TSTP Solution File: ITP099^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP099^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:49 EDT 2024
% Result : Theorem 189.33s 96.63s
% Output : Refutation 189.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 321
% Syntax : Number of formulae : 606 ( 108 unt; 40 typ; 0 def)
% Number of atoms : 2005 ( 484 equ; 10 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 7110 ( 165 ~; 49 |; 97 &;5755 @)
% ( 0 <=>;1044 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 233 ( 233 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 40 usr; 7 con; 0-4 aty)
% Number of variables : 2090 ( 118 ^1852 !; 85 ?;2090 :)
% ( 35 !>; 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(minus_type,type,
minus:
!>[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(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(dense_order_type,type,
dense_order:
!>[TA: $tType] : $o ).
thf(dense_linorder_type,type,
dense_linorder:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(condit1656338222tinuum_type,type,
condit1656338222tinuum:
!>[TA: $tType] : $o ).
thf(condit1037483654norder_type,type,
condit1037483654norder:
!>[TA: $tType] : $o ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > 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(listIn1569887318i_drop_type,type,
listIn1569887318i_drop:
!>[TA: $tType] : ( nat > ( nat > TA ) > nat > TA ) ).
thf(listIn1033672622i_take_type,type,
listIn1033672622i_take:
!>[TA: $tType] : ( nat > ( nat > TA ) > ( list @ TA ) ) ).
thf(append_type,type,
append:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(drop_type,type,
drop:
!>[TA: $tType] : ( nat > ( list @ TA ) > ( list @ TA ) ) ).
thf(last_type,type,
last:
!>[TA: $tType] : ( ( list @ TA ) > 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(f_type,type,
f: nat > a ).
thf(n_type,type,
n: nat ).
thf(xs_type,type,
xs: list @ a ).
thf(260,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_57_Nat_Oex__has__greatest__nat) ).
thf(1105,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)],[260]) ).
thf(115,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_97_nat__diff__left__cancel__le1) ).
thf(628,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)],[115]) ).
thf(252,axiom,
! [TA: $tType,A: list @ TA,B: nat > TA,C: list @ TA,D: nat > TA] :
( ( ( listIn521021761append @ TA @ A @ B )
= ( listIn521021761append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( listIn521021761append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( listIn521021761append @ TA @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_i__append__eq__i__append__conv2) ).
thf(1083,plain,
! [TA: $tType,A: list @ TA,B: nat > TA,C: list @ TA,D: nat > TA] :
( ( ( listIn521021761append @ TA @ A @ B )
= ( listIn521021761append @ TA @ C @ D ) )
= ( ? [E: list @ TA] :
( ( ( A
= ( append @ TA @ C @ E ) )
& ( ( listIn521021761append @ TA @ E @ B )
= D ) )
| ( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( listIn521021761append @ TA @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(129,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_dual__order_Ostrict__implies__not__eq) ).
thf(666,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(25,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_134_dual__order_Otrans) ).
thf(352,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)],[25]) ).
thf(121,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_34_diff__strict__mono) ).
thf(645,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)],[121]) ).
thf(200,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_195_dense__ge) ).
thf(892,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)],[200]) ).
thf(135,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_nat__less__le) ).
thf(683,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(151,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_86_nat__diff__left__cancel__le2) ).
thf(730,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)],[151]) ).
thf(225,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( minus_minus @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_add__diff__cancel__left) ).
thf(994,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( minus_minus @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(10,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_133_linorder__wlog) ).
thf(308,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)],[10]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(440,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(111,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_171_ord__eq__less__subst) ).
thf(614,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)],[111]) ).
thf(190,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_less__imp__not__eq2) ).
thf(861,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(81,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_add__diff__cancel__left_H) ).
thf(523,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(279,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_26_size__neq__size__imp__neq) ).
thf(1158,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)],[279]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_less__not__refl3) ).
thf(582,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(162,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_60_diff__left__mono) ).
thf(762,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)],[162]) ).
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_96_less__diff__le__imp__less) ).
thf(741,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(249,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_less__not__refl2) ).
thf(1073,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(194,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_8_nat__diff__left__cancel__eq2) ).
thf(873,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)],[194]) ).
thf(56,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_225_minf_I1_J) ).
thf(449,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)],[56]) ).
thf(32,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_235_list__strict__desc__imp__list__desc) ).
thf(385,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)],[32]) ).
thf(90,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_less__induct) ).
thf(550,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(281,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_194_dense__le) ).
thf(1164,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)],[281]) ).
thf(62,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_nat__add__left__cancel__le) ).
thf(472,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(140,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_181_order_Ostrict__implies__order) ).
thf(698,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)],[140]) ).
thf(207,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_108_list__asc__trans__le) ).
thf(913,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)],[207]) ).
thf(130,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_93_list__eq__iff__nth__eq) ).
thf(670,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)],[130]) ).
thf(202,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: nat > TA] :
( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( listIn1569887318i_drop @ TA @ A @ ( listIn521021761append @ TA @ B @ C ) )
= ( listIn521021761append @ TA @ ( drop @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_i__append__i__drop__eq1) ).
thf(898,plain,
! [TA: $tType,A: nat,B: list @ TA,C: nat > TA] :
( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( listIn1569887318i_drop @ TA @ A @ ( listIn521021761append @ TA @ B @ C ) )
= ( listIn521021761append @ TA @ ( drop @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(144,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_101_diff__right__commute) ).
thf(709,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)],[144]) ).
thf(197,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_98_nat__diff__right__cancel__le1) ).
thf(885,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)],[197]) ).
thf(8,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_126_antisym__conv) ).
thf(301,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)],[8]) ).
thf(14,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_110_list__strict__asc__imp__list__asc) ).
thf(320,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)],[14]) ).
thf(182,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_159_less__asym_H) ).
thf(829,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)],[182]) ).
thf(40,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_123_le__cases) ).
thf(404,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)],[40]) ).
