__subst2, fact_9_nat__diff__left__cancel__eq2, fact_11_nat__diff__right__cancel__eq1, fact_64_eq__imp__le, conj_0, fact_5_diff__less__mono2, fact_225_not__le, fact_138_ord__eq__le__trans, fact_209_order_Oorder__iff__strict, fact_36_diff__eq__diff__less, fact_57_list__update__id, fact_23_nat__neq__iff, fact_191_minf_I3_J, fact_229_order__le__less__subst1, fact_238_verit__comp__simplify1_I3_J, fact_237_complete__interval, fact_178_order__less__subst2, fact_243_set__update__subsetI, fact_112_diff__right__commute, fact_196_ex__has__least__nat, fact_115_list__desc__trans, fact_103_nth__append1, fact_171_less__imp__neq, fact_110_list__update__same__conv, fact_89_le__diff__iff, fact_141_order__trans, fact_28_diff__commute, fact_111_diff__eq__diff__eq, fact_203_order_Ostrict__implies__order
% 37.78/23.89 % No. of inferences in proof: 552
% 37.78/23.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23370 ms resp. 22762 ms w/o parsing
% 38.65/24.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.65/24.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------