thf(34,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_order__class_Oorder_Oantisym) ).
thf(389,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)],[34]) ).
thf(147,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_74_eq__diff__iff) ).
thf(719,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)],[147]) ).
thf(28,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_131_order__trans) ).
thf(372,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)],[28]) ).
thf(22,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_129_ord__le__eq__trans) ).
thf(344,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)],[22]) ).
thf(211,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_10_nat__diff__right__cancel__eq1) ).
thf(949,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)],[211]) ).
thf(275,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_50_i__append__nth1) ).
thf(1147,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)],[275]) ).
thf(193,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_47_diff__diff__cancel) ).
thf(870,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)],[193]) ).
thf(165,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_223_minf_I3_J) ).
thf(770,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)],[165]) ).
thf(16,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_128_ord__eq__le__trans) ).
thf(325,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)],[16]) ).
thf(12,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_6) ).
thf(316,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(196,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_81_le__diff__swap) ).
thf(881,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)],[196]) ).
thf(44,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(416,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(63,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_add__diff__cancel__right_H) ).
thf(475,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(171,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_105_list__desc__trans__le) ).
thf(789,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)],[171]) ).
thf(243,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_155_ord__eq__less__trans) ).
thf(1040,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)],[243]) ).
thf(113,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_le__refl) ).
thf(623,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(23,axiom,
minus @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ominus_9) ).
thf(348,plain,
minus @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(176,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_189_order_Ostrict__trans1) ).
thf(806,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)],[176]) ).
thf(65,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( minus_minus @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_add__diff__cancel__right) ).
thf(480,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( minus_minus @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(107,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_39_i__append__nth) ).
thf(602,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)],[107]) ).
thf(37,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_119_eq__iff) ).
thf(397,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)],[37]) ).
thf(117,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_215_pinf_I6_J) ).
thf(634,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)],[117]) ).
thf(138,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_200_antisym__conv1) ).
thf(692,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)],[138]) ).
thf(166,axiom,
! [TA: $tType] :
( ( no_bot @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_lt__ex) ).
thf(774,plain,
! [TA: $tType] :
( ( no_bot @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(48,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_111_le__funD) ).
thf(428,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)],[48]) ).
thf(4,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_44_append__same__eq) ).
thf(292,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)],[4]) ).
thf(76,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_less__not__refl) ).
thf(510,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(511,plain,
~ ? [A: nat] : ( ord_less @ nat @ A @ A ),
inference(miniscope,[status(thm)],[510]) ).
thf(512,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(cnf,[status(esa)],[511]) ).
thf(83,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_diff__add__cancel) ).
thf(529,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(85,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_205_order__less__le__subst1) ).
thf(534,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)],[85]) ).
thf(247,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_30_diff__commute) ).
thf(1067,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)],[247]) ).
thf(245,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_180_dual__order_Oorder__iff__strict) ).
thf(1047,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)],[245]) ).
thf(206,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: nat > TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( listIn1569887318i_drop @ TA @ B @ ( listIn521021761append @ TA @ A @ C ) )
= ( listIn1569887318i_drop @ TA @ ( minus_minus @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_i__append__i__drop__eq2) ).
thf(910,plain,
! [TA: $tType,A: list @ TA,B: nat,C: nat > TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( listIn1569887318i_drop @ TA @ B @ ( listIn521021761append @ TA @ A @ C ) )
= ( listIn1569887318i_drop @ TA @ ( minus_minus @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(157,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_38_i__append__nth2) ).
thf(746,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)],[157]) ).
thf(168,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_19_infinite__descent) ).
thf(778,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)],[168]) ).
thf(212,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_18_linorder__neqE__nat) ).
thf(952,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)],[212]) ).
thf(24,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_127_order__class_Oorder_Oeq__iff) ).
thf(349,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)],[24]) ).
thf(94,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_193_le__less__linear) ).
thf(561,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)],[94]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(392,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(179,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_232_pinf_I1_J) ).
thf(815,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)],[179]) ).
thf(150,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_219_minf_I11_J) ).
thf(729,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(42,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_order__refl) ).
thf(407,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(116,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_27_neq__if__length__neq) ).
thf(630,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)],[116]) ).
thf(96,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_158_less__trans) ).
thf(566,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)],[96]) ).
thf(240,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_192_le__imp__less__or__eq) ).
thf(1032,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)],[240]) ).
thf(114,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_add__diff__cancel) ).
thf(625,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(51,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_58_append__eq__append__conv2) ).
thf(435,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)],[51]) ).
thf(17,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_218_verit__la__disequality) ).
thf(329,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)],[17]) ).
thf(128,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(665,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(58,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(461,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)],[58]) ).
thf(69,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_227_pinf_I7_J) ).
thf(493,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)],[69]) ).
thf(237,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1) ).
thf(1027,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(134,axiom,
no_top @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top) ).
thf(682,plain,
no_top @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(266,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_12_nat__diff__right__cancel__less) ).
thf(1128,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)],[266]) ).
thf(231,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_nat__add__left__cancel__less) ).
thf(1012,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(208,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_213_complete__interval) ).
thf(916,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)],[208]) ).
thf(60,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_less__irrefl) ).
thf(467,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(255,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_84_eq__diff__left__iff) ).
thf(1089,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)],[255]) ).
thf(13,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_43_append__assoc) ).
thf(317,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)],[13]) ).
thf(233,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_verit__comp__simplify1_I1_J) ).
thf(1017,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(264,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_eq__imp__le) ).
thf(1121,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(261,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_less__irrefl__nat) ).
thf(1111,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(257,axiom,
! [TA: $tType,A: list @ TA,B: nat,C: nat > TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( listIn1033672622i_take @ TA @ B @ ( listIn521021761append @ TA @ A @ C ) )
= ( append @ TA @ A @ ( listIn1033672622i_take @ TA @ ( minus_minus @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_i__append__i__take__eq2) ).
thf(1096,plain,
! [TA: $tType,A: list @ TA,B: nat,C: nat > TA] :
( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ B )
=> ( ( listIn1033672622i_take @ TA @ B @ ( listIn521021761append @ TA @ A @ C ) )
= ( append @ TA @ A @ ( listIn1033672622i_take @ TA @ ( minus_minus @ nat @ B @ ( size_size @ ( list @ TA ) @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(271,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2) ).
thf(1138,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(73,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_162_dense) ).
thf(499,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)],[73]) ).
thf(223,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_61_diff__right__mono) ).
thf(989,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)],[223]) ).
thf(79,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(519,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(101,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_175_list__strict__asc__trans) ).
thf(578,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)],[101]) ).
thf(169,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_83_le__imp__diff__le) ).
thf(783,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)],[169]) ).
thf(263,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_62_diff__eq__diff__less__eq) ).
thf(1118,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)],[263]) ).
thf(238,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_188_order_Ostrict__trans2) ).
thf(1028,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)],[238]) ).
thf(86,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_216_pinf_I8_J) ).
thf(537,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)],[86]) ).
thf(203,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_less__le) ).
thf(901,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)],[203]) ).
thf(120,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_199_antisym__conv2) ).
thf(642,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)],[120]) ).
thf(82,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_33_diff__eq__diff__less) ).
thf(526,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)],[82]) ).
thf(278,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_165_neqE) ).
thf(1155,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)],[278]) ).
thf(133,axiom,
! [TA: $tType,A: list @ TA,B: nat > TA,C: nat > TA] :
( ( ( listIn521021761append @ TA @ A @ B )
= ( listIn521021761append @ TA @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_same__i__append__eq) ).
thf(679,plain,
! [TA: $tType,A: list @ TA,B: nat > TA,C: nat > TA] :
( ( ( listIn521021761append @ TA @ A @ B )
= ( listIn521021761append @ TA @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(216,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_55_nat__le__linear) ).
thf(970,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)],[216]) ).
thf(262,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_94_less__diff__iff) ).
thf(1114,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)],[262]) ).
thf(258,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_174_list__asc__trans) ).
thf(1099,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)],[258]) ).
thf(276,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__eq__less__or__eq) ).
thf(1150,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(154,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_80_diff__le__mono2) ).
thf(738,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)],[154]) ).
thf(268,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_144_order_Ostrict__trans) ).
thf(1131,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)],[268]) ).
thf(246,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_141_linorder__less__wlog) ).
thf(1050,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)],[246]) ).
thf(221,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_236_minf_I8_J) ).
thf(984,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)],[221]) ).
thf(227,axiom,
! [TA: $tType] : ( size @ ( list @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_10) ).
thf(1002,plain,
! [TA: $tType] : ( size @ ( list @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(108,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA] :
( ( drop @ TA @ A @ ( append @ TA @ B @ C ) )
= ( append @ TA @ ( drop @ TA @ A @ B ) @ ( drop @ TA @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_drop__append) ).
thf(605,plain,
! [TA: $tType,A: nat,B: list @ TA,C: list @ TA] :
( ( drop @ TA @ A @ ( append @ TA @ B @ C ) )
= ( append @ TA @ ( drop @ TA @ A @ B ) @ ( drop @ TA @ ( minus_minus @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(122,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_185_dual__order_Ostrict__trans1) ).
thf(647,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)],[122]) ).
thf(226,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_107_Lattices__Big_Oex__has__greatest__nat) ).
thf(997,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)],[226]) ).
thf(172,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_less__imp__neq) ).
thf(792,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(253,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_198_less__imp__le) ).
thf(1086,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)],[253]) ).
thf(175,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3) ).
thf(805,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(88,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_170_ord__less__eq__subst) ).
thf(541,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)],[88]) ).
thf(241,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_9_nat__diff__left__cancel__less) ).
thf(1035,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)],[241]) ).
thf(92,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_211_leD) ).
thf(558,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)],[92]) ).
thf(282,axiom,
wellorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(1167,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(104,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_224_minf_I2_J) ).
thf(586,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)],[104]) ).
thf(127,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_40_i__append__def) ).
thf(662,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)],[127]) ).
thf(6,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_dual__order_Orefl) ).
thf(298,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(270,axiom,
! [TA: $tType,A: nat,B: list @ TA,C: nat] :
( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( drop @ TA @ A @ B ) @ C )
= ( nth @ TA @ B @ ( plus_plus @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_nth__drop) ).
thf(1135,plain,
! [TA: $tType,A: nat,B: list @ TA,C: nat] :
( ( ord_less_eq @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( nth @ TA @ ( drop @ TA @ A @ B ) @ C )
= ( nth @ TA @ B @ ( plus_plus @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(47,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_add__left__cancel) ).
thf(425,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(180,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_220_minf_I7_J) ).
thf(824,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)],[180]) ).
thf(99,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_221_minf_I5_J) ).
thf(573,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)],[99]) ).
thf(137,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_82_le__diff__imp__le) ).
thf(689,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)],[137]) ).
thf(55,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_71_less__or__eq__imp__le) ).
thf(444,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)],[55]) ).
thf(30,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_118_ord__le__eq__subst) ).
thf(375,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)],[30]) ).
thf(77,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_52_le__trans) ).
thf(513,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)],[77]) ).
thf(49,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_42_append_Oassoc) ).
thf(430,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)],[49]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_measure__induct) ).
thf(904,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(39,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_124_order_Otrans) ).
thf(402,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)],[39]) ).
thf(152,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_92_Skolem__list__nth) ).
thf(732,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)],[152]) ).
thf(181,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_add__less__cancel__left) ).
thf(826,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(3,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(291,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(185,axiom,
! [TA: $tType,A: list @ TA,B: nat > TA,C: list @ TA,D: nat > TA] :
( ( ( listIn521021761append @ TA @ A @ B )
= ( listIn521021761append @ TA @ C @ D ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ? [E: list @ TA] :
( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( listIn521021761append @ TA @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_i__append__eq__i__append__conv2__aux) ).
thf(843,plain,
! [TA: $tType,A: list @ TA,B: nat > TA,C: list @ TA,D: nat > TA] :
( ( ( listIn521021761append @ TA @ A @ B )
= ( listIn521021761append @ TA @ C @ D ) )
=> ( ( ord_less_eq @ nat @ ( size_size @ ( list @ TA ) @ A ) @ ( size_size @ ( list @ TA ) @ C ) )
=> ? [E: list @ TA] :
( ( ( append @ TA @ A @ E )
= C )
& ( B
= ( listIn521021761append @ TA @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(265,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_172_ex__has__least__nat) ).
thf(1125,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)],[265]) ).
thf(272,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_143_less__imp__not__less) ).
thf(1139,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)],[272]) ).
thf(31,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_add__le__cancel__left) ).
thf(382,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(11,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_120_antisym) ).
thf(313,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)],[11]) ).
thf(72,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(498,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(19,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_135_dual__order_Oeq__iff) ).
thf(335,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)],[19]) ).
thf(41,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_8) ).
thf(406,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(183,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_231_pinf_I2_J) ).
thf(831,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)],[183]) ).
thf(45,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_115_order__subst1) ).
thf(419,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)],[45]) ).
thf(274,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_157_less__linear) ).
thf(1144,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)],[274]) ).
thf(123,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: nat > TA,E: nat > TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( listIn521021761append @ TA @ B @ E ) )
=> ( ( listIn521021761append @ TA @ A @ D )
= ( listIn521021761append @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_i__append__eq__i__appendI) ).
thf(649,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: list @ TA,D: nat > TA,E: nat > TA] :
( ( ( append @ TA @ A @ B )
= C )
=> ( ( D
= ( listIn521021761append @ TA @ B @ E ) )
=> ( ( listIn521021761append @ TA @ A @ D )
= ( listIn521021761append @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(106,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_7_nat__diff__left__cancel__eq1) ).
thf(599,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)],[106]) ).
thf(163,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_76_Nat_Odiff__diff__eq) ).
thf(764,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)],[163]) ).
thf(219,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: nat > TA,D: nat > TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ( listIn521021761append @ TA @ A @ C )
= ( listIn521021761append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_i__append__eq__i__append__conv) ).
thf(979,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: nat > TA,D: nat > TA] :
( ( ( size_size @ ( list @ TA ) @ A )
= ( size_size @ ( list @ TA ) @ B ) )
=> ( ( ( listIn521021761append @ TA @ A @ C )
= ( listIn521021761append @ TA @ B @ D ) )
= ( ( A = B )
& ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(199,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_178_dual__order_Ostrict__implies__order) ).
thf(890,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)],[199]) ).
thf(33,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_113_le__funI) ).
thf(387,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)],[33]) ).
thf(251,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_146_linorder__cases) ).
thf(1080,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)],[251]) ).
thf(189,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_67_le__greater__neq__conv) ).
thf(858,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)],[189]) ).
thf(112,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_160_less__asym) ).
thf(621,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)],[112]) ).
thf(66,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_202_not__less) ).
thf(483,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)],[66]) ).
thf(201,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_fun__diff__def) ).
thf(895,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_minus__apply) ).
thf(964,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TB )
=> ( ( minus_minus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( minus_minus @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(235,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_164_neq__iff) ).
thf(1022,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)],[235]) ).
thf(280,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_diff__le__self) ).
thf(1162,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(149,axiom,
! [TA: $tType,A: nat,B: nat,C: nat > TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( listIn1569887318i_drop @ TA @ A @ C @ ( minus_minus @ nat @ B @ A ) )
= ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_i__drop__nth__sub) ).
thf(726,plain,
! [TA: $tType,A: nat,B: nat,C: nat > TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( listIn1569887318i_drop @ TA @ A @ C @ ( minus_minus @ nat @ B @ A ) )
= ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(186,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_186_order_Ostrict__iff__order) ).
thf(848,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)],[186]) ).
thf(141,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_90_nth__append) ).
thf(700,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)],[141]) ).
thf(80,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_176_list__desc__trans) ).
thf(520,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)],[80]) ).
thf(136,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_183_dense__ge__bounded) ).
thf(685,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)],[136]) ).
thf(164,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_140_dual__order_Ostrict__trans) ).
thf(768,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)],[164]) ).
thf(192,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_order_Oasym) ).
thf(868,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)],[192]) ).
thf(232,axiom,
! [TA: $tType] :
( ( no_top @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_gt__ex) ).
thf(1015,plain,
! [TA: $tType] :
( ( no_top @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(109,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order_Ostrict__implies__not__eq) ).
thf(608,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(95,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_diff__diff__left) ).
thf(563,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(124,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_85_le__diff__le__imp__le) ).
thf(653,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)],[124]) ).
thf(139,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_169_order__less__subst1) ).
thf(695,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)],[139]) ).
thf(118,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_95_diff__less__mono) ).
thf(636,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)],[118]) ).
thf(244,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_6_less__diff__imp__less) ).
thf(1044,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)],[244]) ).
thf(36,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_add__right__cancel) ).
thf(394,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(222,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_4_diff__less__mono2) ).
thf(986,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)],[222]) ).
thf(187,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_182_dense__le__bounded) ).
thf(851,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)],[187]) ).
thf(259,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_11_nat__diff__right__cancel__eq2) ).
thf(1102,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)],[259]) ).
thf(75,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_20_nat__less__induct) ).
thf(505,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)],[75]) ).
thf(52,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_112_le__funE) ).
thf(438,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)],[52]) ).
thf(68,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_54_le__antisym) ).
thf(490,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)],[68]) ).
thf(209,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_237_minf_I6_J) ).
thf(944,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)],[209]) ).
thf(89,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_59_diff__mono) ).
thf(548,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)],[89]) ).
thf(29,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_7) ).
thf(374,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(178,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_201_le__neq__trans) ).
thf(812,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)],[178]) ).
thf(158,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( drop @ TA @ A @ B ) )
= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_length__drop) ).
thf(749,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( size_size @ ( list @ TA ) @ ( drop @ TA @ A @ B ) )
= ( minus_minus @ nat @ ( size_size @ ( list @ TA ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(78,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_5_less__imp__diff__less) ).
thf(516,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)],[78]) ).
thf(91,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_29_eq__imp__diff__eq) ).
thf(553,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)],[91]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_measure__induct__rule) ).
thf(458,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(167,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_151_less__not__sym) ).
thf(776,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)],[167]) ).
thf(145,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_75_le__diff__iff) ).
thf(712,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)],[145]) ).
thf(188,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_139_not__less__iff__gr__or__eq) ).
thf(855,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)],[188]) ).
thf(248,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_66_greater__le__neq__conv) ).
thf(1070,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)],[248]) ).
thf(142,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_87_nat__diff__right__cancel__le2) ).
thf(705,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)],[142]) ).
thf(143,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_190_not__le__imp__less) ).
thf(707,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)],[143]) ).
thf(198,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_206_order__le__less__subst2) ).
thf(887,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)],[198]) ).
thf(43,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_117_ord__eq__le__subst) ).
thf(409,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)],[43]) ).
thf(236,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_197_le__less__trans) ).
thf(1025,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)],[236]) ).
thf(5,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_46_same__append__eq) ).
thf(295,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)],[5]) ).
thf(131,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__less__cancel__right) ).
thf(673,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(74,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_65_less__ge__neq__conv) ).
thf(502,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)],[74]) ).
thf(184,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_203_not__le) ).
thf(840,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)],[184]) ).
thf(20,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_114_le__fun__def) ).
thf(338,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)],[20]) ).
thf(177,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_222_minf_I4_J) ).
thf(808,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)],[177]) ).
thf(267,axiom,
condit1037483654norder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder) ).
thf(1130,plain,
condit1037483654norder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(205,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_217_less__fun__def) ).
thf(907,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)],[205]) ).
thf(156,axiom,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_ex__gt__or__lt) ).
thf(744,plain,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(273,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_25_nat__neq__iff) ).
thf(1141,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)],[273]) ).
thf(125,axiom,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
! [C: nat] :
( ( drop @ TA @ C @ A )
= ( drop @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_list__drop__eq__conv) ).
thf(656,plain,
! [TA: $tType] :
( ( (=) @ ( list @ TA ) )
= ( ^ [A: list @ TA,B: list @ TA] :
! [C: nat] :
( ( drop @ TA @ C @ A )
= ( drop @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(229,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_147_less__imp__triv) ).
thf(1008,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)],[229]) ).
thf(98,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_31_diff__strict__right__mono) ).
thf(571,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)],[98]) ).
thf(105,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_79_le__diff__iff_H) ).
thf(595,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)],[105]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__imp__le__nat) ).
thf(612,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(224,axiom,
! [TA: $tType,A: nat,B: nat,C: list @ TA] :
( ( drop @ TA @ A @ ( drop @ TA @ B @ C ) )
= ( drop @ TA @ ( plus_plus @ nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_drop__drop) ).
thf(991,plain,
! [TA: $tType,A: nat,B: nat,C: list @ TA] :
( ( drop @ TA @ A @ ( drop @ TA @ B @ C ) )
= ( drop @ TA @ ( plus_plus @ nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(71,axiom,
size @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize) ).
thf(497,plain,
size @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(195,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_48_append__eq__append__conv) ).
thf(876,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)],[195]) ).
thf(87,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_228_pinf_I5_J) ).
thf(539,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)],[87]) ).
thf(218,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_149_antisym__conv3) ).
thf(976,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)],[218]) ).
thf(102,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(581,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(70,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_210_leI) ).
thf(495,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)],[70]) ).
thf(161,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_214_verit__comp__simplify1_I3_J) ).
thf(759,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)],[161]) ).
thf(230,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_196_less__le__trans) ).
thf(1010,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)],[230]) ).
thf(9,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_122_eq__refl) ).
thf(304,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)],[9]) ).
thf(210,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_49_i__append__assoc) ).
thf(946,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)],[210]) ).
thf(170,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_191_less__le__not__le) ).
thf(786,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)],[170]) ).
thf(239,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_dual__order_Oirrefl) ).
thf(1030,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(97,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_177_order_Onot__eq__order__implies__strict) ).
thf(568,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)],[97]) ).
thf(146,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_102_nth__append2) ).
thf(716,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)],[146]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType] :
( ( minus @ TA )
=> ( minus @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ominus) ).
thf(433,plain,
! [TA: $tType,TB: $tType] :
( ( minus @ TA )
=> ( minus @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(250,axiom,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( last @ TA @ ( drop @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_last__drop) ).
thf(1077,plain,
! [TA: $tType,A: nat,B: list @ TA] :
( ( ord_less @ nat @ A @ ( size_size @ ( list @ TA ) @ B ) )
=> ( ( last @ TA @ ( drop @ TA @ A @ B ) )
= ( last @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(64,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_109_list__strict__asc__trans__le) ).
thf(478,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)],[64]) ).
thf(269,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_153_dual__order_Oasym) ).
thf(1133,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)],[269]) ).
thf(7,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_5) ).
thf(300,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(159,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_168_order__less__subst2) ).
thf(752,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)],[159]) ).
thf(215,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_72_le__neq__implies__less) ).
thf(967,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)],[215]) ).
thf(46,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_dual__order_Oantisym) ).
thf(422,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)],[46]) ).
thf(191,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_187_order_Oorder__iff__strict) ).
thf(865,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)],[191]) ).
thf(153,axiom,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Ex__list__of__length) ).
thf(735,plain,
! [TA: $tType,A: nat] :
? [B: list @ TA] :
( ( size_size @ ( list @ TA ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(174,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_less__imp__not__eq) ).
thf(801,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(21,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_116_order__subst2) ).
thf(341,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)],[21]) ).
thf(27,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_125_le__cases3) ).
thf(358,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)],[27]) ).
thf(38,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_121_linear) ).
thf(400,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)],[38]) ).
thf(84,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_32_diff__strict__left__mono) ).
thf(532,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)],[84]) ).
thf(213,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_106_nat__descend__induct) ).
thf(955,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)],[213]) ).
thf(173,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_91_nth__equalityI) ).
thf(796,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)],[173]) ).
thf(1,conjecture,
( ( ( ord_less @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) )
=> ( ( listIn1569887318i_drop @ a @ n @ ( listIn521021761append @ a @ xs @ f ) )
= ( listIn521021761append @ a @ ( drop @ a @ n @ xs ) @ f ) ) )
& ( ~ ( ord_less @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) )
=> ( ( listIn1569887318i_drop @ a @ n @ ( listIn521021761append @ a @ xs @ f ) )
= ( listIn1569887318i_drop @ a @ ( minus_minus @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) ) @ f ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( ord_less @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) )
=> ( ( listIn1569887318i_drop @ a @ n @ ( listIn521021761append @ a @ xs @ f ) )
= ( listIn521021761append @ a @ ( drop @ a @ n @ xs ) @ f ) ) )
& ( ~ ( ord_less @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) )
=> ( ( listIn1569887318i_drop @ a @ n @ ( listIn521021761append @ a @ xs @ f ) )
= ( listIn1569887318i_drop @ a @ ( minus_minus @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) ) @ f ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(283,plain,
~ ( ( ( ord_less @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) )
=> ( ( listIn1569887318i_drop @ a @ n @ ( listIn521021761append @ a @ xs @ f ) )
= ( listIn521021761append @ a @ ( drop @ a @ n @ xs ) @ f ) ) )
& ( ~ ( ord_less @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) )
=> ( ( listIn1569887318i_drop @ a @ n @ ( listIn521021761append @ a @ xs @ f ) )
= ( listIn1569887318i_drop @ a @ ( minus_minus @ nat @ n @ ( size_size @ ( list @ a ) @ xs ) ) @ f ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(256,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_13_length__induct) ).
thf(1093,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)],[256]) ).
thf(59,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_17_infinite__descent__measure) ).
thf(464,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)],[59]) ).
thf(18,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(332,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(100,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_179_dual__order_Ostrict__iff__order) ).
thf(575,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)],[100]) ).
thf(277,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_100_diff__eq__diff__eq) ).
thf(1152,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)],[277]) ).
thf(234,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_204_order__less__le__subst2) ).
thf(1019,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)],[234]) ).
thf(148,axiom,
! [TA: $tType] :
( ( wellorder @ TA )
=> ( ( '?' @ TA )
= ( ^ [A: TA > $o] :
? [B: TA] :
( ( A @ B )
& ! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_exists__least__iff) ).
thf(723,plain,
! [TA: $tType] :
( ( wellorder @ TA )
=> ( ( '?' @ TA )
= ( ^ [A: TA > $o] :
? [B: TA] :
( ( A @ B )
& ! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(442,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(220,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_184_dual__order_Ostrict__trans2) ).
thf(982,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)],[220]) ).
thf(228,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_73_less__mono__imp__le__mono) ).
thf(1004,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)],[228]) ).
thf(15,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_add__le__cancel__right) ).
thf(322,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(67,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_229_pinf_I4_J) ).
thf(486,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)],[67]) ).
thf(61,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_207_order__le__less__subst1) ).
thf(469,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)],[61]) ).
thf(26,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_56_append__eq__appendI) ).
thf(354,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)],[26]) ).
thf(126,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_212_list__strict__desc__trans) ).
thf(659,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)],[126]) ).
thf(119,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_77_diff__le__mono) ).
thf(639,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)],[119]) ).
thf(254,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_226_pinf_I11_J) ).
thf(1088,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(217,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_154_ord__less__eq__trans) ).
thf(972,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)],[217]) ).
thf(242,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_le__less) ).
thf(1037,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)],[242]) ).
thf(93,axiom,
minus @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ominus_4) ).
thf(560,plain,
minus @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(160,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_230_pinf_I3_J) ).
thf(755,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)],[160]) ).
thf(132,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_64_ge__less__neq__conv) ).
thf(676,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)],[132]) ).
thf(1181,plain,
$false,
inference(cvc4,[status(thm)],[1105,628,1083,666,352,645,892,683,730,994,308,440,614,861,523,1158,582,762,741,1073,873,449,385,550,1164,472,698,913,670,898,709,885,301,320,829,404,389,719,372,344,949,1147,870,770,325,316,881,416,475,789,1040,623,348,806,480,602,397,634,692,774,428,292,512,529,534,1067,1047,910,746,778,952,349,561,392,815,729,407,630,566,1032,625,435,329,665,461,493,1027,682,1128,1012,916,467,1089,317,1017,1121,1111,1096,1138,499,989,519,578,783,1118,1028,537,901,642,526,1155,679,970,1114,1099,1150,738,1131,1050,984,1002,605,647,997,792,1086,805,541,1035,558,1167,586,662,298,1135,425,824,573,689,444,375,513,430,904,402,732,826,291,843,1125,1139,382,313,498,335,406,831,419,1144,649,599,764,979,890,387,1080,858,621,483,895,964,1022,1162,726,848,700,520,685,768,868,1015,608,563,653,695,636,1044,394,986,851,1102,505,438,490,944,548,374,812,749,516,553,458,776,712,855,1070,705,707,887,409,1025,295,673,502,840,338,808,1130,907,744,1141,656,1008,571,595,612,991,497,876,539,976,581,495,759,1010,304,946,786,1030,568,716,433,510,1077,478,1133,300,752,967,422,865,735,801,341,358,400,532,955,796,283,1093,464,332,575,1152,1019,723,442,982,1004,322,486,469,354,659,639,1088,972,1037,560,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : ITP099^2 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n020.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 14:28:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.00/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.92/1.18 % [INFO] Parsing done (265ms).
% 1.92/1.19 % [INFO] Running in sequential loop mode.
% 2.73/1.40 % [INFO] eprover registered as external prover.
% 2.73/1.41 % [INFO] cvc4 registered as external prover.
% 2.73/1.41 % [INFO] Scanning for conjecture ...
% 2.89/1.50 % [INFO] Found a conjecture and 281 axioms. Running axiom selection ...
% 3.21/1.59 % [INFO] Axiom selection finished. Selected 280 axioms (removed 1 axioms).
% 3.73/1.77 % [INFO] Problem is higher-order (TPTP THF).
% 3.73/1.79 % [INFO] Type checking passed.
% 3.73/1.79 % [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 ...
% 189.33/96.62 % External prover 'cvc4' found a proof!
% 189.33/96.62 % [INFO] Killing All external provers ...
% 189.33/96.62 % Time passed: 96086ms (effective reasoning time: 95426ms)
% 189.33/96.62 % 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)>
% 189.33/96.62 % Axioms used in derivation (280): fact_77_diff__le__mono, fact_231_pinf_I2_J, fact_174_list__asc__trans, tcon_fun___Groups_Ominus, fact_149_antisym__conv3, fact_146_linorder__cases, fact_87_nat__diff__right__cancel__le2, fact_99_i__drop__nth__sub, fact_238_i__append__i__take__eq2, fact_176_list__desc__trans, fact_15_measure__induct, fact_125_le__cases3, fact_32_diff__strict__left__mono, fact_246_add__diff__cancel, fact_145_dual__order_Oirrefl, fact_170_ord__less__eq__subst, fact_34_diff__strict__mono, tcon_Nat_Onat___Orderings_Oorder_2, fact_219_minf_I11_J, tcon_Nat_Onat___Orderings_Ono__top, fact_178_dual__order_Ostrict__implies__order, fact_214_verit__comp__simplify1_I3_J, tcon_Nat_Onat___Orderings_Olinorder, tcon_Nat_Onat___Nat_Osize, fact_236_minf_I8_J, fact_206_order__le__less__subst2, fact_105_list__desc__trans__le, fact_211_leD, fact_78_diff__le__self, fact_5_less__imp__diff__less, fact_44_append__same__eq, tcon_List_Olist___Nat_Osize_10, fact_156_less__irrefl, tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, fact_122_eq__refl, fact_222_minf_I4_J, fact_123_le__cases, fact_98_nat__diff__right__cancel__le1, fact_97_nat__diff__left__cancel__le1, fact_133_linorder__wlog, fact_223_minf_I3_J, fact_64_ge__less__neq__conv, fact_153_dual__order_Oasym, fact_248_add__diff__cancel__left, fact_193_le__less__linear, fact_6_less__diff__imp__less, fact_9_nat__diff__left__cancel__less, fact_233_verit__comp__simplify1_I1_J, fact_197_le__less__trans, fact_229_pinf_I4_J, fact_135_dual__order_Oeq__iff, fact_101_diff__right__commute, fact_140_dual__order_Ostrict__trans, fact_96_less__diff__le__imp__less, fact_30_diff__commute, fact_79_le__diff__iff_H, tcon_fun___Orderings_Oord, fact_11_nat__diff__right__cancel__eq2, fact_199_antisym__conv2, fact_39_i__append__nth, fact_228_pinf_I5_J, fact_110_list__strict__asc__imp__list__asc, tcon_HOL_Obool___Groups_Ominus_9, fact_80_diff__le__mono2, fact_59_diff__mono, fact_152_less__imp__not__eq, fact_209_le__less, fact_177_order_Onot__eq__order__implies__strict, fact_3_minus__apply, fact_150_less__induct, fact_63_i__append__eq__i__append__conv2__aux, fact_217_less__fun__def, fact_212_list__strict__desc__trans, fact_126_antisym__conv, fact_194_dense__le, fact_65_less__ge__neq__conv, fact_131_order__trans, fact_148_less__imp__not__eq2, fact_35_i__append__i__drop__eq1, fact_166_gt__ex, fact_29_eq__imp__diff__eq, fact_37_last__drop, fact_147_less__imp__triv, fact_60_diff__left__mono, fact_75_le__diff__iff, fact_200_antisym__conv1, fact_56_append__eq__appendI, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, fact_175_list__strict__asc__trans, tcon_HOL_Obool___Orderings_Olinorder_6, fact_50_i__append__nth1, fact_160_less__asym, fact_134_dual__order_Otrans, fact_242_add__le__cancel__right, fact_109_list__strict__asc__trans__le, fact_255_drop__drop, fact_57_Nat_Oex__has__greatest__nat, fact_26_size__neq__size__imp__neq, fact_14_measure__induct__rule, tcon_Nat_Onat___Groups_Ominus_4, fact_70_le__eq__less__or__eq, fact_186_order_Ostrict__iff__order, fact_85_le__diff__le__imp__le, fact_161_less__imp__neq, fact_202_not__less, help_If_1_1_T, fact_40_i__append__def, fact_22_less__not__refl3, fact_143_less__imp__not__less, fact_83_le__imp__diff__le, fact_136_dual__order_Oantisym, fact_27_neq__if__length__neq, fact_155_ord__eq__less__trans, fact_61_diff__right__mono, fact_28_Ex__list__of__length, fact_187_order_Oorder__iff__strict, fact_67_le__greater__neq__conv, fact_218_verit__la__disequality, fact_213_complete__interval, tcon_HOL_Obool___Orderings_Oord_8, fact_243_add__le__cancel__left, fact_207_order__le__less__subst1, fact_58_append__eq__append__conv2, tcon_HOL_Obool___Orderings_Opreorder_5, fact_189_order_Ostrict__trans1, fact_47_diff__diff__cancel, fact_12_nat__diff__right__cancel__less, fact_13_length__induct, fact_250_add__diff__cancel__right, fact_216_pinf_I8_J, fact_171_ord__eq__less__subst, fact_215_pinf_I6_J, fact_237_minf_I6_J, fact_91_nth__equalityI, fact_230_pinf_I3_J, fact_33_diff__eq__diff__less, fact_55_nat__le__linear, tcon_Nat_Onat___Orderings_Owellorder, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_210_leI, fact_253_nat__add__left__cancel__le, fact_76_Nat_Odiff__diff__eq, fact_74_eq__diff__iff, fact_204_order__less__le__subst2, fact_241_add__left__cancel, fact_208_less__le, fact_168_order__less__subst2, fact_17_infinite__descent__measure, fact_73_less__mono__imp__le__mono, fact_38_i__append__nth2, fact_89_i__append__eq__i__append__conv2, fact_127_order__class_Oorder_Oeq__iff, fact_68_nat__less__le, fact_93_list__eq__iff__nth__eq, fact_53_eq__imp__le, fact_46_same__append__eq, fact_169_order__less__subst1, fact_41_drop__append, fact_108_list__asc__trans__le, fact_72_le__neq__implies__less, fact_8_nat__diff__left__cancel__eq2, fact_49_i__append__assoc, fact_31_diff__strict__right__mono, fact_42_append_Oassoc, fact_179_dual__order_Ostrict__iff__order, fact_128_ord__eq__le__trans, tcon_Nat_Onat___Orderings_Oord_3, fact_36_i__append__i__drop__eq2, fact_84_eq__diff__left__iff, fact_129_ord__le__eq__trans, fact_159_less__asym_H, fact_185_dual__order_Ostrict__trans1, fact_195_dense__ge, fact_252_nat__add__left__cancel__less, fact_167_lt__ex, fact_115_order__subst1, fact_184_dual__order_Ostrict__trans2, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_71_less__or__eq__imp__le, fact_224_minf_I2_J, help_If_3_1_T, fact_137_dual__order_Ostrict__implies__not__eq, fact_234_ex__gt__or__lt, help_If_2_1_T, fact_151_less__not__sym, fact_180_dual__order_Oorder__iff__strict, fact_232_pinf_I1_J, fact_121_linear, fact_69_less__imp__le__nat, fact_10_nat__diff__right__cancel__eq1, fact_132_dual__order_Orefl, tcon_HOL_Obool___Orderings_Oorder_7, fact_16_fun__diff__def, fact_227_pinf_I7_J, fact_120_antisym, fact_1_i__append__eq__i__append__conv, fact_20_nat__less__induct, fact_116_order__subst2, fact_112_le__funE, fact_158_less__trans, fact_254_diff__diff__left, fact_165_neqE, fact_66_greater__le__neq__conv, fact_183_dense__ge__bounded, fact_19_infinite__descent, fact_106_nat__descend__induct, fact_48_append__eq__append__conv, fact_118_ord__le__eq__subst, fact_226_pinf_I11_J, fact_191_less__le__not__le, fact_220_minf_I7_J, fact_82_le__diff__imp__le, fact_94_less__diff__iff, fact_240_add__right__cancel, fact_102_nth__append2, tcon_fun___Orderings_Opreorder, fact_0_same__i__append__eq, fact_163_order_Oasym, fact_157_less__linear, fact_154_ord__less__eq__trans, fact_164_neq__iff, fact_245_add__less__cancel__right, fact_90_nth__append, tcon_Nat_Onat___Orderings_Opreorder_1, fact_201_le__neq__trans, fact_100_diff__eq__diff__eq, fact_54_le__antisym, fact_172_ex__has__least__nat, fact_88_i__append__eq__i__appendI, fact_86_nat__diff__left__cancel__le2, fact_25_nat__neq__iff, fact_4_diff__less__mono2, fact_196_less__le__trans, fact_95_diff__less__mono, fact_2_length__drop, fact_111_le__funD, fact_142_exists__least__iff, fact_203_not__le, fact_225_minf_I1_J, fact_247_diff__add__cancel, fact_173_list__drop__eq__conv, tcon_fun___Orderings_Oorder, fact_192_le__imp__less__or__eq, fact_198_less__imp__le, fact_249_add__diff__cancel__left_H, fact_221_minf_I5_J, fact_139_not__less__iff__gr__or__eq, fact_81_le__diff__swap, fact_117_ord__eq__le__subst, fact_205_order__less__le__subst1, fact_7_nat__diff__left__cancel__eq1, fact_181_order_Ostrict__implies__order, fact_24_less__not__refl, fact_130_order__class_Oorder_Oantisym, fact_92_Skolem__list__nth, fact_114_le__fun__def, fact_18_linorder__neqE__nat, fact_188_order_Ostrict__trans2, fact_113_le__funI, fact_124_order_Otrans, fact_182_dense__le__bounded, fact_51_le__refl, fact_239_nth__drop, fact_244_add__less__cancel__left, fact_251_add__diff__cancel__right_H, fact_104_order__refl, fact_23_less__not__refl2, fact_144_order_Ostrict__trans, fact_235_list__strict__desc__imp__list__desc, fact_190_not__le__imp__less, fact_119_eq__iff, fact_107_Lattices__Big_Oex__has__greatest__nat, fact_103_nth__append1, fact_62_diff__eq__diff__less__eq, fact_141_linorder__less__wlog, fact_21_less__irrefl__nat, fact_43_append__assoc, fact_138_order_Ostrict__implies__not__eq, fact_162_dense, fact_52_le__trans
% 189.33/96.62 % No. of inferences in proof: 566
% 189.33/96.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 96086 ms resp. 95426 ms w/o parsing
% 189.72/96.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 189.72/96.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------